Chien-Chih Yu
email: ccyu@nccu.edu.tw

Developing Value-Centric Business Models for Mobile Government

Keywords: Business model, value creation, mobile government, Balanced Scorecard, performance measurement

This paper proposes a value-centric business model (BM) framework and development process for building suitable business models to support the planning, implementation, operation, and evaluation of mobile government (MG) applications. MG stakeholders, values, systems, services, resources, costs, performances, as well as strategies and action plans are included as components to be specified in the BM framework. To achieve the objectives of creating value for all participating parties in the mobile government environment, four stakeholder and value perspectives taken into account are public beneficiaries, government internal organizations, government service chain, as well as society and nation. Based on the BM framework and value dimensions, a business model can be created by identifying and structurally linking values, objectives, systems, services, and performance measures for all stakeholders. To direct and facilitate the launching and evaluation of mobile government programs based on a value-centric business model, an adaptive balanced scorecard (BSC) with other methods and tools are used.

Introduction

Mobile government (m-government, MG) can be collectively referred to as the adoption of mobile technologies to enhance e-government (EG) functionalities for enabling citizens, businesses, and agencies, with the use of mobile devices, to access government information and services, to exchange documents, knowledge, and experiences, as well as to participate and/or collaborate in government related activities [START_REF] Traummuller | Mobile Government[END_REF][START_REF] Trimi | Emerging Trends in M-government[END_REF][START_REF] Wu | User Aspects of Electronic and Mobile Government: Results From a Review of Current Research[END_REF]. Specific functional features of mobile networks and systems such as mobility, ubiquity, portability, accessibility, and localization provide new forms of connections, communications and interactions among stakeholders in the online government services environment. The aims are to eventually create added value and benefits for all MG participants. Value proposed and created for MG users and participating parties include convenience, efficiency, effectiveness, personalization, cost reduction, profitability, productivity, accountability, transparency, etc. [START_REF] Yu | Value Proposition in Mobile Government[END_REF]. Major identified MG service domains include m-communication (notice and mail), m-public services (transaction and payment), m-administration (internal operation and document management), m-democracy (voting and participation), and m-communities (user generated content sharing and social networking) [START_REF] Criado | Government Innovation Through Social Media[END_REF][START_REF] Wu | User Aspects of Electronic and Mobile Government: Results From a Review of Current Research[END_REF]. Business model (BM), on the other hand, has been defined as an architecture of the information, product and financial flows, including a description of the various business actors and their roles, a description of the potential benefits for the various business actors, and a description of the sources of revenues [START_REF] Timmers | Business Models for Electronic Markets[END_REF]. Commonly mentioned BM types in the e-business domain include business-to-consumer (B2C), business-to-business (B2B), and consumer-to-consumer (C2C), etc. In the e-government literature, identified BM categories include government-to-citizens (G2C), government-to-businesses (G2B), government-to-government (G2G), government internal efficiency and effectiveness (IEE), and overarching infrastructure (Cross-cutting) [START_REF] Lee | Current Practices of Leading e-Government Countries[END_REF]. Similarly, in the mgovernment applications, adopted BM types include m-government-to-citizen (mG2C), m-government-to-business (mG2B), m-government-to-government (mG2G), and mgovernment-to-employee (mG2E) [START_REF] Ntalinai | Mobile Government: A Challenge for Agriculture[END_REF].

It has been noted that value proposition and creation are central tasks for the development and delivery of electronic/mobile business and government services. In the mean time, business models have been pointed out as proper means to illustrate the concepts and methods for value proposition, creation, capture, and assessment in business and government domains [START_REF] Afuah | Internet Business Models and Strategies: Text and Cases[END_REF][START_REF] De Reuver | Mobile Business Models: Organizational and Financial Design Issues That Matter[END_REF][START_REF] Janssen | E-government Business Models for Public Service Networks[END_REF][START_REF] Keen | Value Architectures for Digital Business: Beyond the Business Model[END_REF][START_REF] Luna-Reyes | Towards a Multidimensional Model for Evaluating Electronic Government: Proposing a More Comprehensive and Integrative Perspective[END_REF][START_REF] Ntalinai | Mobile Government: A Challenge for Agriculture[END_REF][START_REF] Teece | Business Models, Business Strategies and Innovation[END_REF][START_REF] Yu | Linking the Balanced Scorecard to Business Models for Value Based Strategic Management in E-Business[END_REF][START_REF] Yu | Value Proposition in Mobile Government[END_REF][START_REF] Zott | The Fit Between Product Market Strategy and Business Model: Implications for Firm Performance[END_REF]. Therefore, e-/mgovernment related business modeling should focus on specifying values and their relationships with other structural components to facilitate value creation for all stakeholders through EG/MG services system development and operation. Developing and conducting suitable mobile business models are thus critical to the success in promoting and delivering mobile public services, creating mobile public values for stakeholders, as well as sustaining continuous operation of MG services systems. In recent years, although emerging issues regarding value creation and business model development for m-government have attracted increasing attentions, an integrated BM framework and process for guiding the construction of a value-centric MG business model are still lacking in the literature. This goal of this paper is to propose a valuecentric business model framework and development process for building business models to support the planning, implementation, operation, and evaluation of mobile government systems and applications. The rest of this paper is organized as follows. In section 2, a brief literature review on value creation and business models is provided. In section 3, an integrated MG business model framework is presented based on value chain and value management concepts. In section 4, the development process of business model suitable for m-government based on design science is illustrated. Conclusion and future research directions are provided in the final section.

Literature Review

In both research and practices, previous works regarding value creation and business modeling for mobile government are still very limited. In this section, a brief literature review on value creation and business model for e-/m-business and e-/m-government is provided as a foundation for developing a value-centric business model framework suitable for mobile government applications.

