F Bompaire

Boulogne S8

Auxemery Y6

Bompaire Flavie
email: flavie.bompaire@intradef.gouv.fr

Keywords: PNES, depression, epilepsy, anxiety, epidemiology, functional disorder

Psychogenic non-epileptic seizures (PNES) are clinically defined as events resembling epileptic seizures but presumed to be not conscious and an involuntary expression of emotional distress similar to panic attacks. Their neurobiological physiopathology is different. However, PNES-like states are recognized in some cultures as a cultural phenomenon.

PNES rank among the top three neuropsychiatric problems and are targeted by an International League Against Epilepsy Task Force that published in 2017 an actualization concerning PNES epidemiology renewing the interest concerning PNES. Studies concerning PNES are complicated: these patients are difficult to identify, and a have tendency to disengage from medical services after diagnosis.

The incidence and prevalence estimates in the literature are based on diagnoses from tertiary care epilepsy monitoring units, where approximately 20 to 40% of adult patients and 10 to 23% of children presenting with "drug-resistant epilepsy" are diagnosed with PNES, making the incidence of PNES to be 1.4-4.9 cases per 100,000 people per year and the prevalence range of 2-33/100,000 However, epilepsy can be associated with PNES with estimated comorbidity range from 5 to 50%. 75% of patients with PNES are young adult women. PNES are uncommon under 6 and after 50 years of age. The female predominance is classically not found in children, late-onset or intellectual disability (ID) subgroups (about 10% PNES patients). Psychiatric comorbidities such as anxiety, post traumatic stress disorders and history of trauma are frequent in PNES patients.

One recent change concerning the epidemiology of PNES is the awareness that this condition is present worldwide, and not only in western developed countries.

Highlights 1) PNES epidemiology study is of growing interest after ILAE task force publication.

2) PNES are found worldwide and sometimes recognized as a cultural phenomenon.

3) New studies are warranted to improve PNES epidemiology knowledge worldwide.

INTRODUCTION

Psychogenic Non-Epileptic Seizures (PNES) are clinically defined as events resembling epileptic seizures but presumed to be not conscious and involuntary expression of emotional distress similar to panic attacks. They mimic epileptic seizures, but their neurobiological physiopathology is different. PNES are the most common type of conversion disorders or functional neurologic symptom disorders, both terms used interchangeably in the Diagnostic and Statistical Manual -Fifth Edition (DSM-5) [START_REF] Dworetzky | Psychogenic Nonepileptic Seizures in Women[END_REF].

The Scottish Neurological Symptom study [START_REF] Stone | Who is referred to neurology clinics?--the diagnoses made in 3781 new patients[END_REF] stated that functional and psychological symptoms are the second most frequent referral symptom in neurology (after headache), PNES being the most frequent motive in this category.

The International League Against Epilepsy (ILAE) established that "gold standard" diagnosis of PNES is based on a history consistent with PNES and the recording of a typical event with semiological features of PNES such as resistance to eye opening but no epileptiform activity on the electroencephalogram (EEG) before, during, or after the ictus. The combination of a history, semiology, and video EEG findings consistent with PNES provides the level "documented" PNES (3).

It is estimated that 20-30% of patients referred to epilepsy centers with intractable seizures have been misdiagnosed with epilepsy. The vast majority of these patients are eventually diagnosed with PNES (4).

An international consensus clinical practice statement issued in 2011 [START_REF] Kerr | International consensus clinical practice statements for the treatment of neuropsychiatric conditions associated with epilepsy[END_REF] ranked PNES among the top three neuropsychiatric problems : Assessment and management of nonepileptic seizures and imitators of epilepsy was preceded by assessment and management of depressive disorders in epilepsy and assessment and management of concomitant anxiety disorders in epilepsy.

