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User talk:Jim-henry-utc-edu

Hello Jim-henry-utc-edu,

I have made some changes to Heat Transfer:

The link added to Wikibooks doe snot contain content. Do you know the exact link ?

Welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

If you're already excited about editing, our sandbox is the perfect place for all test edits. Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity!

P.S. Do you want live feedback ? You can find us in #wikiversity-en (see Chat) Erkan Yilmaz ( evaluate me!, discussion ) 08:02, 12 September 2007 (UTC)

title: User talk:Jim-henry-utc-edu


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Bloom Clock/Keys/New Hampshire/September/All/DPL

This list is used to create a key. DPL code on this page runs off of Category:BCP/NHAMP/9.

 category=BCP/NHAMP/9 order=descending ordermethod=lastedit

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Bloom Clock/Keys/New Hampshire/September/All

The plants pictured below have been recorded as blooming during the month of September in New Hampshire.


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BCP/Achillea filipendulina/Logs

2007 Logs

 * SB Johnny-LM 09:37, 9 June 2007 (UTC)

2008 Logs

 * SB Johnny-LM 10:56, 31 May 2008 (UTC)
 * --SB_Johnny | talk 12:19, 14 June 2008 (UTC)

title: BCP/Achillea filipendulina/Logs


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User talk:Klseifert

Hello Klseifert, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
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P.S. Do you want live feedback ? You can find us in #wikiversity-en (see Chat) Erkan Yilmaz ( evaluate me!, discussion ) 13:38, 12 September 2007 (UTC)

title: User talk:Klseifert


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User:Dionysios/Consensus

Consensus Defined

 * consensus: 2. A specific method of community decision making where consent by all parties is required.

Date: 2007-09-21 (September 21, 2007) Time:  UTC
 * Proposed Wikiversity Consensus Policy definition of Consensus:
 * Consensus is a specific method of decision making at Wikiversity; in those situations in which Consensus is needed, the consent by all parties is required.

title: User:Dionysios/Consensus


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Project management/Components I

010 PM
 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Components III

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

title: Project management/Components III


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Project management/Components IV

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

title: Project management/Components IV


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Project management/Phases

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

title: Project management/Phases


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Project management/Project life cycles

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Project organization

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Project preparation

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Analysis

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Task-responsibility-competence

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps


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Project management/Project resources

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Teams

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Leadership

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Systemic manager

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Statement of work

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Kick-off-meeting

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Documentation

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

title: Project management/Documentation


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Project management/Presentation

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Transfer results

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Project management/Auditing

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Project management/Work packages

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Project management/Creativity

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Goals

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Work place

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Telephoning

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Budgets

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

title: Project management/Budgets


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Project management/Balanced scorecard

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Customers

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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Project management/Total productive management

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps


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Project management/Corporate identity

 * Main Page -->  Practical Arts and Sciences  -->  School of Project Management  -->  Project Management - A course in Project Management based on Mindmaps

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User talk:Hfeldman

Hello Hfeldman, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

If you're already excited about editing, our sandbox is the perfect place for all test edits. Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity!

P.S. Do you want live feedback ? You can find us in #wikiversity-en (see Chat) Erkan Yilmaz ( evaluate me!, discussion ) 17:52, 12 September 2007 (UTC)

title: User talk:Hfeldman


text:
Talk:Technical writing/Project management

This page is really bullshit.

It's a mixed up batch of project management lightweight description and documentation process, but neither is well organized or complete leaving a mess.

Fix it please.


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Philosophy/Resources

Students are encouraged to use their initiative in using online and offline resources. Is there a broken link? Just delete it! Or, if you want to do something that will really help - why don't you hunt the page down and repair it?

The following links will get you started:

Wikimedia
Wikimedia wikis have a number of free resources including:
 * An encyclopedic article on English Wikipedia.
 * A simpler article in Simple Wikipedia.
 * An Index of Philosophers on English Wikipedia.
 * An introductory textbook on Wikibooks.
 * A set of quotes on Wikiquote.
 * A set of source texts on Wikisource.
 * A set of images on Wikimedia Commons.

Encyclopedias

 * Stanford Encyclopedia of Philosophy Go to the main page, then select your local mirror.
 * Internet Encyclopedia of Philosophy
 * Routledge Encyclopedia of Philosophy
 * ISCID Encyclopedia of Science and Philosophy
 * Larry Hauser's Mostly Modern Philosophical Glossary

eTexts

 * Philosophy Archive Philosophy eTexts
 * Project Gutenberg This is the original etext project.  There are others.  You should find copies of all the major works in philosophy there which are not still protected by copyright.
 * Online Papers in Philosophy
 * University of Adelaide Library's "eBooks@Adelaide" Free Web Books, Online
 * Internet Public Library 20,000 titles. Nice.
 * Search eBooks.com
 * Etext Centre 8.5 million free eBooks. Don't know about notable philosophers though.
 * Internet Medieval Sourcebook
 * Online Books Opens at Philosophy Section.
 * Philosophy of Science Archive A repository for preprints in the philosophy of science: an excellent research resource.
 * Digital Text International

Online Texts

 * Camus, Albert - The Stranger
 * Hegel, Georg Wilhelm Friedrich - Philosophy of Mind
 * Tarski, Alfred - The Semantical Conception of Truth

Study Guides

 * Spark Notes A very useful study guide on various works of a great philosophers

Search Engines

 * Google
 * Lycos
 * Yahoo
 * MetaCrawler Searches multiple search engines.

Web Pages

 * Guide to Philosophy on the Web
 * Amercian Society for Aesthetics
 * John Cleese "Why Philosophy is Nothing to Laugh at"
 * Philosophical Gourmet Report (The Closest Thing to an Official Ranking of Philosophy Departments Around the World)
 * Response to the Gourmet Report (Harvard)
 * Philosophy in Cyberspace
 * Philosophy Resource Directory
 * Philosophy Research Directory
 * Philosopher's Web Magazine
 * Philosophy Now magazine
 * I Love Philosophy Forum Forum for Philosophers
 * Philosophy Dictionary of Arguments

title: Philosophy/Resources


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Talk:Philosophy/Resources

 * So, I'm not exactly sure what this page was is supposed to go to. archive.org has thousands of e-texts, available because their copyright has expired, so maybe we could link to some of those that seem valuable.  Just an idea, someone feel free to scrap this if this section is supposed to do something else.  - Liftyrfists 17:47, 28 January 2007 (UTC)

 * The ISCID site seems to no longer be available (I get a domain registrar's page). I replaced it with a link to the WayBackMachine but the site didn't seem to work correctly... Don't know if it's best to keep it or throw it away. O andras (discuss • contribs) 10:20, 21 June 2022 (UTC)
 * @O andras: Missing a trailing slash. See . -- Dave Braunschweig (discuss • contribs) 13:26, 21 June 2022 (UTC)
 * @Dave Braunschweig Thanks for taking a look! :) However, I think you may have misunderstood my doubt, and I don't see any (practical) difference between the before and after of your change. It's not the Wiki page that wasn't working, but the ISCD site in the WayBackMachine! :/ --O andras (discuss • contribs) 17:45, 23 June 2022 (UTC)
 * @O andras: The site doesn't work unless you include a trailing slash. Look carefully again at the edit I made. -- Dave Braunschweig (discuss • contribs) 00:30, 24 June 2022 (UTC)
 * @Dave Braunschweig I did look, I did notice the difference, and I did open the URL to see if it made a difference (it didn't) -- plus, my browser automatically added the trailing slash when I entered the URL without it. But if it works for you, then I guess it's a problem with my browser. -- O andras (discuss • contribs) 06:20, 9 July 2022 (UTC)

title: Talk:Philosophy/Resources


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User:TenOfAllTrades

I am User:TenOfAllTrades on Wikipedia.

title: User:TenOfAllTrades


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The Great War and Versailles/Assignment One

Please note that I have included both a long and a short assignment so students can determine their involvement in the course based upon their own time commitment. It is not required to do both, but please at least try to accomplish the shorter one. Also, let me know if anyone is having a problem obtaining the Howard book so we can work something out. I'll be assigning other sections from that book in the future, as that is the main book of the class. --Polizano 17 July 2005 (UTC)

 * Short assignment: Read pages 1-31 in The First World War by Michael Howard (Oxford University Press, 2003) ISBN 0192804456.
 * Longer assignment: Read (or skim) The Long Fuse: An Interpretation of the Origins of World War I  by Laurence Lafore (Waveland Press, 1997) ISBN 0881339547 -- This book is 284 pages. It is a little too soft on Germany and Austria-Hungary, focusing on strict mobilization schedules as the cause of the war, and totally trashes Serbia. Still, it does an excellent job of chronicling each of the prewar crises and how they affected the view of each power going into the crisis of 1914. It does an especially notable job breaking down the makeup of Austria-Hungary. It also goes through the diplomacy of 1914, though takes a rather superficial look at Germany's actions.
 * Supplemental: Timeline of the July Crisis.


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The Great War and Versailles/Further Reading

This is a list of books with information on selected subjects. If the book name is a link, you can use it to go to a searchable version at Google Print or Amazon.com.

General overviews of the entire war
John Keegan, The First World War: an Illustrated History
 * London: Hutchinson, 1998, ISBN 0091801788
 * New York: A. Knopf/Random House, 1999, ISBN 0375400524 (hardcover)
 * Vintage, May 16, 2000, ISBN 0375700455
 * London: Hutchinson, 2001, ISBN 0091793920
 * Random House Large Print, May 1, 1999, ISBN 0375706844 (Large Print)
 * Random House Audio, May 11, 1999, ISBN 0375406662 (Audio Cassette, Abridged edition)
 * Random House Audio, May 4, 2004, ISBN 0739312499 (Audio CD, Abridged edition)

David Stevenson, 1914-1918: The History of the First World War
 * London: Allen Lane/Harmondsworth, 2004, ISBN 0713992085 (hardcover)

T. Wilson, The Myriad Faces of War: Britain and the Great War, 1914-1918.
 * Oxford/Blackwell Pub, September 1, 1986, ISBN 074560093X (hardcover)
 * Polity Press/Cambridge, 1988/1989 (reprint), ISBN 0745606458 (Paperback)

Jay M. Winter, The Experience of World War I
 * London/Basingstoke: Macmillan, 1988, ISBN 0333446135

Trench Warfare

 * Ashworth, Tony, Trench Warfare, 1914-1918 : The Live and Let Live system. New York: Holmes & Meier Publishers, Inc., 1980 (ISBN 0841906157)

Enthusiasm and Alienation

 * Fuller, J.G., Troop Morale and Popular Culture in the British and Dominion Armies 1914-1918. Oxford: Clarendon Press, 1990 (ISBN 0198201788)

How far did cultural and intellectual trends provoke the outbreak of the Great War c.1870-1914?
P. Attridge, Nationalism Imperialism and Identity in Late Victorian Britain.
 * Basingstoke, Palgrave, 2002, ISBN 0333802519.

Michael D. Bidiss, The Age of the Masses : Ideas and Society in Europe Since 1870.
 * Hassocks: Harvester Press, 1977, ISBN 0855277904.