Value Creation in e-/m-Business and e-/m-Government

In the e-commerce and e-business domain, value is defined as the amount buyers are willing to pay for what a firm provides them. It also refers to a preferred combination of benefits that services afford the end users compared with acquisition costs [START_REF] Amit | Value Creation in E-Business[END_REF]. In the value chain and value management context, value proposition is a statement of what and how value is to be delivered to customers, or is referred to as an equation of the all positive factors that interest the individual and value chain partners. Value creation can be realized as the contribution of utilizing the final products and services to end users, as well as of attaining productivity and profit to the firm and other value chain participating parties. Value capture is defined as the difference between benefits/revenues and costs eventually retained by customers and the firm as well as other chain participants. Being considered as a cycle of value creation, communication, capture, and assessment stages, the value management process generally involves developing and structuring objectives for all stakeholders, establishing a value proposition, creating a value based measurement framework, developing briefs and specifications, designing and reviewing options, and assessing outputs and outcomes [START_REF] Barber | How to Measure the Value in Value Chains[END_REF][START_REF] Fong | A Framework for Benchmarking the Value Management Process[END_REF][START_REF]Understanding m-Government Adoption: M-Government Mobile Technologies for Responsive Governments and Connected Societies[END_REF][START_REF] Ivm | Online document of The Institute of Value Management[END_REF][START_REF] Ntalinai | Mobile Government: A Challenge for Agriculture[END_REF]. As for value model or framework in the e-business domains, [START_REF] Barber | How to Measure the Value in Value Chains[END_REF] provides two frameworks based on the balanced scorecard (BSC) to incorporate both the tangible and intangible value aspects [START_REF] Barber | How to Measure the Value in Value Chains[END_REF]. [START_REF] Keen | Value Architectures for Digital Business: Beyond the Business Model[END_REF] propose a three dimensional value architecture to fit the dynamic nature of innovation and to sustain business growth [START_REF] Keen | Value Architectures for Digital Business: Beyond the Business Model[END_REF]. For m-business specific value creation, Nah, Siau, and Sheng (2005) present a value-focused thinking procedure in which identify values, convert values to objectives, distinguish between means and fundamental objectives, and build means-ends objective network are listed as four consecutive steps [START_REF] Nah | The Value of Mobile Applications: A Utility Company Study[END_REF]. [START_REF] Lariviere | Value Fusion: The Blending of Consumer and Firm Value in Distinct Context of Mobile Technologies and Social Media[END_REF], focusing on value in the mobile and social media environment, emphasize the concept of value fusion that aims at achieving value for the entire network of consumers and firms [START_REF] Lariviere | Value Fusion: The Blending of Consumer and Firm Value in Distinct Context of Mobile Technologies and Social Media[END_REF].

In the e-government domain, typical public and social values concerned in the public sector include equal opportunities, privacy, security, personalization, accountability, transparency, and participation, etc. Among previous works presenting value related framework, Hossain et al (2011) specify the measurement of EG system value in three dimensions including organizational efficiency, operational transparency, and public satisfaction [START_REF] Hossain | Impacts of Organizational Assimilation of e-Government Systems on Business Value Creation: A Structuration Theory Approach[END_REF]. Luna-Reyes, Gil-Garcia, and Romero (2012), aiming at creating value for government, citizens, and other end users, propose a three dimensional performance measurement model comprising EG determinants, EG characteristics, and EG results [START_REF] Luna-Reyes | Towards a Multidimensional Model for Evaluating Electronic Government: Proposing a More Comprehensive and Integrative Perspective[END_REF]. As for very few works addressing mobile government value models, Trimi and Sheng (2008) identify MG value-added advantages in various aspects including improving the delivery of government information and services, providing best solutions to Internet connectivity problems and digital divide issues, offering a more cost-effective choice for national networking, helping to avoid problems of corruption and low productivity, as well as increasing government employees'efficiency and effectiveness [START_REF] Trimi | Emerging Trends in M-government[END_REF]. [START_REF] Yu | Value Proposition in Mobile Government[END_REF], considering value as tangible and intangible benefits perceived by and exchanged between stakeholders in the MG value chain, presents a three dimensional value framework encompassing functional features, user acceptance, and user benefits. The user benefits dimension is further classified into four specific constituent categories, namely, public beneficiaries, government officers and employees, participating parties of the government service chain, as well as society and nation [START_REF] Yu | Value Proposition in Mobile Government[END_REF].

It can be seen that since issues of value creation regarding mobile government applications are largely unexplored and no consensus in views and architectures of MG value exists, more research efforts in the direction of developing an integrated value framework for m-government are strongly demanded.

Business Models in e-/m-Business and e-/m-Government

Business model is widely used to depict the design of transaction content, structure, and governance for creating value through the exploitation of business opportunities [START_REF] Amit | Value Creation in E-Business[END_REF]. To develop and implement an appropriate business model is a key to success and a crucial source of value creation for the firm, its customers, and all value chain participants. Commonly mentioned BM types include e-shop, e-marketplace, virtual communities, etc. when business functions are highlighted, or mobile portals, platform operators, wireless gateway and service providers, mobile application and content providers when mobile environment is involved.

As for component structures of e-business models proposed in the literature, Afuah and Tucci (2001) identifies value, scope, revenue sources, pricing, connected activities, implementation, capabilities, and sustainability as BM related elements [START_REF] Afuah | Internet Business Models and Strategies: Text and Cases[END_REF]. [START_REF] Yu | Linking the Balanced Scorecard to Business Models for Value Based Strategic Management in E-Business[END_REF] provides a business model framework with four value dimensions including market, supply chain, customers, and business organizations [START_REF] Yu | Linking the Balanced Scorecard to Business Models for Value Based Strategic Management in E-Business[END_REF]. [START_REF] Osterwalder | Business Model Generation: A Handbook for Visionaries, Game Changers, and Challengers[END_REF] present an e-business model ontology that includes four component groups i.e. infrastructure, offering, customers, and finances [START_REF] Osterwalder | Business Model Generation: A Handbook for Visionaries, Game Changers, and Challengers[END_REF]. As for the mbusiness domain, [START_REF] Schubert | Mobile Communities: How Viable are Their Business Models? An Exemplary Investigation of the Leisure Industry[END_REF] adopt four main components including value proposition, product or service, value architecture, and revenue model to describe business models for mobile communities [START_REF] Weinhardt | Business Models in the Service World[END_REF]. By adopting a design research perspective, de Reuver, Bouwman, and Haaker (2009) point out four domains (STOF), namely service, technology, organization and finance, for assigning common model components to build mobile business models [START_REF] De Reuver | Mobile Business Models: Organizational and Financial Design Issues That Matter[END_REF]. To design mobile value co-creation services, Schmidt-Rauch and Schwabe (2014) adopt a user-centered design process (UCD) based on the design science methodology that emphasizes on a build-andevaluate loop with five major steps [START_REF] Schmidt-Rauch | Designing for Mobile Value Co-creation -The Case of Travel Counselling[END_REF].