Followingly, an ILAE PNES Task Force published in 2017 an actualization concerning PNES epidemiology in adults and in patients subgroups, such as children, older adults, and those with intellectual disability [START_REF] Kanemoto | PNES around the world: Where we are now and how we can close the diagnosis and treatment gaps-an ILAE PNES Task Force report[END_REF]. We searched PubMed central using the keywords "psychogenic non epileptic seizure", "PNES", "epidemiology" on August 27th, 2019. We obtained 122 results. We selected among the results reviews and studies in French or English that we considered of interest, concerning aspects of PNES epidemiology. We were careful that the methodology of PNES diagnosis in the selected papers used Video-EEG exploration.

Findings

PNES epidemiology is a topic of growing interest. The most ancient publication we found dated from 1984. Between 1984 and 2009, there were less than 10 publications per year. This number increased in the last years with a maximum of 25 publications in 2018.

PNES are a topic of interest not only from the medical and caregiver point of view but also from the societal and economical health aspect. Studies concerning PNES medico-economic consequences report a heavy burden for healthcare systems and societies at large, as well as for affected individuals and their families [START_REF] Lafrance | Avoiding the costs of unrecognized psychological nonepileptic seizures[END_REF]. The lack of money for treatment concerns 70% and 50% of the low and middleincome countries respectively and is identified as one of the major hurdles to the diagnoses and treatment of PNES [START_REF] Hingray | Access to diagnostic and therapeutic facilities for psychogenic nonepileptic seizures: An international survey by the ILAE PNES Task Force[END_REF]. In addition to the direct healthcare costs associated with PNES, indirect costs to patients and caregivers caused by loss of employment and reduced availability for household work have great societal impact [START_REF] Stone | The burden of psychogenic nonepileptic seizures (PNES) in context: PNES and medically unexplained symptoms. In: Gates and Rowan's nonepileptic seizures[END_REF]. Several studies have found that direct healthcare costs decline following the diagnosis of PNES because of substantial reductions in healthcare resource utilization [START_REF] Martin | Improved health care resource utilization following video-EEG-confirmed diagnosis of nonepileptic psychogenic seizures[END_REF] [START_REF] Razvi | Newly diagnosed psychogenic nonepileptic seizures: health care demand prior to and following diagnosis at a first seizure clinic[END_REF].

The early reduction in healthcare use is often sustained over the longer term, although long-term employment outcomes do not seem favorable [START_REF] Duncan | Primary and secondary care attendance, anticonvulsant and antidepressant use and psychiatric contact 5-10 years after diagnosis in 188 patients with psychogenic non-epileptic seizures[END_REF] [START_REF] Reuber | Outcome in psychogenic nonepileptic seizures: 1 to 10-year follow-up in 164 patients[END_REF].

Studying PNES epidemiology is complicated. One major recent improvement is the publication of clearly defined diagnostic criteria after ILAE interest in this domain, that allowed to harmonize PNES patient's definition around the world.

PNES diagnosis delay from first seizure to definitive diagnosis of PNES is usually reported (13) (14)(15) (16) between 3 and 8,4 years. Two recent studies [START_REF] Kerr | Diagnostic delay in psychogenic seizures and the association with anti-seizure medication trials[END_REF] [START_REF] Bahrami | Why is psychogenic nonepileptic seizure diagnosis missed? A retrospective study[END_REF] noticed that the presence of antiseizure medication is associated with longer diagnostic delay (odds ratio 6,1) and each anti-seizure medication trial extends this diagnostic delay. Younger age at onset and the presence of ictal injury (odds ratio 3,6) are also associated with longer diagnostic delay in PNES patients [START_REF] Bahrami | Why is psychogenic nonepileptic seizure diagnosis missed? A retrospective study[END_REF]. This long diagnosis delays and a tendency for patients with PNES to disengage from medical services after diagnosis are two issues that make patients with PNES disorders difficult to identify, even in developed countries.