K. Bracher, The Age of Ideologies: A History of Political Thought in the Twentieth Century.
 * London: Weidenfeld and Nicolson, 1984, ISBN 029778434X.
 * New York: St. Martin's Press, 1984, ISBN 0312012292.
 * New York: Palgrave Macmillan, 1985, ISBN 0312012306.

I.D. Forbes, "Social Imperialism and Wilhelmine Germany" in Historical Journal #22
 * Cambridge, New York: Cambridge University Press, 1979, pp. 331-350, ISSN 0018-246X 0440-9302.

D. Feldman, "Nationality and Ethnicity" in P. Johnson (ed.), Twentieth-Century Britain: Economic, Social and Cultural Change
 * Longman, 1994, ISBN 0582228174.

P. Gay & R.K. Webb, Modern Europe Since 1815
 * Harpercollins College Div, 1973, ISBN 0060422831.

Robert Gildea, Barricades and Borders: Europe 1800-1914.
 * Oxford University Press, 1986, ISBN 0198730284.
 * Oxford University Press, 1987, ISBN 0198730292.
 * Oxford University Press, 1996 (2nd ed.), ISBN 0198206240.
 * Oxford University Press, 2003 (3rd ed.), ISBN 0199253005.

M. Howard, "Empire, Race and War in Pre-1914 Britain", History Today, December 1981.

J. Joll, Europe Since 1870: An International History.
 * New York: Harper & Row, 1973, ISBN 0060434155.
 * London: Weidenfeld and Nicolson, 1973, ISBN 0297765248.
 * London: Penguin, 1990, ISBN 0140138439.

A. Summers, "Militarism in Britain before World War I" in History Workshop Journal, Autumn, 1976.

Michael Sturmer, The German Empire, 1870-1918.
 * New York: Modern Library, 2000, ISBN 0679640908.

Hans-Ulrich Wehler, The German Empire, 1871-1918.
 * Leamington Spa: Berg, 1985, ISBN 090758232X (paperback)
 * Leamington Spa: Berg, 1985, ISBN 0907582222 (cased)

Paul Weindling, Health, Race, And German Politics Between National Unification And Nazism, 1870-1945 (Amazon.com Search Inside)
 * Cambridge, New York: Cambridge University Press, 1989, ISBN 0521363810
 * Cambridge University Press, July 22, 1993, ISBN 052142397X

What effect did the Great War have on the British Empire c.1918-1939?
Michael Adas, Peter N. Stearns and Stuart B. Schwartz, Turbulent Passage: a Global History of the Twentieth Century.
 * Longman Publishing Group, December 1, 1993 / New York: HarperCollins, 1994, ISBN 0065010396
 * Harpercollins College Div, October 1, 1995 (reissue), ISBN 1886746494
 * Longman, September 17, 2002 (2nd ed.), ISBN 0321097696
 * Longman, July 7, 2005 (3rd ed.), ISBN 0321338901

Neville Bennett, "White Discrimination against Japan: Britain, the Dominions and the United States, 1908-28", New Zealand Journal of Asian Studies, 3, 2, 2001, pp.91-105.

Patrick French, Liberty or Death: India's Journey to Independence and Division (Amazon.com Look Inside)
 * London: HarperCollins, 1997, ISBN 0002557711
 * London: Flamingo, October 1, 1998, ISBN 0006550452

David McIntyre, The Significance of the Commonwealth, 1965-90.
 * Basingstoke: Macmillan Academic and Professional, 1991 / Palgrave Macmillan, December, 1991, ISBN 0333553160

Paul Rich, Race and Empire in British Politics.
 * Cambridge, New York: Cambridge University Press, 1986, ISBN 0521320178
 * Cambridge, New York: Cambridge University Press, 1989, ISBN 0521389585

Lt.-Col. Sir Arnold T. Wilson, Loyalties: Mesopotamia, 1914-1917: a personal and historical record.
 * London: Oxford University Press, H. Milford, 1930, (pre-ISBN)
 * London: Oxford University Press, 1936, (pre-ISBN)
 * Greenwood Press (1969), ASIN: B0006BYJGO (pre-ISBN)

To what extent did the Great War provoke the 'birth of the Modern' in relation to the arts?
Bernard Bergonzi, Heroes' Twilight: a Study of the Literature of the Great War.
 * Coward-McCann, 1966, ASIN B0006BNPOG
 * Macmillan Press; 1980 (2nd ed.), ISBN 0333281578
 * Macmillan Press, January 1, 1981 (2nd ed.), ISBN 0333281268
 * Carcanet Pr, August 1, 1996 (3rd ed.), ISBN 1857541359

M. Eksteins, Rites of Spring: The Great War and the Birth of the Modern Age (Amazon.com Search Inside)
 * Transworld, 1989, (ISBN unknown)
 * London: Bantam, 1989, ISBN 0593018621
 * Lester & Orpen Dennys, 1989 (1st ed.), ISBN 0886192005
 * Boston: Houghton Mifflin Company, February 1, 1989, ISBN 0395498562
 * New York, London: Doubleday, 1990; Anchor, March 1, 1990 (reprint), ISBN 0385412029
 * Houghton Mifflin Books, September 1, 2000, ISBN 0395937582

John Ferguson, The Arts in Britain in World War I.
 * London: Stainer and Bell, 1980, ISBN 085249548X

Samual Hynes, A War Imagined: The First World War and English Culture.
 * London: Bodley Head, 1990, ISBN 0370304519
 * New York: Atheneum/Maxwell Macmillan International, 1991, ISBN 0689121288

George Robb, British Culture and the First World War.
 * Houndmills (Hampshire), Basingstoke, New York: Palgrave, 2002, ISBN 0333715713 (hardcover), ISBN 0333715721 (pbk.)


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The Great War and Versailles/Lecture One

This is the 'lecture' I've been working on. I encourage students to add in details on topics of their own interest in lieu of a formal assignment. The recommended texts should be sufficient for this, but feel free to use any source you deem appropriate, including the Wikibooks listed on the main page of the course. For convenience purposes, please carry on debates/ask questions on the main discussion page for the course. I'll try to check it frequently, and will be adding to it along with the students. Please let me know when everyone feels their work on this part is done and I should post the next assignment. If someone could highlight some of the more obscure terms and make them link to a wikipedia article explaining them, that would be great.--Polizano 23:59, 30 July 2005 (UTC)

Comments on the book by Michael Howard
Michael Howard is a premier scholar on war in European History. While his guide is far from authorative, it does not attempt to be. He briefly introduces a subject with so deep a history that getting lost in the details is a danger for a new student. His short guide is, however, an excellent first taste of the topic. For books of this style covering many other fields of study, try Very Short Introductions.

Howard is one of the few historians to reject the common interpretation that the war was an unnecessary tragedy, viewing it as a worthy battle of liberal civilization against German barbarism, militarism, and authoritarianism.

Comments on the book by Lawrence LaFore (and the difference between his interpretation and Michael Howard's)
Lawrence Lafore approaches the outbreak World War I by identifying long-term causes while avoiding casting overt 'blame' on any of the parties. General historical understanding of the causes of World War I has taken three different forms. His interpretation of the origins of the war is very much so in line with the middle of three chronologically. The original view in the West was that the war was caused by German aggression.

Following disillusionment with the outcome of the war and some new research, historical opinion began to change, focusing instead on rigid mobilization timetables, nationalist pressure from the homefront on all governments, and the belief in the necessity of being the first horse out of the gate, that is, that the side which attacked first had a huge advantage in the outcome of the conflict. Lafore is of this school, and focuses on the details of mobilization plans to portray the war as a tragic act of fate caused by blunders on both sides. Though we cannot be sure, further research has indicated that behind the scenes, major figures in the German high command (ie Moltke) secretly hoped to escalate the Balkan Crisis into a general war. This preventive war thesis is the third school, and it states that Germany believed war between France and Russia was inevitable and hoped to fight it on Germany's terms. Howard falls here.

Note the different intepretation Lafore and Howard have of the German declaration of war on Russia. Lafore focuses on the Russian decision begin general mobilization as tying Germany's hands, and adds to this feeling by noting that the German ambassador began crying after asking the Russians to end their mobilization several times and then delivering the declaration of war. While Howard is critical of the Russian decision to mobilize, his criticism focuses on the assertion that it gave Germany an excuse to declare war, which puts substantially more blame on Germany.

He notes that Russian mobilization did not require invasion, while German mobilization timetables led directly in the later stages to attacking neutral Belgium. Also note: Lafore is very critical of Serbia's handling of the Austro-Hungarian ultimatum, portraying their actions as a facetious rejection. Serbia agreed to all of AH's terms but rejected one, noting that the trial of Serbian nationals by a foreign court violated Serbia's constitution. Most historians are far more critical of AH's intransigence.

Europe in 1914
In 1915, when war broke out in Europe, there had not been a general war since Napoleon's final defeat at Waterloo[w:Battle_of_Waterloo]. But with the collapse of the Concert of Europe [w:Concert_of_Europe] approach to solving European crises after the Moroccan Crisis [w:Tangier_Crisis], the European situation had gotten so tense that many speak of the fatalism of 1914. A system of rival alliances emerged that surrounded Germany, with France and Russia on one side and Germany and Austria-Hungary on the other. France was helping to fund the Russian reconstruction after Russian defeat and near revolution in 1905. Though Britain was formally uncommitted, the naval race with Germany and its Entente Cordiale [w:Entente_cordiale] with France showed that its sympathies lay with the French side. Since the Agadir Crisis [w:Agadir_Crisis] in 1911, Britain and France held detailed staff meetings to dicuss the possibity of Britain sending an expeditionary force to the continent in the event of war with Germany. Germany felt increasingly isolated on the continent, since its only ally, Austria-Hungary, was the weakest of the five powers.

The Outbreak of War
To understand how the assasination of Archduke Franz Ferdinand escalated into a general European war, we must examine the perspective of each party on the crisis. Austria-Hungary, a large multi-national hodgepodge, was eager to undertake a show of force that would crush the Slav nationalism that threatened to disintigrate the empire. Germany at first hoped that a large diplomatic victory would bolster the position of its ally among the powers, and gave Austria-Hungary an alleged blank check. After Russia's defeat at the hands of Japan in 1905, it turned its attention to Southeastern Europe, and to Slavic nationalism there. After the Congress of Berlin and the Balkan wars, Russia's relations with Austria-Hungary got so bad that compromise became impossible. British and French press largely ignored the crisis at first. When Austria-Hungary lived up to its reputation for notoriously slow diplomacy, the attention of the German high-command turned to the possibility of a preventive war. Germany considered a war with Russia and France inevitable, and prefered one on its own terms.

Germany's plan for the war was framed in the Schlieffen Plan [], which called for Austria-Hungary to hold off Russia while Germany exacted a quick defeat on France. This would be impossible if Russia was given time to rebuild and increase its mobilization speed. But Germany needed to give the appearance of Russia throwing the first stone. Since Russia was notoriously barbarous, Germany hoped that this would keep Britain neutral in the war. Also, the largest party in the German Reichstag was that of the Social Democrats, and Germany needed to ensure a unified homefront in the event of war. Figures in the German High Command (Moltke) knew the intracacies of mobilization plans, and hoped Russia would be forced to mobilize first, since it was the power with the slowest mobilization speed.