As for BM component structures for e-government, only very limited efforts have been undertaken previously. Among these few works, [START_REF] Janssen | E-government Business Models for Public Service Networks[END_REF] propose an EG-applicable BM framework that comprises six elements, namely, organizations in the public service network, service offerings, network coordination, business processes, shared resources, and network capabilities [START_REF] Janssen | E-government Business Models for Public Service Networks[END_REF]. Towards developing a value-based e-government services framework, [START_REF] Yu | Building a Value-Centric e-Government Service Framework Based on a Business Model Perspective[END_REF] proposes a BSC-based business model to highlight four value dimensions including public beneficiaries, government organizations and processes, government service chain, as well as society and national/global environments. Model elements specified in each of the four BM perspectives include values, stakeholders, services, systems, and performances [START_REF] Yu | Building a Value-Centric e-Government Service Framework Based on a Business Model Perspective[END_REF]. Peinel, Jarke, and Rose (2010), in their work of presenting a business modeling approach for e-government services, identify value chain, partners, object exchange, role, services, policy, and advantage/disadvantage as BM elements [START_REF] Peinel | Business Models for eGovernment Services[END_REF]. [START_REF] Panagiotopoulos | A Business Model Perspective for ICTs in Public Engagement[END_REF], focusing on evaluating ICTs in public engagement, adopt a business model perspective that consists of four dimensions including value proposition (effects), value network (actors), value architecture (resources), and value finance (costs) [START_REF] Panagiotopoulos | A Business Model Perspective for ICTs in Public Engagement[END_REF]. For m-government specific business models, it is still a relatively unexplored area. Some researchers treat m-government as a subset of e-government and simply present mobile characteristics within the aspects of conventional G2C, G2B, and IEE business model types [START_REF] Ntalinai | Mobile Government: A Challenge for Agriculture[END_REF][START_REF] Trimi | Emerging Trends in M-government[END_REF]. By illustrating an example of mgovernment services project, Peinel, Jarke, and Rose (2010) use the similar approach as in e-government cases to identify options of value chain with public and private partners, as well as their relationships with individual advantages and disadvantages [START_REF] Peinel | Business Models for eGovernment Services[END_REF]. For addressing the m-government adoption with the focus on public-private partnerships (PPP), ITU (2011) describes a basic MG business model that contains a set of constructs including user groups of mobile services, specific benefit and value to user groups, revenue or benefit to the providers/partners, processes and activities, resources and competencies, costs, and suppliers of required resources [START_REF]Understanding m-Government Adoption: M-Government Mobile Technologies for Responsive Governments and Connected Societies[END_REF]. To address the design issues of service platform and business model for mobile participation (MP), de Reuver, Stein, and Hampe (2013) adopt the STOF business model framework to the public domain aiming for creating MP services value [START_REF] De Reuver | From eParticipation to Mobile Participation: Designing a Service Platform and Business Model for Mobile Participation[END_REF].

The design and implementation of m-government specific business models, although considered as crucial to the success of m-government, are still less touched issues in the literature. Previous works discussing MG related business model framework, development process, and performance evaluation are extremely scarce in both research and practices. Therefore, more research endeavors are needed to explore mobile business model issues in the m-government domain.

Value-centric Business Model Framework for M-government

By integrating different views from previous works and taking a value chain perspective, value in mobile government refers to functional features and acceptance characteristics of MG systems and services, as well as tangible and intangible benefits perceived and captured by MG stakeholders. To facilitate value proposition, creation, and management, MG users and stakeholders are further classified into four constituent groups including public beneficiaries, government agencies, government service chain participants, as well as society and nation. A value-centric business model framework for mobile government (MGvBM) can then be formed to structurally organize stakeholders, values, systems, services, performances, and associated resources, costs, functions, processes, and activities for all stakeholder groups and value dimensions. Figure 1 For instance, value elements of systems and services value and public beneficiaries value in a m-tax services system include mobility, accessibility, localization, personalization, convenience, security, responsiveness, and ease of use, as well as being able to attain cost and time reduction, access location-based and personalized recommendation services, access cloud storage services, select m-payment methods, and report on user satisfaction, etc. Strategic objectives are specified goals transformed from the value elements associated with systems, services, and constituent groups. MG performances: MG performances are actual outputs and outcomes generated and measured from implementing, operating, and controlling MG systems and services. Collected data of specified key performance indicators (KPIs) can be analyzed to reflect levels of objective achievement and satisfaction in terms of differences between proposed and created MG values for services systems and all stakeholders. For instance, some KPIs for citizen value of the m-Tax case afore-mentioned can be level of personalization, level of time and cost saving, level of satisfaction in ease of use and usefulness, etc. And subsequently the strategic objectives for MG performances can be set to achieve 90% and 85% for level of user satisfaction regarding ease of use and usefulness respectively. MG resources: MG resources are financial and other necessary supports for MG development and operation. Major resources include budgets, equipments, human resources, technology infrastructure, management capabilities, and domain knowledge. MG costs: MG costs are necessary expenditures for initiating and implementing MG programs, for managing and sustaining MG operations, and for accessing and utilizing MG services. Essential costs include expenses and charges on MG systems and services development, promotion, operation, maintenance, improvement, usage, feedback processing, as well as security and privacy control. MG strategies and action plans: MG strategies and action plans are the specifications of strategic objectives, implementation processes, management functions and activities for building and operating MG business models, as well as for assuring value creation for all stakeholders in the MG environment.