One limitation concerning PNES epidemiology, clearly underlined by ILAE, is the absence of wellresourced, formal population-based epidemiological studies. Most estimates of the incidence and prevalence in the literature are based on diagnoses from tertiary care epilepsy monitoring units (EMU), where approximately 20 to 40% of adult patients and approximately 10 to 23% of children presenting with "drug-resistant epilepsy" are diagnosed with PNES (18)(19) (20) [START_REF] Asadi-Pooya | Epidemiology of psychogenic nonepileptic seizures[END_REF]. A study in Tanzania ( 22) observed a higher proportion with half the patients referred to a tertiary medical center with functional neurological disorders presenting PNES. A study by Salinsky et al. indicated that up to 25% of veterans entering epilepsy monitoring units were finally diagnosed with PNES [START_REF] Salinsky | Psychogenic nonepileptic seizures in US veterans[END_REF].

The incidence of PNES has recently been determined to be 4.09/100,000 in a study based in the United Kingdom [START_REF] Duncan | Newly presenting psychogenic nonepileptic seizures: incidence, population characteristics, and early outcome from a prospective audit of a first seizure clinic[END_REF]. Other studies estimated the incidence of PNES to be 1.4-4.9 cases per 100,000 people per year (25) [START_REF] Szaflarski | Four-year incidence of psychogenic nonepileptic seizures in adults in hamilton county[END_REF].

Two prevalence estimates are suggested by ILAE (3): one based on the number of patients referred to epilepsy centers who are thought to have severe epilepsy but who turn out to have PNES. This solution yields a possible prevalence range of 2-33/100,000 (0.002-0.033%) [START_REF] Benbadis | An estimate of the prevalence of psychogenic non-epileptic seizures[END_REF].

The second one is based on the assumption of a similar long-term course for PNES and epilepsy and an extrapolation from incidence figures. Following this approach, an incidence figure of 5/100,000/year would yield an estimated prevalence of approximately 1/10 that of epilepsy, or 5/100,000.

There is a predominance of female gender among patients with PNES with a ratio classically considered of 3 to 1 in favor of women. This may vary as published in a recent study concerning 330 patients retrospectively included over 10 years [START_REF] Bahrami | Why is psychogenic nonepileptic seizure diagnosis missed? A retrospective study[END_REF], in which sex ratio was only 1,89 in favor of women. The female sex preponderance occurs after puberty but is also found in some pediatrics studies [START_REF] Valente | Risk Factors for Diagnostic Delay in Psychogenic Nonepileptic Seizures Among Children and Adolescents[END_REF] and does not vary with the country development status (( 7),(29) (30) [START_REF] Pretorius | People with psychogenic non-epileptic seizures: A South African perspective[END_REF]. This sex ratio is also found in other conversion disorders such as functional movement disorders [START_REF] Ekanayake | Personality traits in psychogenic nonepileptic seizures (PNES) and psychogenic movement disorder (PMD): Neuroticism and perfectionism[END_REF]. Neurobiological, social and vulnerability differences may explain why PNES are predominantly seen in female gender (33)(34) (35) (36)(37) : many of the PNES risk factors are more common in women [START_REF] Dworetzky | Psychogenic Nonepileptic Seizures in Women[END_REF]. Studies have reported differing but high rates of previous sexual abuse in women with PNES in Eastern and Western countries (38) (39) (21) [START_REF] Lazarus | A study of nonepileptic seizures in an Indian population[END_REF]. ( 33). Yet, one study comparing men and women with PNES found similar overall rates of psychiatric comorbidity between the two genders [START_REF] Oto | Gender differences in psychogenic non-epileptic seizures[END_REF]. Interestingly, another study using a personality profile evaluation showed worse emotional adjustment in men compared with women with PNES [START_REF] Holmes | Evidence That Emotional Maladjustment Is Worse in Men Than in Women with Psychogenic Nonepileptic Seizures[END_REF].

The clinical course of PNES in men and women may differ : a recent study including 41 video-EEG diagnosed PNES patients found that PNES started later in women compared to men (24,3 versus 17,5 years), with longer PNES episode duration in women (10 versus 2 minutes) and no gender specific difference in the semiologic expression of PNES [START_REF] Korucuk | Semiological characteristics of patients with psychogenic nonepileptic seizures: Gender-related differences[END_REF].