When Serbia rejected one item on the Austro-Hungarian list of ultimatums, Austria-Hungary declared war on Serbia, and Russia mobilized partially on the Austro-Hungarian front. When this mobilization proved chaotic, Russia mobilized generally (including along the German front). This gave Germany its needed excuse, and after Russia rejected a call to stand down, Germany declared war. Germany demanded that France state whether it would remain neutral in a German-Russian war, knowing full well it could not, and when France refused to declare neutrality, Germany declared war on France. When Germany refused to guarantee Belgium's neutrality (a British concern because an occupied Belgium would have allowed Germany to control the English Channel and because Britain imported a substantial portion of its food supply by sea). Britain declared war on Germany. Historians are extremely harsh on the British Prime Minister for Britain's unclear foreign policy, believing a clearer stance by Britain earlier in the crisis could have prevented its escalation to total war.


text:
The Great War and Versailles/Ideas or proposed study tasks or essay topics.

Instructions: Be Bold. Propose action. Reorganize this page to accurately reflect current reality. Sign on to assist. Help anonymously. Pat someone on the back or go award a barnstar for valuable contributions to Wikiversity and ultimately to future Terran and Galactic students and sophonts. Have some fun. Do not panic but do something you are convinced is useful, appropriate, and personally enjoyable. Invite a friend to dance, study, or think freely either with you and your team or solo. Later.

Proposed

 * Insert new tasks here

Active

 * Draft and polish concise wiktionary definition and thorough wikipedia article regarding diplomatic concept and phrase casus foederis and the role it played in escalating an assassination and conflicting national interests into global war, in general as well as World War I.
 * Current Team Members
 * Lazyquasar 02:51, 26 November 2005 (UTC)

Completed substantially by this course's participants to date:

Section One

 * Research the "Morrocan Crisis", add an article to Wikipedia if appropriate and link it in from Morroco and World War I if appropriate. Put the reference link into Lecture One for convenience and eddification of future course participants.
 * Also known as the "Tangier Crisis" or "First Moroccan Crisis". Link to Tangier Crisis added to lecture one. Lazyquasar 08:16, 26 November 2005 (UTC)


text: Wikiversity:Requests for CheckUser

title: Wikiversity:Requests for CheckUser


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Military studies

Introduction
Military Studies can be described as the art and science of military applications. Throughout the ages, warfare has been all around us. Much of the world depends on warfare to advance both technologically and culturally. For example, without the development of the Manhattan Project, it may have taken much longer to utilize the practical energy uses of the atom for nuclear power.

Now, the military itself is a big part of what makes up this world of ours. So where do you start in something that can be approached in so many different ways? History, of course. The only way you can learn is by experience. History is nothing but experience--a few thousand years of it at least.

Ancient
If you follow evolution, you know you shared a common ancestor with a monkey. If you're more religious, then you believe that we are God's divine creatures. Divine creature or monkey, ancient history covers that period of time as well as it can. The further back you go into history, the fewer records there are. Today, you will even have records on your shoe size. The records for back a few thousand years only give us hints of great wars and campaigns commanded by leaders such as Alexander the Great and Julius Caesar.

These men were both generals and kings of their respective empires, which they would have to have taken by force and luck. The armies they commanded demanded respect, extraordinary leadership, and--most of all--standing with their men right at the frontlines. There are many other generals and warlords that lived in Alexander's and Caesar's times, but these two great men risked their lives just like their soldiers. This is what separates leaders from great leaders.

Armies operated much the same from ancient times to even the 19th century in the American Civil War as large tight formations of moving blocks. Even if you applied modern tactics to ancient soldiers with swords and spears, they would have to be a guerilla force to be successful with what they had then. But these men would have to operate like North Vietnamese soldiers and not modern U.S. Special Forces. But this would have a bad effect on your reputation as a commander, and commanders in the day had to be honorable by ancient standards.

Commanders would have to be usually of a noble line or regarded as upper class to go through officer training to later lead armies. These commanders were plenty, but their valor was not. These commanders were mostly surrounded by veteran bodyguards far from the frontlines, but close enough to command the battle effectively. Battles would be long and fierce, and could be decided by simply looking at the number of forces alone. Sometimes this was not always true. While nations in general had average training and weapons, some like the Spartans or Romans would take training and weapons to a whole new level.

Spartan warriors were before the time of Roman supremacy. Even then, these Spartans could easily match Romans. Spartans lived and breath military training from almost the time of birth. This group of Spartans were only a city which was probably the most productive and efficient city in all the world. As a Spartan, you only did what was needed. You would never indulge except in physical and formation training. Spartan's were the Iron Men of all world history and would die in outnumbered battles such as in the battle of Thermopylae if it was a strategically reasonable. While the Romans operated differently then the Spartans, they would become the first world superpower we would see.

Medieval
Medieval warfare is the warfare of the Middle Ages. Technological, cultural, and social advancements had forced a severe transformation in the character of warfare from antiquity, changing military tactics and the role of cavalry and artillery (see military history). In terms of fortification, the Middle Ages saw the emergence of the castle in Europe, which then spread to the Holy Land (modern day Israel and Palestine).

The Battle of Crécy (1346) between the English and the French in the Hundred Years' War.

Cold War
After the Allies had defeated Nazi Germany in 1945, two nations emerged out of the war as world superpowers - the United States of America (USA) and the Union of Soviet Socialist Republics (the Soviet Union or the USSR).

By the end of World War 2, they had earned their place as the strongest countries in the world. But although they had been fighting the war as allies, there were many things which seperated them:

 * Economic System - the USA had a capitalist economic system which basically means that the industry is owned by private individuals who can make and keep their profit independently. The Soviet Union had a socialist economic system which made all industry and land owned by the government and the wealth generated from them shared out equally for the population.

 * Social System - the USA believed in freedom of speech (for example, criticizing the government) and personal belief and freedom of the press and that each citizen had their own right to excercise this and express it without getting shot or arrested. The Soviet Union believed in censorship of things undesirable and potentially dangerous to the government, and control of the media and citizens.

 * Election Process - the USA believed in free, multi-party elections which allowed all types of parties no matter how far right or left they were, to be represented and allowed to be voted for in elections, and the party which won the majority of votes by the population would get into power. The Soviet Union only allowed one type of party in the election process.

So what was the problem?
They might have been fighting the war hand in hand, but when it was over and there was no common enemy to unite against, they soon fell out and bore a deep grudge against each other which lasted for the next 40 years or so and became known as the 'Cold War'.

East vs West: The Ultimate Love-Hate Relationship
The countries in the West never had a particularly good relationship with communism. It dates way back to 1917, when the Bolsheviks, a powerful and very popular hardline communist party back then took control of Russia in a coup. Russia, back then was a hundred years behind the West and was in a terrible position - there was a lack of food, all-time low living conditions, mass poverty and an expensive war that was draining away the limited money and resources. There were three main events that eventually led up to the Bolshevik take-over:

1) Revolution of 1905 - this wasn't really a revolution but it was a massive spasm of violence with no real political aim directed against the ruling monarchy at that time, but the government still manages to just cling on and ruthlessly suppress it

2) February Revoution of 1917 - this was what you'd call a revolution. There is again a massive rebellion against the government but this time it is a co-ordinated assault on government buildings by various anti-monarchist forces. In March, the government is deposed and a new provisional government is formed

3) October Revolution of 1917 - another assault on key buildings, but this time by Bolshevik communist forces under Lenin. The privisional government is eventually deposed and a new communist government is formed. Russia makes peace with Germany and withdraws from World War 1

But this comes as very bad news for the West. They have just lost a crucial ally in the war against Germany and it's allies, and having witnessed the bloody events in Russia they are absolutely terrified that it might happen to them, from their own socialist parties.

Personnel Development
Numerous paths for service exist in each of the armed forces. In addition to active duty, there are reserve, national guard, state guard/defense force, auxiliary, civilian and contractor opportunities. Each has its own features and benefits, as well as its own advantages and disadvantages. A prospective service member may serve in several of these paths during his/her career.

Basic
Basic Combat Training, or BCT, is a nine-week training period that teaches identical skills for all MOSs (Military Occupational Specialties). This is because the Army believes that no matter the soldier's specialty, they should all be taught the basic skills of combat so they will be ready to properly defend themselves (as well as their fellow soldiers) when and if necessary.

BCT is divided into three phases, each phase lasting three weeks. The three phases are each represented by a color (red, white, and blue). BCT trainees are progressively allowed more responsibility, privileges, and independence each time they achieve a new phase of training. Whereas trainees in Phase I are constantly monitored and led around by their drill sergeants, Phase III trainees are largely responsible for making sure tasks are completed correctly and on-time, and keeping themselves on-schedule.

At some Basic Training stations, the current phase is denoted by the color of guidon carried by the platoon. Following the recruits' successful completion of the Field Training Exercise (a final exercise just before graduation), the Phase III blue guidon is sometimes traded for a tri-color red, white, and blue guidon that symbolizes successful completion of all three BCT phases.

Phase I During Phase I or "Red Phase", also called the "Patriot phase" recruits are subject to "Total Control", meaning their every action is monitored and constantly corrected by drill sergeants. As may be expected, recruits are often subjected to group "corrective action" for even minor infractions. The purpose being to develop an acute attention to detail as well as foster a sense of common responsibility among the unit.

Week 1 Week 1 begins with the recruits meeting the drill sergeants who will be responsible for their training throughout BCT. The drill sergeants pick up their recruits from Reception Battalion and either transport or march them to their company area. The company area is the common area for the entire company, and is surrounded by four barracks — one for each platoon in the company.

Upon arrival at the company area, recruits are subjected to exercises such as the "bag drill". This is a training exercise in which all the recruits' duffel bags are dumped into one large pile, and the recruits are told to find their personal duffel bags simultaneously, and within a set time limit. The exercise is designed so that the soldiers fail in their task and must keep trying again, until they realize that they must work together in order to complete the task within the time limit. Following the bag drill, the recruits are divided into platoons.

Drill & Ceremony training begins during week 1. This refers to correct procedures for marching, and body movements such as standing at attention, "facing" (right-face/left-face), "at ease," etc. For this and many other exercises, soldiers are sometimes issued fake rifles known as "rubber ducks", so that they can become familiar with the proper handling of their weapon before they have actually been trained to use it. More recently recruits have begun to be issued fully functional M16A2/A4s during the first week of BCT to allow for early familiarization with the weapon.

Classroom instructions are given in each of the seven "Army Core Values," which include loyalty, duty, respect, selfless service, honor, integrity, and personal courage. Note that the initials spell out the mnemonic LDRSHIP (leadership). There are also classes held on subjects that involve day-to-day personal life in the Army, such as sexual harassment and race relations.

Week 2 During week 2, recruits begin unarmed combat training, also known as hand-to-hand combat, Combatives, or Ground Fighting Technique (GFT). The training often culminates in a competition where each platoon chooses one recruit to compete. At gender-integrated training stations, the platoons each choose one male and one female recruit.