Based on this MG business model framework, the planning and design of a suitable business model, the implementation and operation of the created business model in a proper way, as well as the evaluation and control of the performance outcomes for sustaining continuous improvement, can be carried out efficiently and effectively. The MGvBM framework incorporates concepts and methods in the fields of value chain, value management, strategic management and performance measurement. It takes into account all components of major previously presented EG and MG business models in the literature such as in [START_REF] De Reuver | Mobile Business Models: Organizational and Financial Design Issues That Matter[END_REF][START_REF]Understanding m-Government Adoption: M-Government Mobile Technologies for Responsive Governments and Connected Societies[END_REF][START_REF] Janssen | E-government Business Models for Public Service Networks[END_REF][START_REF] Panagiotopoulos | A Business Model Perspective for ICTs in Public Engagement[END_REF][START_REF] Peinel | Business Models for eGovernment Services[END_REF][START_REF] Yu | Value Proposition in Mobile Government[END_REF], and enables a broader scope as well as flexibility for developing and using business models in the public domain. The MGvBM framework is applicable to different levels of MG programs/projects and applications. Foe validation purpose, a 5-year nation wide m-/u-government program, a few central government led m-taxation and m-tourism services systems projects, and a couple of local government launched m-marketing and smart city projects on mobile apps are reviewed for revealing the feasibility of adopting the MGvBM framework and for proposing BM restructuring and improvement suggestions for subsequent MG development.

The Development and Management of MG Business Models

To enhance the development and management of MG business models, we adopt the build-evaluate approach from design science technology and extend it to cover the whole process. The complete development and management process for MG business models contains planning, design, implementation, operation, evaluation, and control stages. Steps to be taken in the planning stage for building MG business models include (1) identifying MG stakeholders with roles and relationships, (2) identifying MG values for proposing to all stakeholder groups, (3) identifying MG systems and services for different user groups to create, deliver, and capture MG values, (4) identifying resources needed and available for MG project management as well as service system development and operations, (5) identifying costs required for conducting necessary development works and management processes to sustain continuous operation and improvement, (6) identifying performance indicators for evaluating MG effectiveness and success, and (7) transforming value into strategic objectives and formulating associated strategies. In the design stage, work steps include [START_REF] Afuah | Internet Business Models and Strategies: Text and Cases[END_REF] specifying relationships between objectives, critical success factors (CSF), and actions, (2) selecting, classifying and weighting key performance indicators (KPIs) based on the ends-CSF-means relationships, and (3) setting up action plans with management functions and processes for achieving specified performances and goals. In the implementation and operation stages, action plans are implemented and operated with output data collected for all performance indicators. In the evaluation and control stages, performance outcomes associated with all stakeholder groups and the entire MG project/application are measured, the gap analysis is conducted, and necessary improvement actions are specified and taken.

To facilitate the MGvBM development processes through strategic planning, to performance measurement, a number of methods and tools are used in different stages including the balanced scorecard (BSC), strategy map (SM), ends-means analysis (EMA), critical success factors (CSF), analytic hierarchy process (AHP), and strategy gap analysis (SGA), etc. Specifically for the adoption and adaptation of the BSC method, four specified BSC perspectives representing MG stakeholder groups and associated value dimensions are the public beneficiaries perspective with citizen value and business value, the government internal organization and process perspective with employee value and organization value, the government service chain perspective with entire service chain value and values for all participating parties, as well as the society and national environments perspective with society value and nation value. Figure 2 illustrates the MGvBM-BSC perspectives with some major identified BM components and elements for m-government.

Figure 2. The four MGvBM-BSC perspectives

Within each of the MGvBM-BSC perspectives, values, stakeholder groups, systems, services, and performance indicators related to MG projects and applications can be structurally linked and presented. For instance, in the public beneficiaries perspective, the MG user groups include citizens and businesses. The value types considered are citizen value and business value. The associated MG systems include mG2C and mG2B. The value-added MG services provided in mG2C and/or mG2B systems include m-information, m-taxation, m-tourism, m-registration, m-transaction, and mpayment services, etc. The MG value indicators for performance measurement include information and service accessibility, time and location convenience, cost efficiency, level of satisfaction, level of personalization, and level of participation, etc. For all the BM components in the BSC perspectives, more detailed specifications can be provided. For example, specific mG2C services identified for MG tourism applications may include (1) mobile information services for accessing government information about news, weather, traffic, and tourism events, (2) mobile notification and alert services for sending text message alerts about emergency conditions, and reminders about other environmental regulations, (3) mobile transaction and payment services for purchasing tickets to enter national parks or other sightseeing destinations, (4) location-based services for accessing GPS-enabled tour guides and road maps, nearby available perking lots, as well as restaurants and stores with price promotion in an acceptable distance range, (5) mobile community services for connecting friends to share information and experiences, (6) mobile reporting services for sending multimedia information to the authorities about real-time traffic conditions or accidents, and/or (6) other mobile tourism related services with personalized, collaborative, location-based, and context-aware features. Value proposition to all stakeholders is undertaken in the planning stage. In the implementation and operation stage, values can be created when systems are developed with sufficient functions and high acceptance, and services are delivered that users'needs with high satisfaction. Whether values have been created, and/or whether the actual created values meet the pre-specified performance goals need to be assessed and analyzed in the evaluation stage. In the control stage, necessary actions for improvement are taken to ensure value capture and to sustain the continuous MG development and operations.

Conclusions

In this paper, we propose a value-centric business model framework for mobile government. Model components of the BM framework include MG stakeholders, MG values, MG systems, MG services MG resources, MG costs, MG performances, and MG strategies and action plans. MG stakeholders are classified into four constituent groups including public beneficiaries, government internal organization and process, government service chain, as well as society and national environments. Based on the proposed MGvBM framework, suitable MG business models can be built to support the planning, design, implementation, operation, and evaluation of various scales of MG projects and applications. An adaptive balanced scorecard with four stakeholder groups and value perspectives is created to facilitate the strategic planning through performance measurement processes of the MG development and management cycle. For any specific MG projects and applications, corresponding stakeholders, values, systems, services, strategic objectives, critical success factors, action plans, and key performance indicators can be structurally linked and presented with respect to each of the MGvBM-BSC perspectives. The contributions of this paper include (1) providing a value-centric business model framework that is taking a broader view, more flexible, and practically operable and measurable for guiding the development and utilization of MG business models, (2) incorporating value chain, value management, and design science concepts to take into account major issues such as creating values for all value chain stakeholders, managing the value proposition, creation, capture, assessment, and control cycle, as well as enabling design-build-operate-evaluate processes, and (3) creating a potential for adopting and adapting the proposed vBM framework and development process to fit the characteristics and needs of e-government and eparticipation. Future works will include validating the proposed business model framework and development process by conducting empirical testing in a variety of MG application domains.