PNES occur mainly in young adults (second and third decades) but are also reported in children [START_REF] Reilly | Psychogenic nonepileptic seizures in children: a review[END_REF].

A recent study in Brazil [START_REF] Valente | Risk Factors for Diagnostic Delay in Psychogenic Nonepileptic Seizures Among Children and Adolescents[END_REF] about 53 children aged between 7 to 17 with video-EEG documented PNES showed an average delay until referral of 17,76 month (elongating with an earlier age of onset), and a female predominance (60,4%). However, there is a lack of population-based data on the prevalence or incidence of PNES in the pediatric population.

Studies of children up to 12 years of age have identified the following patient characteristics:

-PNES have been reported from the age of 3 years but are uncommon under 6 years of age [START_REF] Mayor | Long-term outcome of brief augmented psychodynamic interpersonal therapy for psychogenic nonepileptic seizures: seizure control and health care utilization[END_REF]; -Unlike in adults, there is no female predominance (45); -Motor inhibition (dialeptic attacks) are more common than hyper-motor-type events (46) (47); -A history of physical or sexual abuse is reported less commonly by pediatric than by adult patients [START_REF] Reilly | Psychogenic nonepileptic seizures in children: a review[END_REF]; -School phobia or difficulties in school (including bullying, specific learning difficulties, or unrealistic expectations) are the most common precipitating or perpetuating factors (43); -A better outcome for children than for adults with PNES [START_REF] Wyllie | Outcome of psychogenic seizures in children and adolescents compared with adults[END_REF].

Concerning older patients, PNES are uncommon after the age of 50 years and little is known about patients with late onset PNES. In Duncan et al. [START_REF] Duncan | Newly presenting psychogenic nonepileptic seizures: incidence, population characteristics, and early outcome from a prospective audit of a first seizure clinic[END_REF] cohort, late onset PNES were more likely to be male, less likely to report history of sexual abuse and more likely to have severe physical health issues and to report health-related traumatic experiences. PNES semiology and mental health status seemed similar between early and late onset PNES.

Psychiatric comorbidities are very common in PNES, with estimates ranging between 53 and 100%

of PNES patients with at least one comorbid psychiatric disorder [START_REF] Turner | Patients with epilepsy and patients with psychogenic non-epileptic seizures: video-EEG, clinical and neuropsychological evaluation[END_REF].

When compared to patients with conversion disorders such as functional movement disorders [START_REF] Ekanayake | Personality traits in psychogenic nonepileptic seizures (PNES) and psychogenic movement disorder (PMD): Neuroticism and perfectionism[END_REF], PNES patients have more anxiety disorders (56% versus 44%), and similar rates of mood disorders.

Study using personality measure scales (such as the Personality Assessment inventory) (50)(51) have found significantly higher somatic, conversion, depressed, anxious and suicidal symptoms in PNES patients.

In comparison with epileptic patients, PNES patients have significantly elevated risks found for Post-Traumatic Stress Disorder (PTSD), personality disorder, and anxiety but not depression (52) but this result is not consistent in every study [START_REF] Walsh | Comorbid depression and associated factors in PNES versus epilepsy: Systematic review and meta-analysis[END_REF]. In a recent review [START_REF] Walsh | Comorbid depression and associated factors in PNES versus epilepsy: Systematic review and meta-analysis[END_REF], considering only video EEG proven PNES and ES, Walsh et al. concluded that PNES patient's depression level was better explained by interpersonal factors whereas epileptic patient's depression level were influenced by illness related factors. When PNES are associated with depression (21% to 60% patients) [START_REF] Kanner | Depression and epilepsy, pain and psychogenic non-epileptic seizures: clinical and therapeutic perspectives[END_REF], patients have lower level of functioning and worse quality of life [START_REF] Szaflarski | Seizure disorders, depression, and health-related quality of life[END_REF] [START_REF] Myers | Psychogenic non-epileptic seizures: predisposing factors to diminished quality of life[END_REF]. The reduction in quality of life experienced by people with PNES is well documented and is a major global public health issue [START_REF] Jones | Correlates of health-related quality of life in adults with psychogenic nonepileptic seizures: A systematic review[END_REF].