Recruits are also instructed in map reading, land navigation, and compass use. These skills are put to the test at the Compass Course, where recruits are divided into groups and must navigate their way to a series of points throughout a wooded area.

Recruits will also tackle other physical challenges including Victory Tower and the Teamwork Development Course. Victory Tower is an exercise where recruits must navigate through several obstacles at extreme heights, including climbing and traversing rope ladders and bridges. They must then rappel down a 50-foot wall (back-first, with rope harness). In the Teamwork Development Course, squads must negotiate a series of obstacles, with emphasis on working as a team rather than as individuals.

First aid training is also given during this period. Recruits are trained in evaluating and properly treating casualties, ranging from the simple dressing of a wound to application of a tourniquet. Recruits are also trained in how to evaluate and treat heat casualties such as dehydration. Proper procedures for setting up and removing an IV are now being introduced, including closely supervised live practice on each other.

Week 3 Recruits begin training for bayonet use using pugil sticks and then move on to the Bayonet Assault Course. Other hands-on instruction sessions include person-carrying methods and physical problem-solving.

Recruits are also commonly sent to the "gas chamber" during this week, which is a large, sealed chamber where soldiers are subjected to CS gas while wearing their protective masks. The gas chamber is the culmination of a series of instructions on gas mask use. Recruits are forced to unmask just before exiting the chamber, so that they can briefly experience the effects of the gas. Drill sergeants will usually ask each recruit to recite information while they are unmasked, such as name, rank, social security number, the Pledge of Allegiance, the Soldiers' Creed, or the three Army general orders, so that the recruit is forced to open their mouth/eyes and/or take a breath. Recruits that answer incorrectly are sometimes sent for another trip through the gas chamber.

Week 3 is also when the recruits are introduced to their standard-issue weapon, the M16A2 assault rifle or the M4 carbine. This does not yet involve the actual firing of the rifle. It does include Basic Rifle Marksmanship (BRM) fundamentals training (instruction in marksmanship techniques without firing the rifle), as well as maintenance tasks, including "field stripping" (quickly disassembling) the rifle, cleaning it, and reassembling it correctly. With the focus toward Weapon Familiarization, many of these tasks (such as maintenance, and disassembly and reassembly) are now done during Week 1 as a part of the initial round of classroom instruction.

Phase II

Phase II, called the "White Phase," or "Gunfighter Phase," is where soldiers begin actually firing weapons. With the M16A2 assault rifle, they will fire at various targets, which are progressively further and further downrange, resulting in more and more difficult shooting. Additionally, there are pop-up targets at long range. Other weapons the soldier becomes familiarized with include various grenades (such as the M67 fragmentation grenade) and grenade launchers (such as the M203 grenade launcher).

A soldier practices using his fixed bayonet, attached to a dummy rifle.The second week of Phase II involves familiarization with the bayonet, anti-tank/armor weaponry and other heavy weapons. There is also an obstacle course which the soldiers are expected to negotiate in a certain amount of time. This is also known as the confidence course since the main objective of running the course is to build self-confidence. There is also the expectation of working as a team with the assigned Battle Buddy.

Additionally, there is continual, intense physical training (PT), as well as drill and ceremony training. At the conclusion of Phase II, soldiers are expected to demonstrate proficiency with the various weaponry in which they trained, using numerous "go or no-go" (pass/fail) exercises, prior to being allowed to move on to Phase III.

Phase III

Phase III, the "Blue Phase" or "Warrior Phase" is the culmination and the most challenging of all the training phases. During this phase, there is a PT final. At some locations, soldiers that fail are not allowed to go into the field with the rest of the platoon. The Final PT Test consists of the Standard Army Annual PT Examination. A minimum of 150 points is required to pass US Army Basic Training. Those that pass will move on to "Bivouac" (camping) and FTX (Field Training Exercises), such as nighttime combat operations and MOUT training. There is no access to the dining facility during these exercises, so meals are given in the form of either MREs (Meal Ready to Eat) or "hot alphas". Drill sergeants will make much of this an adversarial process, working against the recruits in many of the night operations, trying to foil plans, etc. Other BCT companies also in their FTX weeks may join in simulated combat scenarios, generally at night, with intense competition to prove their particular company the better trained.

Week 2 of Phase III (the 8th week of Basic Training) culminates in a special tactical FTX (Field Training Exercise), during which the drill sergeants will advise, but allow recruit platoon leaders and squad leaders to exercise primary decision-making. They attempt to make virtually every one of these exercises different. Due to the fact that being a soldier is potentially an extremely hazardous job, recruits must demonstrate extreme aggression and fearlessness, tempered by intelligence and common sense. Only those that demonstrate these vital attributes will be permitted to move on to AIT.

Following their FTX, recruits then move into the final week of training, often called "recovery week". At this time, soldiers must service and/or repair any items they are not taking on to AIT including weapons, bedding, issued equipment (helmet, canteen, gas mask, etc.) as well as ensuring the platoon barracks is in good order to receive the next platoon of trainees. This week also includes a final fitting of the recruit's dress uniform as well as practice for the graduation ceremony which takes place at the end of the week.

Advance Training
Advanced Individual Training, or AIT, is where new soldiers receive specific training in their chosen MOS. The length of AIT training varies depending on the MOS and can last anywhere from three weeks to nearly two years. The current longest AIT training lasts 84 weeks (1 year and 8 months).

Just like BCT, AIT progressively allows trainees more and more privileges. At the start of AIT, trainees are in Phase IV. After a varying length of time and satisfactory performance, the trainees are awarded Phase V. Phase V often includes the privilege of applying for off-post passes or use of a cell phone. Phase V+ is awarded after a similar length of time and continued good conduct. Phase V+ trainees may walk about the base without having a battle buddy present, be able to drink alcohol on weekends (provided one is of legal drinking age), and even stay off-post overnight on weekends. These privileges vary, however.

AIT schools Army AIT schools include (not a complete list):

Adjutant General School, located at Fort Jackson, SC. Air Defense Artillery School, located at Fort Bliss, TX. Armor School, located at Fort Knox, KY. Army Aviation Center, located at Fort Rucker, AL. Aviation Logistics School, located at Fort Eustis, VA. Chaplain Center and School, located at Fort Jackson, SC. Chemical, Biological, Radiological and Nuclear School, located at Fort Leonard Wood, MO. Engineer School, located at Fort Leonard Wood, MO. Field Artillery Center, located at Fort Sill, OK. Finance Corps School, located at Fort Jackson, SC. Infantry School, located at Fort Benning, GA. Intelligence Center, located at Fort Huachuca, AZ. Medical Department Center and Schools, located at Fort Sam Houston, TX. Military Police School, located at Fort Leonard Wood, MO. Ordnance Mechanical Maintenance School, located at Aberdeen Proving Ground, MD. Ordnance Munitions and Electronics Maintenance School, located at Redstone Arsenal, AL. Quartermaster School, located at Fort Lee, VA. Signal School, located at Fort Gordon, GA. United States Army Signals Intelligence Analysts School, located at Goodfellow Air Force Base, TX. Transportation School, located at Fort Eustis, VA.

Coast Guard
The United States Coast Guard is one of the five armed military forces. At various times under the Commerce Department and the Transportation Department, it currently serves as part of the US Department of Homeland Security. Like the other armed services, it contains enlisted and officer personnel, auxiliarists and civilian employees. Rank structure is similar to the US Navy for enlisted and officer servicemembers.

U.S. ARMY HISTORICAL SERIES : AMERICAN MILITARY HISTORY

 * AMERICAN MILITARY HISTORY

World War II
European Theater

 * CMH Pub. 100-7: SALERNO : American Operations From the Beaches to the Volturno, 9 September - 6 October 1943
 * CMH Pub. 100-8: FROM THE VOLTURNO TO THE WINTER LINE, 6 October - 15 November 1943
 * CMH Pub. 100-9: FIFTH ARMY AT THE WINTER LINE, 15 November 1943 - 15 January 1944
 * CMH Pub. 100-10: ANZIO BEACHHEAD, 22 JANUARY - 25 MAY 1944
 * CMH Pub. 100-11: OMAHA BEACHHEAD, 6 June-13 June 1944
 * CMH Pub. 100-12: UTAH BEACH TO CHERBOURG, 6 June-27 June 1944
 * CMH Pub. 100-13: ST-LO, 7 July - 19 July 1944

North African/Middle East Theater
 * CMH Pub. 100-6: TO BIZERTE WITH THE II CORPS : 23 April - 13 May 1943

Pacific Theater

 * CMH Pub. 100-1: PAPUAN CAMPAIGN : The Buna-Sanananda Operation, 16 November 1942 - 23 January 1943
 * CMH Pub. 100-2: THE CAPTURE OF MAKIN : 20 - 24 November 1943
 * CMH Pub. 100-3: THE ADMIRALTIES : Operations of the 1st Cavalry Division, 29 February - 18 May 1944
 * CMH Pub. 100-4: MERRILL'S MARAUDERS : February - May 1944
 * CMH Pub. 100-5: GUAM : Operations of the 77th Division, 21 July - 10 August 1944

Small Unit Actions
 * CMH Pub 100-14: SMALL UNIT ACTIONS

title: Military studies


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Edible plant identification

Course Description
Learn the skills necessary to identify edible plants.

Wikibooks

 * Botany

Wikipedia

 * List of vegetables
 * Wikipedia: List of wild foods
 * Wikipedia: List of food plants native to the Americas
 * Category:Edible plants
 * Edible plants
 * List of forageable plants
 * Edible plant stem
 * List of edible seeds
 * Edible flower
 * List of edible plants and mushrooms of Southeast Alaska
 * Wild edible and medicinal plants of British Columbia
 * Wild edible plants of Israel / Palestine
 * List of forageable plants

The Outside World
Many plants that can be found outside of most homes are edible. A short list of some of these in addition to familiar fruits and berries: beechnuts, burdock leaf stalks (peeled), cattail young shoots, immature flowers and pollen, dandelions, the young green leaves, tubers and flowers of daylilies, elderberry flower and fruit, foxtail grains, the stems, leaves and flowers of fireweed, juniper/cedar twigs and berries,oak and pine seeds, reindeer moss, rock tripe, waterlilly, thistle stalks and roots and wild rose.

If you have these plants around your home or find them while in the forest, many of these are best if boiled which takes away much of the bitter flavoring.

title: Edible plant identification


text: Java Tutorial/Template:Navigation

title: Java Tutorial/Template:Navigation


text: Template:Java Tutorial/Navigation

title: Template:Java Tutorial/Navigation


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Nonlinear finite elements/Objectivity of constitutive relations

Material frame indifference
An important consider in nonlinear finite element analysis is  material frame indifference or  objectivity of the material response. The idea is that the position of the observer frame should not affect the constitutive relations of a material. You can find more details and a history of the idea in Truesdell and Noll (1992) - sections 17, 18, 19, and 19A.

We have already talked about the objectivity of kinematic quantities and stress rates. Let us now discuss the same ideas with a particular constitutive model in mind.