Figure 1. A value-centric business model framework for mobile government MG systems: MG

  depicts the value-centric business model MG values refer to tangible and intangible benefits that are proposed to, created for, and captured by all MG stakeholders. Also identified as MG values include function, process and acceptance features of the MG systems and services. Specific MG values for stakeholder groups include citizen value, business value, and NGO value, employee value and organization value, service chain value, as well as society value and nation value. Value elements are specific functions and benefits corresponding to various value types in different services systems and stakeholder groups.

	framework with major model components and their relationships. Key MGvBM exchanging personal experience and comments regarding government
	components with related elements and factors are described below. transactions, engaging with government agencies and/or service chain partners,
	MG stakeholders: MG stakeholders are actors involve in the m-government services and participating in government activities, etc. MG services are often classified
	environment. For the four classified constituent groups mentioned above, as mG2C, mG2B, mG2E, and mG2G services, as m-information, m-transaction,
	potential MG stakeholders include (1) citizens, businesses, communities, and m-payment, m-community, m-administration, and m-democracy services, or as
	NGOs for the public beneficiaries group, (2) local authorities, internal m-tourism, m-taxation, m-healthcare, m-learning, m-agriculture, and m-police
	organizations, and employees for the government agencies group, (3) wireless services, etc.
	and mobile network operators, mobile content and application service providers, MG values:
	mobile device and software/hardware vendors, mobile payment and financial
	service providers, mobile security and trust service providers, horizontal and/or
	vertical integration of participated government agencies for the group of
	government service chain participants, as well as (4) other actors in the society
	and national environments for the society and nation group.
		Government Service Chain
	Resources	Costs	Value	Performances
	Gov. Organizations			Public Beneficiaries
	Resources	Systems	Services	Resources
	Costs	Functions Value	Processes Value	Costs
	Value	Perform.	Perform.	Value
	Performances				Performances
		Society and Nation
	Resources	Costs	Value	Performances
	systems involve mobile related networks, infrastructure, platforms,
	channels, devices and hardware/software that provide integrated functions for
	service providers to offer and maintain, as well as for users to access and utilize
	MG services in a secure and trust environment. MG system types include mG2C,
	mG2B, mG2E, mIEE, mG2G, etc, or m-gateway, m-cloud, m-tax, m-tourism, etc.
	System functions may include profile management, search and navigation,
	transaction and payment, personalization and collaboration, tracking and
	monitoring, community and social networking, voting and participation, etc.
	Functional features include mobility, ubiquity, portability, accessibility,
	personalization, localization, multimedia data handling, and GPS-capability, etc.
	MG services: MG services are functional oriented and categorized value-added
	objects that are developed by government and associated service chain
	participating parties to enable users in accessing government information,


Martin Schanz

A BOUNDARY ELEMENT FORMULATION IN TIME DOMAIN FOR VISCOELASTIC SOLIDS

Keywords: viscoelasticity, boundary integral equations, time domain, transform methods

Viscoelastic solids may be eectively treated by the boundary element method (BEM) in the Laplace domain. However, calculation of transient response via the Laplace domain requires the inverse transform. Since all numerical inversion formulas depend heavily on a proper choice of their parameters, a direct evaluation in the time domain seems to be preferable. On the other hand, direct calculation of viscoelastic solids in the time domain requires the knowledge of viscoelastic fundamental solutions.

Such solutions are simply obtained in the Laplace domain with the elastic viscoelastic correspondence principle, but not in the time domain. Due to this, a quadrature rule for convolution integrals, the `convolution quadrature method' proposed by Lubich, is applied. This numerical quadrature formula determines their integration weights from the Laplace transformed fundamental solution and a linear multistep method. Finally, a boundary element formulation in the time domain using all the advantages of the Laplace domain formulation is obtained. Even materials with complex Poisson ratio, leading to timedependent integral free terms in the boundary integral equation, can be treated by this formulation.

Two numerical examples, a 3D rod and an elastic concrete slab resting on a viscoelastic halfspace, are presented in order to assess the accuracy and the parameter choice of the proposed method.

INTRODUCTION

The boundary element method (BEM) has become a widely used numerical tool in statics and dynamics. A review about the eorts in dynamics is published by Beskos. [START_REF] Beskos | Boundary element methods in dynamic analysis[END_REF][START_REF] Beskos | Boundary element methods in dynamic analysis: Part II (1986[END_REF] The main advantages of the method are reduction of the problem dimension by one and the implicit ful®lment of the radiation condition for unbounded domains. Due to the last advantage the BEM seems to be preferable for the calculation of in®nite or semi-in®nite domains, e.g. soil.

Modelling soil as an elastic solid can only be a crude approximation of the real material. A better description of the material properties can be achieved using viscoelastic constitutive equations. In these equations, normally, the stress strain relation is a dierential or integral equation of hereditary type. [START_REF] Christensen | Theory of Viscoelasticity[END_REF] Improved curve ®tting of measured material properties by constitutive equations with fewer parameters is achieved with the concept of fractional dierintegration. [START_REF] Bagley | On the fractional calculus model of viscoelastic behaviour[END_REF][START_REF] Drozdov | Fractional dierential models in ®nite viscoelasticity[END_REF] A review about fractional calculus applied to dynamic problems has recently been given by Rossikhin and Shitikova. [START_REF] Rossikhin | Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids[END_REF] Viscoelastic boundary element formulations are mostly published for the quasi-static case (see, for example, References 7 9), or in dynamics using a frequency or Laplace domain representation of the governing integral equation. These formulations are developed by applying the elastic viscoelastic correspondence principle to the elastodynamic boundary element formulation, e.g. Reference 10 for a frequency domain or Reference 11 for a Laplace domain formulation. In these formulations, the complex moduli concept is used which can be extended to fractional operator viscoelasticity allowing not only integer powers of the frequency, e.g. Reference 12.