Traumatic life experiences in childhood or adulthood are associated with PNES :

Adverse childhood experiences have been identified as a factor predisposing to the development of PNES in later life [START_REF] Bakvis | Trauma, stress, and preconscious threat processing in patients with psychogenic nonepileptic seizures[END_REF] [START_REF] Sharpe | Non-epileptic seizures and child sexual abuse: a critical review of the literature[END_REF]. Childhood sexual abuse is reported between 5,9 to 84,6% PNES patients (PNES patients are three time more likely to report sexual abuse than controls) [START_REF] Sharpe | Non-epileptic seizures and child sexual abuse: a critical review of the literature[END_REF]. In a study comparing subjects with epilepsy or PNES, using the 28-item brief screening version of the Childhood Trauma Questionnaire, the prevalence of childhood trauma was significantly higher (36% vs 16%) in PNES patients than epilepsy patients [START_REF] Johnstone | Early childhood trauma and hippocampal volumes in patients with epileptic and psychogenic seizures[END_REF]. Patients with PNES scored significantly higher across all childhood trauma domains, including emotional abuse, physical abuse, sexual abuse, emotional neglect, and physical neglect. Patients with PNES and a history of childhood repeated trauma have more frequent dissociative experiences and psychiatric comorbidities, with an association between their psychiatric symptoms and diagnosis criteria of complex PTSD [START_REF] Hingray | Link between psychogenic nonepileptic seizures and complex PTSD: A pilot study[END_REF].

Concerning trauma in adulthood, a review of 7 studies by Fiszman et al [START_REF] Fiszman | Traumatic events and posttraumatic stress disorder in patients with psychogenic nonepileptic seizures: a critical review[END_REF] indicated that 82,6% PNES patients report trauma in adult life ("general traumatic events other than abuse") [START_REF] Fiszman | Traumatic events and posttraumatic stress disorder in patients with psychogenic nonepileptic seizures: a critical review[END_REF]. Among veterans, in a retrospective study including 50 PNES confirmed patients, PTSD was the most frequent DSM-axis 1 diagnosis preceding admissions (58%), followed by depression (46%) and alcohol abuse.

These axis 1 diagnosis were frequently associated in those patients (34% had all 3 diagnoses and 58% had at least 2). In addition, 36% patients had a personality disorder [START_REF] Salinsky | Psychiatric comorbidity in veterans with psychogenic seizures[END_REF].

PNES clinical presentation is close from epileptic seizure. Video-EEG is key to differential diagnosis between those conditions. However, it is not unusual to find both epileptic seizure and PNES in a single patient : the association of PNES and epilepsy is not consistently reported in the literature, with estimates ranging from 5 to 50% (21) (27) (63) (64) (65) (66) (18) (67) [START_REF] Reuber | The etiology of psychogenic non-epileptic seizures: toward a biopsychosocial model[END_REF]. The criteria for diagnosis of concomitant epilepsy are not consistent among studies. Some considered interictal spikes sufficient to define epilepsy even if interictal epileptiform abnormalities have been reported in nonepileptic conditions [START_REF] Kollar | The importance of interictal electroencephalography in paroxysmal states[END_REF] and even in normal people [START_REF] Binnie | Modern electroencephalography: its role in epilepsy management[END_REF].

After temporal lobe epilepsy surgery, patients presenting with epileptic seizures and PNES improve in both [START_REF] Otárula | Psychogenic nonepileptic seizures in patients with surgically treated temporal lobe epilepsy: Presurgical and de novo postsurgical occurrence[END_REF], but rarely PNES occur de novo after epilepsy surgery (>5%).