Hyperelastic materials
A detailed description of thermoelastic materials can be found in Continuum mechanics/Thermoelasticity. In this discussion we will avoid the complications induced by including the temperature.

In the material configuration, a hyperelastic material satisfies two requirements:

 * 1) a stored energy function ($$W$$) exists for the material.
 * 2) the stored energy function depends locally only on the deformation gradient.

Given these requirements, if $$\boldsymbol{N} = \boldsymbol{P}^T$$ is the nominal stress ($$\boldsymbol{P}$$ is the first Piola-Kirchhoff stress tensor), then

\boldsymbol{N}^T(\mathbf{X}, t) = \boldsymbol{P}(\mathbf{X},t) = \rho_0~\frac{\partial W}{\partial \boldsymbol{F}}\left[\mathbf{X}, \boldsymbol{F}(\mathbf{X},t)\right] $$

Objectivity
The stored energy function $$W(\mathbf{X},\boldsymbol{F})$$ is said to be objective or frame indifferent if

W(\mathbf{X}, \boldsymbol{Q}\cdot\boldsymbol{F}) = W(\mathbf{X}, \boldsymbol{F}) $$ where $$\boldsymbol{Q}$$ is an orthogonal tensor with $$\boldsymbol{S}\cdot\boldsymbol{Q}^T = \boldsymbol{\mathit{1}}$$.

This objectivity condition can be achieved only if (in the material configuration)

W(\mathbf{X}, \boldsymbol{F}) = \hat{W}(\mathbf{X}, \boldsymbol{C}) ~; \boldsymbol{C} = \boldsymbol{F}^T\cdot\boldsymbol{F} $$ since $$\boldsymbol{C}_r = \boldsymbol{F}^T\cdot\boldsymbol{Q}^T\cdot\boldsymbol{Q}\cdot\boldsymbol{F} = \boldsymbol{C}$$.

We can show that

 Proof:

The stress strain relation for a hyperelastic material is

\boldsymbol{P} = \rho_0~\frac{\partial W}{\partial \boldsymbol{F}}\left[\mathbf{X}, \boldsymbol{F}(\mathbf{X},t)\right] $$ The chain rule then implies that

\boldsymbol{P}:\boldsymbol{T} = \rho_0~\frac{\partial \hat{W}}{\partial \boldsymbol{C}}:\left(\frac{\partial \boldsymbol{C}}{\partial \boldsymbol{F}}:\boldsymbol{T}\right) $$ for any second order tensor $$\boldsymbol{T}$$.

Now, using the product rule of differentiation,

\frac{\partial \boldsymbol{C}}{\partial \boldsymbol{F}}:\boldsymbol{T} = \frac{\partial }{\partial \boldsymbol{F}}\left(\boldsymbol{F}^T\cdot\boldsymbol{F}\right):\boldsymbol{T} = \left(\frac{\partial \boldsymbol{F}^T}{\partial \boldsymbol{F}}:\boldsymbol{T}\right)\cdot\boldsymbol{F} + \boldsymbol{F}^T\cdot\left(\frac{\partial \boldsymbol{F}}{\partial \boldsymbol{F}}:\boldsymbol{T}\right) $$ or,

\frac{\partial \boldsymbol{C}}{\partial \boldsymbol{F}}:\boldsymbol{T} = \left(\boldsymbol{\mathsf{I}}^T:\boldsymbol{T}\right)\cdot\boldsymbol{F} + \boldsymbol{F}^T\cdot\left(\boldsymbol{\mathsf{I}}:\boldsymbol{T}\right) = \boldsymbol{T}^T\cdot\boldsymbol{F} + \boldsymbol{F}^T\cdot\boldsymbol{T} $$ where $$\boldsymbol{\mathsf{I}}$$ is the fourth order identity tensor. Therefore,

\boldsymbol{P}:\boldsymbol{T} = \rho_0~\frac{\partial \hat{W}}{\partial \boldsymbol{C}}:\left(\boldsymbol{T}^T\cdot\boldsymbol{F} + \boldsymbol{F}^T\cdot\boldsymbol{T}\right) $$ Using the identity

\boldsymbol{A}:(\boldsymbol{B}^T\cdot\boldsymbol{C}) = (\boldsymbol{C}\cdot\boldsymbol{A}^T):\boldsymbol{B} = (\boldsymbol{B}\cdot\boldsymbol{A}):\boldsymbol{C} $$ we have

\frac{\partial \hat{W}}{\partial \boldsymbol{C}}:(\boldsymbol{T}^T\cdot\boldsymbol{F}) = \left[\boldsymbol{F}\cdot\left(\frac{\partial \hat{W}}{\partial \boldsymbol{C}}\right)^T\right]:\boldsymbol{T} \quad \text{and} \quad \frac{\partial \hat{W}}{\partial \boldsymbol{C}}:(\boldsymbol{F}^T\cdot\boldsymbol{T}) = \left[\boldsymbol{F}\cdot\frac{\partial \hat{W}}{\partial \boldsymbol{C}}\right]:\boldsymbol{T} $$ Therefore, invoking the arbitrariness of $$\boldsymbol{T}$$, we have

\boldsymbol{P} = \rho_0~\boldsymbol{F}\cdot\left(\frac{\partial \hat{W}}{\partial \boldsymbol{C}}\right)^T + \rho_0~\boldsymbol{F}\cdot\frac{\partial \hat{W}}{\partial \boldsymbol{C}} $$ Since $$\boldsymbol{C} = \boldsymbol{C}^T$$ we have

\left(\frac{\partial \hat{W}}{\partial \boldsymbol{C}}\right)^T = \frac{\partial \hat{W}}{\partial \boldsymbol{C}} $$ which implies that

\boldsymbol{P} = 2~\rho_0~\boldsymbol{F}\cdot\frac{\partial \hat{W}}{\partial \boldsymbol{C}} \quad \text{or} \quad \boldsymbol{N} = 2~\rho_0~\frac{\partial \hat{W}}{\partial \boldsymbol{C}}\cdot\boldsymbol{F}^T $$ Recall the relations between the 2nd Piola-Kirchhoff stress tensor and the first Piola-Kirchhoff stress tensor (and the nominal stress tensor)

\boldsymbol{S} = \boldsymbol{F}^{-1}\cdot\boldsymbol{P} $$ Therefore, we have

\boldsymbol{S} = 2~\rho_0~\frac{\partial \hat{W}}{\partial \boldsymbol{C}} $$ Also from the relation between the Cauchy stress and the 2nd Piola-Kirchhoff stress tensor

\boldsymbol{\sigma} = J^{-1}~\boldsymbol{F}\cdot\boldsymbol{S}\cdot\boldsymbol{F}^T = \cfrac{\rho}{\rho_0}~\boldsymbol{F}\cdot\boldsymbol{S}\cdot\boldsymbol{F}^T $$ we have

\boldsymbol{\sigma} = 2~\rho~\boldsymbol{F}\cdot\frac{\partial \hat{W}}{\partial \boldsymbol{C}}\cdot\boldsymbol{F}^T \quad \text{or} \quad \boldsymbol{\tau} = 2~\rho_0\boldsymbol{F}\cdot\frac{\partial \hat{W}}{\partial \boldsymbol{C}}\cdot\boldsymbol{F}^T $$

We may also express these relations in terms of the Lagrangian Green strain

\boldsymbol{E} = \frac{1}{2}(\boldsymbol{F}^T\cdot\boldsymbol{F} - \boldsymbol{\mathit{1}}) = \frac{1}{2}(\boldsymbol{C} - \boldsymbol{\mathit{1}}) $$ Then we have

\frac{\partial W}{\partial \boldsymbol{C}} = \frac{\partial W}{\partial \boldsymbol{E}}:\frac{\partial \boldsymbol{E}}{\partial \boldsymbol{C}} = \frac{1}{2}~\frac{\partial W}{\partial \boldsymbol{E}} $$ Hence, we can write

The stored energy function $$W$$ is objective if and only if the Cauchy stress tensor is symmetric, i.e., if the balance of angular momentum holds.  Show this.


text:
Nonlinear finite elements/Rate form of hyperelastic laws

Rate equations
Let us now derive rate equations for a hyperelastic material.

First elasticity tensor
We start off with the relation

\boldsymbol{P} = \rho_0~\frac{\partial W}{\partial \boldsymbol{F}} $$ Then the material time derivative of $$\boldsymbol{P}$$ is given by where the fourth order tensor $$\boldsymbol{\mathsf{A}}$$ is call the  first elasticity tensor. This tensor has major symmetries but not minor symmetries. In index notation with respect to an orthonormal basis

\dot{P}_{iJ} = \mathsf{A}_{iJkL}~\dot{F}_{kL} = \rho_0~\frac{\partial^2 W}{\partial F_{iJ}\partial F_{kL}}~\dot{F}_{kL} $$

 Proof:

We have

\dot{\boldsymbol{P}} = \rho_0~\frac{\partial }{\partial t}\left(\frac{\partial W}{\partial \boldsymbol{F}}\right) = \rho_0~\frac{\partial }{\partial \boldsymbol{F}}\left(\frac{\partial W}{\partial t}\right) = \rho_0~\frac{\partial }{\partial \boldsymbol{F}}\left(\frac{\partial W}{\partial \boldsymbol{F}}:\dot{\boldsymbol{F}}\right) $$ Using the product rule, we have

\dot{\boldsymbol{P}} = \rho_0~\frac{\partial^2 W}{\partial \boldsymbol{F}\partial\boldsymbol{F}}:\dot{\boldsymbol{F}} + \rho_0~\frac{\partial W}{\partial \boldsymbol{F}}:\frac{\partial^2 \boldsymbol{F}}{\partial \boldsymbol{F}\partial t} = \rho_0~\frac{\partial^2 W}{\partial \boldsymbol{F}\partial\boldsymbol{F}}:\dot{\boldsymbol{F}} + \rho_0~\frac{\partial W}{\partial \boldsymbol{F}}:\frac{\partial }{\partial t}\left(\frac{\partial \boldsymbol{F}}{\partial \boldsymbol{F}}\right) $$ Therefore,

\dot{\boldsymbol{P}} = \rho_0~\frac{\partial^2 W}{\partial \boldsymbol{F}\partial\boldsymbol{F}}:\dot{\boldsymbol{F}} = \boldsymbol{\mathsf{A}}:\dot{\boldsymbol{F}} \qquad \square $$

Second elasticity tensor
Similarly, if we start off with the relation

\boldsymbol{S} = 2~\rho_0~\frac{\partial W}{\partial \boldsymbol{C}} $$ the material time derivative of $$\boldsymbol{S}$$ can be expressed as where the fourth order tensor $$\boldsymbol{\mathsf{C}}$$ is called the  material elasticity tensor or the  second elasticity tensor. Since this tensor relates symmetric second order tensors it has minor symmetries. It also has major symmetries because the two partial derivatives are with the same quantity and an interchange does not change things. In index notation with respect to an orthonormal basis

\dot{S}_{IJ} = \frac{1}{2}~\mathsf{C}_{IJKL}~\dot{C}_{KL} = \frac{1}{2}~\left(4~\rho_0~\frac{\partial^2 W}{\partial C_{IJ}\partial C_{KL}}\right)~\dot{C}_{KL} $$