Calculation of transient response, however, requires the inverse transformation. Since all numerical inversion formulas depend on a proper choice of their parameters, [START_REF] Narayanan | Numerical operational methods for time-dependent linear problems[END_REF] a direct evaluation in the time domain seems to be preferable. However, formulations directly in the time domain require the knowledge of viscoelastic fundamental solutions which are not yet known for the general visco elastodynamic case. Only for a simple Maxwell model, a solution has been obtained analytically by Gaul and Schanz [START_REF] Gaul | BEM formulation in time domain for viscoelastic media based on analytical time integration[END_REF] and has been implemented in a boundary element formulation. [START_REF] Schanz | Implementation of viscoelastic behaviour in a time domain boundary element formulation[END_REF] Based on the frequency domain fundamental solution with subsequent inverse transformation, a 1D solution has been proposed by Wolf and Dabre. [START_REF] Wolf | Time-domain boundary element method in viscoelasticity with application to a spherical cavity[END_REF] In the 3D case, Gaul and Schanz [START_REF] Gaul | A viscoelastic boundary element formulation in time domain[END_REF] developed a formulation for a generalized (with fractional derivatives) 3-parameter model using the Laplace transformed fundamental solution which is inverted within each time step. Recently, Schanz and Antes 18 published a viscoelastic formulation based on the so-called `Convolution Quadrature Method' proposed by Lubich. [START_REF] Lubich | Convolution quadrature and discretized operational calculus. I[END_REF][START_REF] Lubich | Convolution quadrature and discretized operational calculus. II[END_REF] In this formulation, the convolution integral is numerically approximated by a quadrature formula whose weights are determined by the Laplace transform of the fundamental solution and a linear multistep method. A comparison of the above-mentioned two time domain formulations and the Laplace transformed formulation with a subsequent inverse transformation was presented by Gaul and Schanz. [START_REF] Gaul | A comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains[END_REF] However, all published formulations assumed the same viscoelastic behaviour of the deviatoric and the hydrostatic part of the stress strain relations, leading to a constant, real numbered Poisson ratio which does not represent all viscoelastic materials. Now, here, the formulation based on the convolution quadrature will be extended to the case of a complex Poisson ratio. For this, ®rst, the constitutive equations are recalled and also, in the second step, the governing integral equation for linear visco elastodynamics. With a spatial discretization and applying the `Convolution Quadrature Method' for temporal discretization a time-stepping procedure is achieved. Some tests of the method with respect to the spatial and temporal discretization will show the eciency of the proposed method. Finally, as a more realistic example, an elastic foundation slab resting on a viscoelastic half space is studied.

CONSTITUTIVE EQUATION

Decomposing the stress and strain tensors s ij , e ij into the hydrostatic parts d ij s kk /3, d ij e kk /3 and the deviatoric parts s ij , e ij and assuming for both parts a linear isothermal viscoelastic material, e.g. a generalized three parameter model, two independent sets of constitutive equations exist in the Laplace domain: shows that the constitutive parameters p, q and the fractional power a can be dierent for the hydrostatic part H and the deviatoric part D of the stress strain relation.

1 p D s a D ŝ ij E 1 êij 1 q D s a D 1 p H s a H ŝkk E 1 À 2 êkk 1 q H s
A plausible model of the viscoelastic phenomenon should predict non-negative internal work, a non-negative rate of energy dissipation [START_REF] Bagley | On the fractional calculus model of viscoelastic behaviour[END_REF] and ®nite wave velocities. Therefore, the parameters are constrained by 22 0 4 p D 5 q D 0 5 a D 5 2 04 p H 5 q H 0 5 a H 5 2 2

Comparing the viscoelastic constitutive equations ( 1) with Hook's law, the elastic viscoelastic correspondence principle is obtained.

E D 3E1 q H s a H 1 q D s a D 21 1 q H s a H 1 p D s a D 1 À 21 q D s a D 1 p H s a H D 1 1 q H s a H 1 p D s a D À 1 À 21 q D s a D 1 p H s a H 21 1 q H s a H 1 p D s a D 1 À 21 q D s a D 1 p H s a H 3
This means that every elastodynamic solution of a distinct problem can be converted to the solution of the related viscoelastic problem by inserting the correspondence (3). [START_REF] Christensen | Theory of Viscoelasticity[END_REF] In equation ( 3), the dependence of Poisson's ratio from the Laplace parameter s is clearly observed, which corresponds to a time dependent Poisson ratio. If, however, the parameters satisfy the relation

1 q H s a H 1 p D s a D 1 q D s a D 1 p H s a H 4
which means that the deviatoric and the hydrostatic part of the stress strain relation behave similarly, then Poisson's ratio is also for viscoelasticity no function of s, i.e. time invariant, and equal to the elastic case. [START_REF] Christensen | Theory of Viscoelasticity[END_REF]

VISCOELASTIC BOUNDARY ELEMENT FORMULATION

Assuming homogeneity and a linear strain displacement relation the dynamic behaviour of a viscoelastic structure as well as the wave propagation in a domain O with boundary G is governed by the boundary integral equation [START_REF] De Hoop | An elastodynamic reciprocity theorem for linear, viscoelastic media[END_REF] (* denotes a convolution in time)

c ij y; t*u j y; t Z G U ij x; y; t*p j x; t dG À Z G C P ij x; y; t*u j x; t dG for y P O G 5
where u j u j (x,t) and p j p j (x,t) is the displacement and the traction vector at point x and time t, respectively. The fundamental solutions of the displacements and tractions are denoted by U ij (x,y,t) and P ij (x,y,t), respectively. They are available in the Laplace domain from the elastodynamic fundamental solutions (see Reference 24) via the elastic viscoelastic correspondence principle. [START_REF] Schanz | A new visco-and elastodynamic time domain boundary element formulation[END_REF] As in the elastostatic case, the ®rst integral in equation ( 5) is weakly singular, and the second integral has to be de®ned in the sense of a Cauchy principal value, i.e. the integral is strongly singular. Further on, due to the time dependence of Poisson's ratio (t), now, in general, c ij (t) is also time dependent. However, the integral free terms c ij (t) are independent of time and equal to the elastostatic case, if Poisson's ratio is independent of time. This is true if equation ( 4) is valid, i.e. the hydrostatic and the deviatoric part of the stress strain relation behave similarly.