A recent study from Wissel et al. [START_REF] Wissel | Which patients with epilepsy are at risk for psychogenic nonepileptic seizures (PNES)? A multicenter casecontrol study[END_REF] used video-EEG proven events to separate patients with combined epileptic (ES) and psychogenic nonepileptic seizures (PNES) and age-and gender-matched patients with ES-only and PNES-only. The study (138 patients) showed that in patients with PNES and ES, ES antedated PNES in 70% cases. The PNES-ES patients had higher depression and anxiety scores and had more often epileptic discharges originating the right hemisphere.

The proportion of patients with PNES and comorbid intellectual disability (ID) is similar to that of patients with PNES and additional epilepsy (i.e., about 10%) (72) [START_REF] Krumholz | Psychogenic seizures: a clinical study with follow-up data[END_REF]. In a recent study (74) that focused on patients living at an epilepsy day-care facility in the Netherland, the prevalence of PNES in patients with ID was 7,1%.

One study focusing on patients with PNES and ID suggested differences from patients with PNES without ID : trend towards a male preponderance, relative paucity of antecedent sexual abuse, frequent episodes of psychogenic nonepileptic status, as well as a greater proportion of patients in whom situational or emotional triggers immediately preceding individual PNES were reported [START_REF] Duncan | Psychogenic nonepileptic seizures in patients with learning disability: comparison with patients with no learning disability[END_REF]. Another study [START_REF] Van Ool | Psychogenic nonepileptic seizures in adults with epilepsy and intellectual disability: A neglected area[END_REF] showed that they had more depressive symptoms, experienced more negative life events and had more often an ID discrepancy (ID profile with one domain particularly more impaired than another).

Gates and Erdahl proposed "a reinforced behavior pattern" as a particularly important pathogenetic factor leading to PNES in patients with comorbid ID (76) [START_REF] Magaudda | Identification of three distinct groups of patients with both epilepsy and psychogenic nonepileptic seizures[END_REF].

Unfortunately, no other data are available about PNES in these specific subgroups from less highly developed regions of the world. (3) [START_REF] Plioplys | A multisite controlled study of risk factors in pediatric psychogenic nonepileptic seizures[END_REF]. Discussion:

PNES is a chronic and not rare medical condition that implies long term care and follow-up.

Before PNES diagnosis criteria were clearly defined, PNES patients were mistakenly thought to have drug resistant epilepsy and were treated with anti-seizure medication [START_REF] Salinsky | Psychiatric comorbidity in veterans with psychogenic seizures[END_REF]. After ILAE interest in this condition, our knowledges are increasing with numerous studies associating neurologists, psychiatrists, and epilepsy specialists located around the world.

The sex ratio in favor of women, the highest prevalence among young adults, the association with a history of trauma and psychiatric comorbidities is more and more established. Our knowledges concerning PNES in less frequent patients' subgroups such as children, older adults, or ID subjects improve slowly.

The better knowledge of PNES patients' characteristics improves our understanding of this condition.

In a study that investigated and compared psychiatric features of 25 consecutive patients with PNES on the basis of presence of reported trauma, Hingray et al. [START_REF] Hingray | Psychogenic nonepileptic seizures: characterization of two distinct patient profiles on the basis of trauma history[END_REF] observed two different patients profiles : patients with trauma antecedents correlated with a high rate of psychiatric comorbidity and a strong dissociative mechanism. Patients without trauma had a weaker dissociative mechanism, lower female predominance, less psychiatric comorbidities, more frequent "frustration situations" as a factor triggering PNES and sick leaves as perpetuating factors. Another study observed 2 clusters of patients on the basis of differences concerning alexithymia and emotion regulation [START_REF] Brown | Emotional dysregulation, alexithymia, and attachment in psychogenic nonepileptic seizures[END_REF]. Theoretical models are developed to increase the understanding of PNES [START_REF] Brown | Towards an integrative theory of psychogenic non-epileptic seizures (PNES)[END_REF].