 Proof:

We have

\dot{\boldsymbol{S}} = 2~\rho_0~\frac{\partial }{\partial t}\left(\frac{\partial W}{\partial \boldsymbol{C}}\right) = 2~\rho_0~\frac{\partial }{\partial \boldsymbol{C}}\left(\frac{\partial W}{\partial t}\right) = 2~\rho_0~\frac{\partial }{\partial \boldsymbol{C}}\left(\frac{\partial W}{\partial \boldsymbol{C}}:\dot{\boldsymbol{C}}\right) $$ Again using the product rule, we have

\dot{\boldsymbol{S}} = 2~\rho_0~\frac{\partial^2 W}{\partial \boldsymbol{C}\partial\boldsymbol{C}}:\dot{\boldsymbol{C}} + 2~\rho_0~\frac{\partial W}{\partial \boldsymbol{C}}:\frac{\partial^2 \boldsymbol{C}}{\partial \boldsymbol{C}\partial t}     =  2~\rho_0~\frac{\partial^2 W}{\partial \boldsymbol{C}\partial\boldsymbol{C}}:\dot{\boldsymbol{C}} $$ Therefore,

\dot{\boldsymbol{S}} = 4~\rho_0~\frac{\partial^2 W}{\partial \boldsymbol{C}\partial\boldsymbol{C}}: \frac{1}{2}~\dot{\boldsymbol{C}} = \boldsymbol{\mathsf{C}}:\frac{1}{2}~\dot{\boldsymbol{C}} \qquad \square $$

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Relation between first and second elasticity tensors
The first and second elasticity tensors are related by

{ \mathsf{A}_{iJkL} = \delta_{ik}~S_{JL} + F_{iN}~\mathsf{C}_{NJML}~F_{kM} } $$
 * }

 Proof: Recall that the first and second Piola-Kirchhoff stresses are related by

\boldsymbol{P} = \boldsymbol{F}\cdot\boldsymbol{S} $$ Taking the material time derivative of both sides gives

\dot{\boldsymbol{P}} = \dot{\boldsymbol{F}}\cdot\boldsymbol{S} + \boldsymbol{F}\cdot\dot{\boldsymbol{S}} $$ Using the expression for $$\dot{\boldsymbol{S}}$$ above, we get

\dot{\boldsymbol{P}} = \dot{\boldsymbol{F}}\cdot\boldsymbol{S} + \frac{1}{2}~\boldsymbol{F}\cdot(\boldsymbol{\mathsf{C}}:\dot{\boldsymbol{C}}) $$ Now

\boldsymbol{C} = \boldsymbol{F}^T\cdot\boldsymbol{F} \quad \implies \quad \dot{\boldsymbol{C}} = \dot{\boldsymbol{F}^T}\cdot\boldsymbol{F} + \boldsymbol{F}^T\cdot\dot{\boldsymbol{F}} $$ Therefore,

\dot{\boldsymbol{P}} = \dot{\boldsymbol{F}}\cdot\boldsymbol{S} + \frac{1}{2}~\boldsymbol{F}\cdot[\boldsymbol{\mathsf{C}}:(                \dot{\boldsymbol{F}^T}\cdot\boldsymbol{F} + \boldsymbol{F}^T\cdot\dot{\boldsymbol{F}})] $$ Now

\boldsymbol{\mathsf{C}}:(\dot{\boldsymbol{F}^T}\cdot\boldsymbol{F}) \equiv \mathsf{C}_{IJKL}~\dot{F}_{mK}~F_{mL} \quad \text{and} \qquad \boldsymbol{\mathsf{C}}:(\boldsymbol{F}^T\cdot\dot{\boldsymbol{F}}) \equiv = \mathsf{C}_{IJLK}~F_{mL}~\dot{F}_{mK} = \mathsf{C}_{IJKL}~F_{mL}~\dot{F}_{mK} $$ That means

\boldsymbol{\mathsf{C}}:(\dot{\boldsymbol{F}^T}\cdot\boldsymbol{F}) = \boldsymbol{\mathsf{C}}:(\boldsymbol{F}^T\cdot\dot{\boldsymbol{F}}) $$ which gives us

\dot{\boldsymbol{P}} = \dot{\boldsymbol{F}}\cdot\boldsymbol{S} + \boldsymbol{F}\cdot[\boldsymbol{\mathsf{C}}:(\boldsymbol{F}^T\cdot\dot{\boldsymbol{F}})] $$ In index notation,

\begin{align} \dot{P}_{iJ} & = \dot{F}_{iL}~S_{LJ} + F_{iN}~[\mathsf{C}_{NJML}~F_{kM}~\dot{F}_{kL}]\\ & = S_{LJ}~\delta_{ik}\dot{F}_{kL}+\mathsf{C}_{NJML}~F_{iN}~F_{kM}~\dot{F}_{kL}\\ & = (\delta_{ik}~S_{JL} + F_{iN}~\mathsf{C}_{NJML}~F_{kM})~\dot{F}_{kL} & = \mathsf{A}_{iJkL}~\dot{F}_{kL} \end{align} $$ Therefore,

\mathsf{A}_{iJkL} = \delta_{ik}~S_{JL} + F_{iN}~\mathsf{C}_{NJML}~F_{kM} \qquad \square $$

Fourth elasticity tensor
Now we will compute the spatial elasticity tensor for the rate constitutive equation for a hyperelastic material. This tensor relates an objective rate of stress (Cauchy or Kirchhoff) to the rate of deformation tensor. We can show that

The fourth order tensor $$\boldsymbol{\mathsf{c}}$$ is called the  spatial elasticity tensor or the  fourth elasticity tensor. Clearly, $$\mathsf{c}_{ijkl}$$ cannot be derived from the store energy function $$W$$ because of the dependence on the deformation gradient.

 Proof: Recall that the Lie derivative of the Kirchhoff stress is defined as

\mathcal{L}_\varphi[\boldsymbol{\tau}] = \overset{\circ}{\boldsymbol{\tau}} = \boldsymbol{F}\cdot\dot{\boldsymbol{S}}\cdot\boldsymbol{F}^T $$ We have found that

\dot{\boldsymbol{S}} = \boldsymbol{\mathsf{C}} : \frac{1}{2}~\dot{\boldsymbol{C}} $$ We also know from Continuum_mechanics/Time_derivatives_and_rates that

\dot{\boldsymbol{C}} = 2~\boldsymbol{F}^T\cdot\boldsymbol{d}\cdot\boldsymbol{F} $$ where $$\boldsymbol{d}$$ is the spatial rate of deformation tensor. Therefore,

\mathcal{L}_\varphi[\boldsymbol{\tau}] = \boldsymbol{F}\cdot[\boldsymbol{\mathsf{C}}:(\boldsymbol{F}^T\cdot\boldsymbol{d}\cdot\boldsymbol{F})]\cdot\boldsymbol{F}^T $$ In index notation,

(\mathcal{L}_\varphi[\boldsymbol{\tau}])_{ij} = F_{iK}~\mathsf{C}_{KLMN}~F_{kM}~d_{kl}~F_{lN}~F_{jL} = F_{iK}~F_{jL}~F_{kM}~F_{lN}~\mathsf{C}_{KLMN}~d_{kl} = \mathsf{c}_{ijkl}~d_{kl} $$ or,

\mathcal{L}_\varphi[\boldsymbol{\tau}] = \boldsymbol{\mathsf{c}}:\boldsymbol{d} $$ where

\mathsf{c}_{ijkl} = F_{iK}~F_{jL}~F_{kM}~F_{lN}~\mathsf{C}_{KLMN} \qquad \square $$

Alternatively, we may define $$\boldsymbol{\mathsf{c}}$$ in terms of the Cauchy stress $$\boldsymbol{\sigma}$$, in which case the constitutive relation is written as The proof of this relation between the spatial and material elasticity tensors is very similar to that for the rate of Kirchhoff stress. Many authors define this quantity $$\mathsf{c}_{ijkl}$$ as the spatial elasticity tensor. Note the factor of $$J^{-1}$$. This form of the spatial elasticity tensor is crucial for some of the calculations that follow.

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Relation between first and fourth elasticity tensors
The first and fourth elasticity tensors are related by

{ \mathsf{A}_{iJkL} = F_{Jj}^{-1}[\mathsf{c}_{ijkl} + \tau_{jl}~\delta_{ik}]~F_{Ll}^{-1} } $$ In the above equation $$\mathsf{c}_{ijkl}$$ is the elasticity tensor that relates the rate of Kirchhoff stress to the rate of deformation.

Instead, if we use the Cauchy stress and the spatial elasticity tensor $$\mathsf{c}_{ijkl}$$ that relates the Cauchy stress to the rate of deformation), the above relation becomes

{ \mathsf{A}_{iJkL} = J~F_{Jj}^{-1}[\mathsf{c}_{ijkl} + \sigma_{jl}~\delta_{ik}]~F_{Ll}^{-1} } $$

 * }

 Proof: Recall that

\dot{\boldsymbol{P}} = \boldsymbol{\mathsf{A}}:\dot{\boldsymbol{F}} $$ Therefore,

\dot{\boldsymbol{P}}\cdot\boldsymbol{F}^T = (\boldsymbol{\mathsf{A}}:\dot{\boldsymbol{F}})\cdot\boldsymbol{F}^T $$ Also recall that

\mathsf{A}_{iJkL} = \delta_{ik}~S_{JL} + F_{iN}~\mathsf{C}_{NJML}~F_{kM} $$ Therefore, using index notation,

\dot{P}_{iJ}~F_{lJ} = \delta_{ik}~S_{JL}~F_{lJ}~\dot{F}_{kL} + F_{iN}~\mathsf{C}_{NJML}~F_{kM}~F_{lJ})     ~\dot{F}_{kL} $$ Now,

\boldsymbol{l} = \dot{\boldsymbol{F}}\cdot\boldsymbol{F}^{-1} \qquad \text{or} \qquad \dot{\boldsymbol{F}} = \boldsymbol{l}\cdot\boldsymbol{F} $$ In index notation

\dot{F}_{kL} = l_{km}~F_{mL} $$ Using this we get

\dot{P}_{iJ}~F_{lJ} = \delta_{ik}~S_{JL}~F_{lJ}~l_{km}~F_{mL} + F_{iN}~\mathsf{C}_{NJML}~F_{kM}~F_{lJ})~l_{km}~F_{mL} $$ or,

\dot{P}_{iJ}~F_{lJ} = (\delta_{ik}~F_{lJ}~S_{JL}~F_{mL} +      F_{iN}~F_{lJ}~F_{kM}~F_{mL}~\mathsf{C}_{NJML})~l_{km} $$ Now,

\boldsymbol{\tau} = \boldsymbol{F}\cdot\boldsymbol{S}\cdot\boldsymbol{F}^T \qquad \text{or} \qquad \tau_{lm} = F_{lJ}~S_{JL}~F_{mL} $$ Therefore,

\dot{P}_{iJ}~F_{lJ} = (\delta_{ik}~\tau_{lm} +      F_{iN}~F_{lJ}~F_{kM}~F_{mL}~\mathsf{C}_{NJML})~l_{km} $$ Also,