The numerical implementation of equation ( 5) requires approximations of boundary ®eld variables in both space and time. Therefore, the boundary surface G is discretized by E isoparametric elements G e , where F polynomial shape functions N f e (x) are de®ned. Hence, with the time dependent nodal values u ef j (t) and p ef j (t) the following representation is adapted:

u j x; t X E e1 X F f1 N f e xu ef j t; p j x; t X E e1 X F f1 N f e xp ef j t 6
Inserting these `ansatz' functions in equation ( 5) results in The integration weights o n (Dt) are the coecients of the power series for the function f à (g(z)/Dt) at the point g(z)/Dt. Herein, g(z) is the quotient of the characteristic polynomials of a linear A (a)stable multistep method, e.g. gz 3 2 À 2z 1 2 z 2 for the backward dierential formula of second order (BDF 2). The coecients of this power series are calculated by the integral

c ij y; t*u j y; t X E e1 X F f1 Z G U ij x
o n Dt 1 2pi Z jzj f gz Dt z ÀnÀ1 dz % 1 L X LÀ1 l0 f gx l Dt x Àn l 9
with x l e il 2p L , being the radius of a circle in the domain of analyticity of f à (z). The integral in equation ( 9) is approximated by a trapezoidal rule with L equal steps 2p/L, after a transformation to polar co-ordinates. Further details are described in Reference 18 as well as in the original work of Lubich. [START_REF] Lubich | Convolution quadrature and discretized operational calculus. I[END_REF] The characteristic advantage of the quadrature rule (8) is that only the Laplace transformed function f à is used.

Applying the quadrature formula (8) to the integral equation ( 7) results in the following boundary element time-stepping formulation for n 0, 1, . . . , N. Obviously, although applying only the Laplace transformed fundamental solutions U Ã ij and P Ã ij , a stepping procedure directly in the time domain is achieved, i.e. a viscoelastic boundary element formulation in the time domain without the knowledge of the time dependent fundamental solutions is obtained. Further on, because the integral over each boundary element involves only the Laplace transformed fundamental solution (see equations ( 12) and ( 13)), for the regular integrals a standard Gaussian quadrature rule and for the singular integrals the well known techniques from elastodynamics can be used. This means that the weakly singular integrals in (12) are regularized by co-ordinate transformation and the strongly singular integrals in ( 13) by the method suggested by Guiggiani and Gigante. [START_REF] Guiggiani | A general algorithm for multidimensional cauchy principal value integrals in the boundary element method[END_REF] In order to arrive in equation ( 10) at systems of algebraic equations, collocation is used at every node of the shape functions N f e (x), and, ®nally, a direct equation solver is applied.

Before the method is applied to a numerical example, the time dependence of the integral free terms c ij (t) is shown in Figure 1. For example, the coecient c 13 of a rectangular corner ĉ13 s 1 8p1 À s ( (s) denotes the lengthy expression in equation ( 3)) is convoluted with a unit step function u 3 H(t) . 1m. The related elastic Poisson ratio in this test 0 . 3, leading to c 13 0 . 0568, and a BDF 2 as the underlying multistep method is used. Three cases are considered in Figure 1: (i) hydrostatic damping the deviatoric part of the stress strain relation has an elastic behaviour;

(ii) equal damping mechanisms for the deviatoric and hydrostatic part of the stress strain relation; and (iii) deviatoric damping the hydrostatic part of the stress strain relation has elastic behaviour. The initial values of the three cases are quite dierent. With increasing time a relaxation or a creep behaviour of the results is observed. The case with the equal damping values gives, as expected, a constant value which is equal to the elastic case.

NUMERICAL EXAMPLES

The propagation of waves in a 3D viscoelastic continuum has been calculated by the presented viscoelastic boundary element formulation. The numerical tests are divided into two main parts. First, the displacements and tractions of a 3D rod are compared to a 1D solution with respect to the in¯uence of the time step size, the underlying multistep method and the complex Poisson ratio. In the second part, an elastic concrete foundation slab on a viscoelastic half-space is considered.

For all the tests, the parameters of the convolution quadrature are chosen as suggested by Lubich: [START_REF] Lubich | Convolution quadrature and discretized operational calculus. II[END_REF] L N and N p e with e 10 À10 . For a better comparison with results of other example, the dimensionless parameter b c 1 Dt/r e is used instead of the time step size. This parameter is calculated using the viscoelastic compression wave velocity 21 c 1 and the mean value of a characteristic element length r e .

Three-dimensional rod

The problem geometry and material data of the 3D rod are shown in Figure 2. The rod is taken to be ®xed on one end, and is excited by a pressure jump according to a unit step function p y x; t 1 N m 2 Ht on the other free end. The remaining surfaces are traction free. Linear spatial shape functions on 56 triangles are used.