One recent change concerning the epidemiology of PNES is the awareness that this condition is not present only in western developed countries but present worldwide, as suggested by some authors since 2000 (29) [START_REF] Lazarus | A study of nonepileptic seizures in an Indian population[END_REF]. In addition to presentations closely resembling those observed in western and other highly industrialized societies, PNES-like states are also recognized in some cultures around the world as a cultural phenomenon [START_REF] Martinez-Taboas | Cultural aspects of psychogenic nonepileptic seizures[END_REF].

PNES repartition among a single country population can be heterogenous as in Georgia, where PNES are more frequent in the minority religions and ethnic groups (3) ILAE publication encouraged studies describing PNES in several countries increasing our knowledge concerning PNES patients' care discrepancies : in Subsaharian Africa, diagnosis is more difficult due to the frequent lack of national healthcare and PNES diagnoses rely mostly on clinician expertise [START_REF] Dekker | Psychogenic non-epileptic seizures among patients with functional neurological disorder: A case series from a Tanzanian referral hospital and literature review[END_REF].

But western countries findings are also found in other part of the world : in South Africa (83) a retrospective study comparing video-EEG diagnosed PNES and epilepsy patients showed a high rate of initially misdiagnosed patients (50% epilepsy, 50% PNES), a female predominance, and a tendency toward overmedication with antiepileptic drugs in PNES patients.

The future challenge concerning PNES epidemiology study is the elaboration of well-resourced, formal epidemiological studies with strong methodology, issued from less highly developed regions of the world.


Marouene Zouaoui
email: marouene.zouaoui@utt.fr

Julien Gardan

Pascal Lafon

Carl Labergere

Ali Makke

Naman Recho

st Virtual European Conference on Fracture Transverse Isotropic Behavior Identification using Digital Image Correlation of a Pre-structured Material Manufactured by 3D Printing

Keywords: Fused Deposition modeling, Fracture Mechanics, Additive Manufacturing, Transverse isotropic behavior, FEM, Local references orientations

 that enhances the physical properties in the fracture mechanics area with specimens printed by FDM. 3D printed parts are considered as complex structures and assumed to show a strong anisotropy related to deposition trajectories, air gaps, and welding lines. Therefore, a challenging problem that arises in this domain is the difficulty of predicting the mechanical behavior and controlling the physic properties of parts (tensile strength and fracture toughness…).

.The enhancement is based on a filament deposition optimization in order to reproduce principal stresses directions in a region of interest submitted to crack initiation around the notch tip.

. Thus, the corresponding behavior was assumed to be transverse isotropic and five elastic materials constants must be identified. Hence, a set of tensile tests was performed with fullfield measurements by Digital Image Correlation (DIC) for different filament orientations. Regions of interests were chosen according to the local loading state to activate specific materials constants. The experiments outcomes prove that 3D printed specimens have unexpectedly isotropic stiffness due to similar values found of longitudinal and

Introduction

Most of the sectors are developing the industry of the future or 4.0 with strong expectations for Additive Manufacturing. Advanced applications, such as aeronautics and automotive, which required the implementation of complex assemblies of several components present a major challenge for manufacturers. The integration of functional or "smart" materials is considered at this level as an optimal solution to answer to a number of needs. A smart material is defined according to Gardan et al [START_REF] Gardan | Smart materials in additive manufacturing: state of the art and trends[END_REF] as a static or a dynamic reaction of complex shapes with a material's combination to achieve one or more properties in order to respond to a predefined functionality. The importance of additive manufacturing is therefore highlighted since it makes it possible to produce more optimized structures and more complex shapes than with conventional manufacturing processes. Thus, it allows the development of advanced materials. This work is part of a study that deals with developing pre-structured materials using Fused Deposition Modeling (FDM) process and studying their mechanical behavior. Its main purpose is to identify the elastic constants of a pre-structured material fabricated based on a fracture toughness strengthening where the filaments are oriented according to principal stress directions. Improvement of fracture toughness of both CT specimen [START_REF] Gardan | Improving the fracture toughness of 3D printed thermoplastic polymers by fused deposition modeling[END_REF] and bending Beam specimen [START_REF] Lanzillotti | Enhancement of fracture toughness under mixed mode loading of ABS specimens produced by 3D printing[END_REF] stands proof of this method's efficiency. The major goal is to establish a numerical model that predict with a high accuracy the fracture behavior of this pre-structured material.