\mathsf{c}_{ilkm} = F_{iN}~F_{lJ}~F_{kM}~F_{mL}~\mathsf{C}_{NJML} $$ So we have

\dot{P}_{iJ}~F_{lJ} = (\delta_{ik}~\tau_{lm} + \mathsf{c}_{ilkm})~l_{km} = \mathsf{a}_{ilkm}~l_{km} $$

 Note: The fourth order tensor

\mathsf{a}_{ijkl} = \delta_{ik}~\tau_{jl} + \mathsf{c}_{ijkl} $$ which depends on the symmetry of $$\boldsymbol{\tau}$$ is called the  third elasticity tensor, i.e.,

\dot{\boldsymbol{P}}\cdot\boldsymbol{F}^T = \boldsymbol{\mathsf{a}}:\boldsymbol{l} $$

Therefore, the relation between the first and third elasticity tensors is

\dot{\boldsymbol{P}}\cdot\boldsymbol{F}^T = (\boldsymbol{\mathsf{A}}:\dot{\boldsymbol{F}})\cdot\boldsymbol{F}^T = \boldsymbol{\mathsf{a}}:\boldsymbol{l} = \boldsymbol{\mathsf{a}}:(\dot{\boldsymbol{F}}\cdot\boldsymbol{F}^{-1}) $$ or,

\boldsymbol{\mathsf{A}}:\dot{\boldsymbol{F}} = [\boldsymbol{\mathsf{a}}:(\dot{\boldsymbol{F}}\cdot\boldsymbol{F}^{-1})]\cdot\boldsymbol{F}^{-T} $$ In index notation

\mathsf{A}_{iJkL}~\dot{F}_{kL} = \mathsf{a}_{ijkl}~\dot{F}_{kL}~F^{-1}_{Ll}~F^{-1}_{jJ} $$ Therefore,

\mathsf{A}_{iJkL} = \mathsf{a}_{ijkl}~F^{-1}_{Ll}~F^{-1}_{jJ} = (\delta_{ik}~\tau_{jl} + \mathsf{c}_{ijkl})~F^{-1}_{Ll}~F^{-1}_{jJ} \qquad \square $$

An isotropic spatial elasticity tensor?
An isotropic spatial elasticity tensor cannot be derived from a stored energy function if the constitutive relation is of the form

\mathcal{L}_\varphi[\boldsymbol{\tau}] = \boldsymbol{\mathsf{c}}:\boldsymbol{d} $$ where

\boldsymbol{\mathsf{c}} = \lambda~\boldsymbol{\mathit{1}}\otimes\boldsymbol{\mathit{1}} + 2~\mu~\boldsymbol{\mathsf{I}}^{s} ~. $$ Since a significant number of finite element codes use such a constitutive equation, (also called the equation of a  hypoelastic material of grade 0) it is worth examining why such a model is incompatible with elasticity.

Start with a constant and isotropic material elasticity tensor
Let us start of with an isotropic elastic material model in the reference configuration. The simplest such model is the St. Venant-Kirchhoff hyperelastic model

\boldsymbol{S} = \lambda~\text{tr}(\boldsymbol{E})~\boldsymbol{\mathit{1}} + 2~\mu~\boldsymbol{E} $$ where $$\boldsymbol{S}$$ is the second Piola-Kirchhoff stress, $$\boldsymbol{E}$$ is the Lagrangian Green strain, and $$\lambda,\mu$$ are material constants. We can show that this equation can be derived from a stored energy function.

Taking the material time derivative of this equation, we get

\dot{\boldsymbol{S}} = \lambda~\text{tr}(\dot{\boldsymbol{E}})~\boldsymbol{\mathit{1}} + 2~\mu~\dot{\boldsymbol{E}} $$ Now,

\dot{\boldsymbol{S}} = \boldsymbol{\mathsf{C}}:\frac{1}{2}~\dot{\boldsymbol{C}} = \boldsymbol{\mathsf{C}}:\dot{\boldsymbol{E}} $$ where $$\boldsymbol{\mathsf{C}}$$ is the second (material) elasticity tensor.

Therefore,

\boldsymbol{\mathsf{C}}:\dot{\boldsymbol{E}} = \lambda~\text{tr}(\dot{\boldsymbol{E}})~\boldsymbol{\mathit{1}} + 2~\mu~\dot{\boldsymbol{E}} $$ which implies that

\boldsymbol{\mathsf{C}} = \lambda~\boldsymbol{\mathit{1}}\otimes\boldsymbol{\mathit{1}} + 2~\mu~\boldsymbol{\mathsf{I}}^{s} ~. $$ In index notation,

\mathsf{C}_{IJKL} = \lambda~\delta_{IJ}~\delta_{KL} + \mu~(\delta_{IK}~\delta_{JL} +   \delta_{JK}~\delta_{IL}) $$ Now, from the relations between the second elasticity tensor and the fourth (spatial) elasticity tensor, we have

\mathsf{c}_{ijkl} = F_{iI}~F_{jJ}~F_{kK}~F_{lL}~\mathsf{C}_{IJKL} $$ Therefore, in this case,

\mathsf{c}_{ijkl} = F_{iI}~F_{jJ}~F_{kK}~F_{lL}~\left[ \lambda~\delta_{IJ}~\delta_{KL} + \mu~(\delta_{IK}~\delta_{JL} +   \delta_{JK}~\delta_{IL})\right] $$ or,

{ \mathsf{c}_{ijkl} = \lambda~b_{ij}~b_{kl} + \mu~(b_{ik}~b_{jl} + b_{il}~b_{jk}) } $$ where $$\boldsymbol{b} = \boldsymbol{F}\cdot\boldsymbol{F}^T$$. So we see that the spatial elasticity tensor $$\boldsymbol{\mathsf{c}}$$ cannot be a constant tensor unless $$\boldsymbol{b} = \boldsymbol{\mathit{1}}$$.

Alternatively, if we define

\mathsf{c}_{ijkl} = J^{-1}~F_{iI}~F_{jJ}~F_{kK}~F_{lL}~\mathsf{C}_{IJKL} $$ we get

{ \mathsf{c}_{ijkl} = J^{-1}~\lambda~b_{ij}~b_{kl} + J^{-1}~\mu~(b_{ik}~b_{jl} + b_{il}~b_{jk}) } $$

Start with a constant and isotropic spatial elasticity tensor
Let us now look at the situation where we start off with a constant and isotropic spatial elasticity tensor, i.e.,

\boldsymbol{\mathsf{c}} = \lambda~\boldsymbol{\mathit{1}}\otimes\boldsymbol{\mathit{1}} + 2~\mu~\boldsymbol{\mathsf{I}}^{s} $$ In index notation,

\mathsf{c}_{ijkl} = \lambda~\delta_{ij}~\delta_{kl} + \mu(    \delta_{ik}~\delta_{jl} + \delta_{jk}~\delta_{il}) $$ Since

\mathsf{c}_{ijkl} = F_{iI}~F_{jJ}~F_{kK}~F_{lL}~\mathsf{C}_{IJKL} $$ multiplying both sides by $$F^{-1}_{Ai}~F^{-1}_{Bj}~F^{-1}_{Ck}~F^{-1}_{Dl}$$ we have,

F^{-1}_{Ai}~F^{-1}_{Bj}~F^{-1}_{Ck}~F^{-1}_{Dl}~\mathsf{c}_{ijkl} = \mathsf{C}_{ABCD} $$ Therefore, substituting in the expression for a constant and isotropic $$\boldsymbol{\mathsf{c}}$$, we have

\mathsf{C}_{ABCD} = F^{-1}_{Ai}~F^{-1}_{Bj}~F^{-1}_{Ck}~F^{-1}_{Dl}~\left[ \lambda~\delta_{ij}~\delta_{kl} + \mu(    \delta_{ik}~\delta_{jl} + \delta_{jk}~\delta_{il})\right] $$ or,

\mathsf{C}_{ABCD} = \lambda~F^{-1}_{Aj}~F^{-1}_{Bj}~F^{-1}_{Cl}~F^{-1}_{Dl} + \mu\left( F^{-1}_{Ak}~F^{-1}_{Bl}~F^{-1}_{Ck}~F^{-1}_{Dl} +        F^{-1}_{Al}~F^{-1}_{Bk}~F^{-1}_{Ck}~F^{-1}_{Dl} \right) $$ or,

\mathsf{C}_{ABCD} = \lambda~(\boldsymbol{F}^{-1}\cdot\boldsymbol{F}^{-T})_{AB}~(\boldsymbol{F}^{-1}\cdot\boldsymbol{F}^{-T})_{CD} + \mu\left(\boldsymbol{F}^{-1}\cdot\boldsymbol{F}^{-T})_{AC}~(\boldsymbol{F}^{-1}\cdot~\boldsymbol{F}^{-T})_{BD} + \boldsymbol{F}^{-1}\cdot\boldsymbol{F}^{-T})_{AD}~(\boldsymbol{F}^{-1}\cdot~\boldsymbol{F}^{-T})_{BC}\right) $$ Since $$\boldsymbol{C} = \boldsymbol{F}^T\cdot\boldsymbol{F}$$ which gives us $$\boldsymbol{C}^{-1} = \boldsymbol{F}^{-1}\cdot\boldsymbol{F}^{-T}$$, we can write

{ \mathsf{C}_{ABCD} = \lambda~\boldsymbol{C}^{-1}_{AB}~\boldsymbol{C}^{-1}_{CD} + \mu\left(\boldsymbol{C}^{-1}_{AC}~\boldsymbol{C}^{-1}_{BD} + \boldsymbol{C}^{-1}_{AD}~\boldsymbol{C}^{-1}_{BC}\right) } $$ Alternatively, if we define

\mathsf{c}_{ijkl} = J^{-1}~F_{iI}~F_{jJ}~F_{kK}~F_{lL}~\mathsf{C}_{IJKL} $$ we get

\mathsf{C}_{ABCD} = J~F^{-1}_{Ai}~F^{-1}_{Bj}~F^{-1}_{Ck}~F^{-1}_{Dl}~\mathsf{c}_{ijkl} $$ and therefore,

{ \mathsf{C}_{ABCD} = J~\lambda~\boldsymbol{C}^{-1}_{AB}~\boldsymbol{C}^{-1}_{CD} + J~\mu\left(\boldsymbol{C}^{-1}_{AC}~\boldsymbol{C}^{-1}_{BD} + \boldsymbol{C}^{-1}_{AD}~\boldsymbol{C}^{-1}_{BC}\right) } $$

Hypoelastic material of grade 0
A hypoelastic material of grade zero is one for which the stress-strain relation in rate form can be expressed as

\mathcal{L}_{\varphi}[\boldsymbol{\sigma}] = \boldsymbol{\mathsf{c}}:\boldsymbol{d} $$ where $$\boldsymbol{\mathsf{c}}$$ is constant. When the material is isotropic we have

\boldsymbol{\mathsf{c}} = \lambda~\boldsymbol{\mathit{1}}\otimes\boldsymbol{\mathit{1}} + 2~\mu~\boldsymbol{\mathsf{I}}^{s} $$

We want to show that hypoelastic material models of grade 0 cannot be derived from a stored energy function. To do that, recall that

\mathsf{C}_{IJKL} = 4~\rho_0~\frac{\partial^2 W}{\partial C_{IJ}\partial C_{KL}} $$ and

S_{IJ} = 2~\rho_0~\frac{\partial W}{\partial C_{IJ}} $$ For a material elasticity tensor $$\boldsymbol{\mathsf{C}}$$ to be derivable from a stored energy function it has to satisfy the Bernstein integrability conditions. We have

\frac{\partial S_{IJ}}{\partial C_{KL}} = 2~\rho_0~\frac{\partial^2 W}{\partial C_{IJ}\partial C_{KL}} = \frac{1}{2}~\mathsf{C}_{IJKL} $$ Also, due to the interchangeability of derivatives,

\frac{\partial }{\partial C_{MN}}\left( \frac{\partial S_{IJ}}{\partial C_{KL}}\right) = \frac{\partial }{\partial C_{KL}}\left( \frac{\partial S_{IJ}}{\partial C_{MN}}\right) $$ Therefore,

{ \frac{\partial \mathsf{C}_{IJKL}}{\partial C_{MN}} = \frac{\partial \mathsf{C}_{IJMN}}{\partial C_{KL}} } $$ These integrability conditions have to be satisfied by any material elasticity tensor.