In most boundary element formulations in the time domain, the value b is restricted to a very small range where stable and satisfactory results are achieved. In Figure 3 the displacements for dierent b and BDF 2 as the underlying multistep method are depicted and compared to the 1D solution. The 1D solution is obtained with the elastic viscoelastic correspondence principle applied to the known solution of an elastic rod. [START_REF] Gaul | A comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains[END_REF] Mesh 1 is the mesh shown in Figure 2 and mesh 2 denotes a ®ner mesh (every triangle in Figure 2 is bisected). Both meshes show a critical time step size, corresponding to b 4 0 . 1, below which the results are unstable. For mesh 1 only the tendency, whereas for mesh 2 the instabilities, are clearly observed. Furthermore, the results of mesh 1 strongly depend on b, i.e. the solution deviates more from the 1D solution if b increases. Compared to mesh 2, there the results for all b, except b 0 . 1, are close to the 1D solution. The stronger dependency of the results from b, respectively from the time step size Dt, of mesh 1 has two reasons. First, the spatial integration on mesh 2 has twice the quality as on mesh 1 due to the smaller elements. Second, the same b for mesh 1 and mesh 2 is achieved by half the time step size for mesh 2 compared to mesh 1. Because a ®ner time discretization will always lead to a better approximation of the time history, the time dependency of the displacements must be better approximated by mesh 2. This gives reason to the conclusion, that for a ®ne enough mesh the results are not dependent on the time step size if 0 . 1 5 b 5 1 is regarded.

Not only the time step size but also the underlying multistep method in¯uences the results. Therefore, in Figure 4 the longitudinal displacements and tractions vs. time for dierent multistep methods using mesh 1 are presented. The linear multistep methods backward dierential formulation of ®rst, second and third order (BDF 1, BDF 2 and BDF 3) are compared with the trapezoidal rule. In the test, the relevant optimal time step size for each of the dierent methods was chosen. The traction solution clearly indicates that the BDF 3 and the trapezoidal rule lead to not acceptable results. However, with BDF 1 and BDF 2 good solutions are achieved. The BDF 1 and 2 are A-stable methods, whilst the BDF 3 is an A (a)-stable method. The trapezoidal rule is certainly A-stable but not stable at in®nity. These results might indicate that the usable multistep methods for visco elastodynamics should be restricted to A-stable methods which are also stable at in®nity. However, note that for a proper solution with the BDF 1, a very small time step size has to be taken to avoid numerical damping. Finally, it should be mentioned that the BDF 2 seems to be the best choice. Therefore, in the following, all tests are performed with the BDF 2 as the underlying multistep method.

In the ®nal experiment, dierent viscoelastic behaviour of the stress strain relation is studied. First, the extreme, but not realistic, case of pure hydrostatic damping i.e. the deviatoric part of the stress strain relation is assumed to be elastic is compared to the more realistic cases of equal damping mechanisms and the pure deviatoric case, i.e. the hydrostatic part of the stress strain relation is assumed to be elastic. In Figure 5, the displacement at point P is plotted vs. time for these three cases. This experiment shows that the deviatoric part of the stress strain relation has more in¯uence on the damping behaviour than the hydrostatic part. This is clearly indicated by the nearly identical results for the deviatoric case as for the case where both parts are viscous. On the contrary, when only the hydrostatic part is damped, only a very small in¯uence is observed.

Elastic concrete slab foundation on a viscoelastic clay half-space

The propagation of waves in an elastic concrete foundation slab (1 m  1 m  0 . 5 m) bonded on a viscoelastic clay half-space will be analysed. Both domains are coupled by a substructure technique based on displacement-and traction-continuity at the interface. With this assumption, any uplifting or other non-linear contact eects are neglected. The problem geometry and the associated boundary discretization are shown in Figure 6. The viscoelastic half-space is modelled with the material data of clay, where only for the deviatoric part of the stress strain relation damping is assumed. The spatial discretization is done with linear shape functions on triangles, and a BDF 2 is used as the underlying multistep method. Due to the very dierent wave velocities of the two domains and varying element sizes, the value b cannot be chosen optimal for both domains. The experience shows that the unbounded halfspace is not so sensitive to an optimal choice of b as the bounded domain of the slab. Therefore, the time step is oriented at the material and discretization data of the slab. It is chosen with Dt 0 . 0025, and kept constant during all tests. In Figure 7, the vertical displacements u z at point A vs. time are depicted for dierent viscous damping values p. The great in¯uence of the viscosity is observed. Lower values of p, i.e. increasing viscosity, leads to a stiening of the material, indicated by the reduction of the displacement amplitudes and higher wave velocities. This example shows the proposed method is not only applicable to academic problems as to the rod; it can also be applied to more realistic examples. The insensitivity to the optimal choice of the time step size makes this method feasible for realistic applications.

CONCLUSIONS

In the paper, a novel visco elastodynamic boundary element formulation in time domain is presented. The constitutive equations are formulated in the dierential operator form taking also fractional derivatives into account, and the viscoelastic boundary integral equation is recalled. Next, the spatial discretization with standard techniques is introduced. Due to the lack of time dependent fundamental solutions, the `convolution quadrature method', [START_REF] Lubich | Convolution quadrature and discretized operational calculus. I[END_REF] a quadrature rule for convolution integrals, is used. This numerical quadrature formula determines their integration weights from the Laplace transformed fundamental solution and a linear multistep method. These fundamental solutions can easily be obtained from the elastodynamic ones by applying the elastic viscoelastic correspondence principle. This leads ®nally to a boundary element formulation in the time domain using all the advantages of the Laplace domain formulation. Even materials with complex Poisson ratio, leading to time-dependent integral free terms in the boundary integral equation, can be treated by this formulation.

In two examples, a 3D rod and an elastic concrete slab bonded to a viscoelastic half-space, numerical studies show the accuracy of the proposed formulation.

o

  nÀk ĉij ; y; Dtu j y; kDt X E e1 X F f1 X n k0 fo nÀk Ûij ; y; Dtp ef j kDt À o nÀk Pij ; y; Dtu ef j kDtg 10 with the weights corresponding to equation (9), o nÀk ĉij ; y;

Figure 1 .

 1 Figure 1. Convolution c 13 *u 3 vs. time for a viscoelastic material

Figure 2 .Figure 3 .

 23 Figure 2. Step function excitation of a free-®xed rod

Figure 4 .

 4 Figure 4. Longitudinal displacements and tractions of the free and ®xed end of the rod, respectively, vs. time: dierent multistep methods

Figure 5 .Figure 6 .

 56 Figure 5. Longitudinal displacement of the free end vs. time: dierent behaviour of the hydrostatic and the deviatoric part of the stress±strain relation

Figure 7 .

 7 Figure 7. Displacement u z at point A vs. time for dierent values of p