At this stage we will use the relation

\mathsf{C}_{ABCD} = J~\lambda~\boldsymbol{C}^{-1}_{AB}~\boldsymbol{C}^{-1}_{CD} + J~\mu\left(\boldsymbol{C}^{-1}_{AC}~\boldsymbol{C}^{-1}_{BD} + \boldsymbol{C}^{-1}_{AD}~\boldsymbol{C}^{-1}_{BC}\right) $$

If we plug this into the integrability condition we will see that

{ (\lambda+\mu)~C^{-1}_{KL}(C_{IM}^{-1}~C_{JN}^{-1} + C_{IN}^{-1}~C_{JM}^{-1}) = (\lambda+\mu)~C^{-1}_{MN}(C_{IK}^{-1}~C_{JL}^{-1} + C_{IL}^{-1}~C_{JK}^{-1}) } $$ If we multiply both sides by $$C_{MN}~C_{IK}~C_{JL}$$ we are left with

{  \lambda + \mu = 0 } $$ This is an unphysical situation and hence shows that a hypoelastic material of grade zero requires that $$\lambda = -\mu$$ for it to be derivable from a stored energy function.

 Proof: Let us simplify the notation by writing $$\boldsymbol{A} := \boldsymbol{C}^{-1}$$. Then,

\mathsf{C}_{IJKL} = J~\lambda~A_{IJ}~A_{KL} + J~\mu\left(A_{IK}~A_{JL} + A_{JK}~A_{IL}\right) $$ Then,

\begin{align} \frac{\partial \mathsf{C}_{IJKL}}{\partial C_{MN}} = & \lambda~\frac{\partial J}{\partial C_{MN}}~A_{IJ}~A_{KL} + \\ & J~\lambda~\left[\frac{\partial A_{IJ}}{\partial C_{MN}}~A_{KL} + A_{IJ}~\frac{\partial A_{KL}}{\partial C_{MN}}\right] + \\ & \mu~\frac{\partial J}{\partial C_{MN}}~(A_{IK}~A_{JL} + A_{JK}~A_{IL}) + \\ & J~\mu~\left[\frac{\partial A_{IK}}{\partial C_{MN}}~A_{JL} + A_{IK}~\frac{\partial A_{JL}}{\partial C_{MN}} + \frac{\partial A_{JK}}{\partial C_{MN}}~A_{IL} + A_{JK}~\frac{\partial A_{IL}}{\partial C_{MN}}\right] \end{align} $$ and

\begin{align} \frac{\partial \mathsf{C}_{IJMN}}{\partial C_{KL}} = & \lambda~\frac{\partial J}{\partial C_{KL}}~A_{IJ}~A_{MN} + \\ & J~\lambda~\left[\frac{\partial A_{IJ}}{\partial C_{KL}}~A_{MN} + A_{IJ}~\frac{\partial A_{MN}}{\partial C_{KL}}\right] + \\ & \mu~\frac{\partial J}{\partial C_{KL}}~(A_{IM}~A_{JN} + A_{JM}~A_{IN}) + \\ & J~\mu~\left[\frac{\partial A_{IM}}{\partial C_{KL}}~A_{JN} + A_{IM}~\frac{\partial A_{JN}}{\partial C_{KL}} + \frac{\partial A_{JM}}{\partial C_{KL}}~A_{IN} + A_{JM}~\frac{\partial A_{IN}}{\partial C_{KL}}\right] \end{align} $$ As this stage we use the identities (see Nonlinear finite elements/Kinematics for proofs)

\frac{\partial J}{\partial C_{IJ}} = \cfrac{J}{2}~C_{IJ}^{-1} = \cfrac{J}{2}~A_{IJ} $$ and

\frac{\partial C^{-1}_{IJ}}{\partial C_{KL}} = -\frac{1}{2}~(C^{-1}_{IK}~C^{-1}_{JL} + C^{-1}_{JK}~C^{-1}_{IL}) \qquad \text{or} \qquad \frac{\partial A_{IJ}}{\partial C_{KL}} = -\frac{1}{2}~(A_{IK}~A_{JL} + A_{JK}~A_{IL}) $$

Therefore we have

\begin{align} \frac{\partial \mathsf{C}_{IJKL}}{\partial C_{MN}} = & \cfrac{J~\lambda}{2}~A_{MN}~A_{IJ}~A_{KL} - \\ & \cfrac{J~\lambda}{2}~\left[(A_{IM}~A_{JN} + A_{JM}~A_{IN})~A_{KL} + (A_{KM}~A_{LN} + A_{LM}~A_{KN})~A_{IJ}\right] + \\ & \cfrac{J~\mu}{2}~A_{MN}~(A_{IK}~A_{JL} + A_{JK}~A_{IL}) - \\ & \cfrac{J~\mu}{2}~\left[(A_{IM}~A_{KN}+A_{KM}~A_{IN})~A_{JL} + (A_{JM}~A_{LN}+A_{LM}~A_{JN})~A_{IK}\right. + \\   & \qquad\quad          \left. (A_{JM}~A_{KN}+A_{KM}~A_{JN})~A_{IL} + (A_{IM}~A_{LN}+A_{LM}~A_{IN})A_{JK}\right] \end{align} $$ and

\begin{align} \frac{\partial \mathsf{C}_{IJMN}}{\partial C_{KL}} = & \cfrac{J~\lambda}{2}~A_{KL}~A_{IJ}~A_{MN} - \\ & \cfrac{J~\lambda}{2}~\left[(A_{IK}~A_{JL}+A_{JK}~A_{IL})~A_{MN} + (A_{KM}~A_{LN} + A_{LM}~A_{KN})A_{IJ}\right] + \\ & \cfrac{J~\mu}{2}~A_{KL}~(A_{IM}~A_{JN} + A_{JM}~A_{IN}) - \\ & \cfrac{J~\mu}{2}~\left[(A_{IK}~A_{LM}+A_{KM}~A_{IL})~A_{JN} + (A_{JK}~A_{LN}+A_{JL}~A_{KN})~A_{IM} + \right.\\ & \qquad \qquad \left. (A_{JK}~A_{LM}+A_{JL}~A_{KM})~A_{IN} + (A_{IK}~A_{LN}+A_{IL}~A_{KN})~A_{JM}\right] \end{align} $$ Equating the two, we see that the terms that cancel out are

\cfrac{J~\lambda}{2}~A_{KL}~A_{IJ}~A_{MN} ~; \cfrac{J~\lambda}{2}~(A_{KM}~A_{LN} + A_{LM}~A_{KN})A_{IJ} ~; $$ and

\begin{align} \cfrac{J~\mu}{2}~& \left[(A_{IM}~A_{KN}+A_{KM}~A_{IN})~A_{JL} + (A_{JM}~A_{LN}+A_{LM}~A_{JN})~A_{IK}\right. + \\   &         \left. (A_{JM}~A_{KN}+A_{KM}~A_{JN})~A_{IL} + (A_{IM}~A_{LN}+A_{LM}~A_{IN})A_{JK}\right] \end{align} $$ Therefore,

\frac{\partial \mathsf{C}_{IJKL}}{\partial C_{MN}} = \frac{\partial \mathsf{C}_{IJMN}}{\partial C_{KL}} $$ implies that

\begin{align} -\cfrac{J~\lambda}{2}~ & (A_{IM}~A_{JN} + A_{JM}~A_{IN})~A_{KL} + \cfrac{J~\mu}{2}~A_{MN}~(A_{IK}~A_{JL} + A_{JK}~A_{IL}) = \\ & -\cfrac{J~\lambda}{2}~(A_{IK}~A_{JL}+A_{JK}~A_{IL})~A_{MN} + \cfrac{J~\mu}{2}~A_{KL}~(A_{IM}~A_{JN} + A_{JM}~A_{IN}) \end{align} $$ or,

(\lambda+\mu)~A_{MN}~(A_{IK}~A_{JL} + A_{JK}~A_{IL}) = (\lambda+\mu)~A_{KL}~(A_{IM}~A_{JN} + A_{JM}~A_{IN}) $$ In other words,

(\lambda+\mu)~C^{-1}_{KL}(C_{IM}^{-1}~C_{JN}^{-1} + C_{IN}^{-1}~C_{JM}^{-1}) = (\lambda+\mu)~C^{-1}_{MN}(C_{IK}^{-1}~C_{JL}^{-1} + C_{IL}^{-1}~C_{JK}^{-1}) $$

Now, if we multiply both sides by $$C_{MN}$$ we get

(\lambda+\mu)~C^{-1}_{KL}(\delta_{IN}~C_{JN}^{-1} + \delta_{IM}~C_{JM}^{-1}) = (\lambda+\mu)~\delta_{MM}(C_{IK}^{-1}~C_{JL}^{-1} + C_{IL}^{-1}~C_{JK}^{-1}) $$ or,

2~(\lambda+\mu)~C^{-1}_{KL}~C_{JI}^{-1} = 3~(\lambda+\mu)~(C_{IK}^{-1}~C_{JL}^{-1} + C_{IL}^{-1}~C_{JK}^{-1}) $$ Next, multiplying both sides by $$C_{IK}$$ gives

2~(\lambda+\mu)~\delta_{IL}~C_{JI}^{-1} = 3~(\lambda+\mu)~(\delta_{KK}~C_{JL}^{-1} + \delta_{KL}~C_{JK}^{-1}) $$ or,

2~(\lambda+\mu)~C_{JL}^{-1} = 12~(\lambda+\mu)~C_{JL}^{-1} $$ Finally, multiplying both sides by $$C_{JL}$$ gives

(\lambda+\mu)~\delta_{JJ} = 6~(\lambda+\mu)~\delta_{JJ} $$ Therefore,

\lambda + \mu = 0 $$