Transverse isotropic behavior for 3D printed material

Due to filaments orientations and the built procedure, 3D printed materials are assumed to have an anisotropic behavior. To study their behavior an orthotropic law is commonly used. Zhao and al. developed a mechanical model that highlights the anisotropic tensile strength and elastic property of PLA material supposing an orthotropic behavior [START_REF] Zhao | Novel mechanical models of tensile strength and elastic property of FDM AM PLA materials: Experimental and theoretical analyses[END_REF]. While Alaimo and al. utilized the Classical Lamination Theory (CLT) and Tsai-Hill yielding criterion to predict in-plane stiffness and strength of FDM specimens [START_REF] Alaimo | Influence of meso-structure and chemical composition on FDM 3D-printed parts[END_REF].Likewise Dai and al. identified orthotropic elastic constants of PLA material using an experimental investigation [START_REF] Dai | Orthotropic elastic behaviors and yield strength of fused deposition modeling materials: Theory and experiments[END_REF]. Furthermore, a transversely isotropic model is put forward in form of constitutive equations and is compared with an isotropic model considering the influence of printing orientation to model the mechanical behavior of 3D printed ABS material [START_REF] Zou | Isotropic and anisotropic elasticity and yielding of 3D printed material[END_REF].

If we compare the transverse direction in the built plane and the built direction, we can clearly observe a built similarity. A transverse isotropic behavior is therefore chosen. Such material has five independent elastic constants. Table 1 presents the designation that will be used for this study.

Experimental identification of material's elastic constants

3D printing

Tensile specimens were designed according to ASTM D638-03, "Standard Test Method for Tensile Properties of Plastics" [START_REF]Test Method for Tensile Properties of Plastics[END_REF]. White ABS (Acrylonitrile Butadiene Styrene) filament was used for the purpose of having a better contrast while applying the black speckle. All specimens were printed on A Makerbot replicator x2 in a flat configuration using a layer thickness of 0.25 mm. The filament was extruded at 235°C on a preheated built plate at 120°C. Each specimen was made of 28 Layer. For the infill angle, three kinds of specimen were printed .longitudinal (L) and transverse (T) and 45° directions. The modifier feature of the slicing software Slic3r [START_REF]Slic3r Manual -Welcome to the Slic3r Manual[END_REF] was used to get a unique infill angle for all layers.

Tensile test with Digital Image correlation

The tensile tests were performed on a tensile test machine Instron 4411. A loading rate of 1 mm/min was used. In order the get accurate results using the DIC method one snapshot was saved every 0.6 s during the test. For every tensile test, three Regions Of Interest (ROI) were selected as shown in figure 1.

While performing the tests numerous problems occur, mainly slip problems and filaments delamination between the jaws. For such reason a method was used to access the true value displacement value of the specimen. It can be calculated as the difference between the average displacements calculated over the Upper ROI and the Lower ROI. The total ROI used to calculate the Poisson's ratio. The mean values of both longitudinal and transversal strains are calculated in a range between a starting snapshot and the snapshot 200 (approximately the elastic region for all specimens). The negative value of the transversal strain is plotted as a function of the longitudinal one. The slope gives the value of the Poisson's ratio. This ROI will be later on used for the numerical model validation while comparing measured experimental and numerical strain fields.

Identified elastic constants

For the experimental identifications, three elastic constants are directly calculated through the tensile tests (Longitudinal and transverse Young's modulus ( , ) and the in plane Poisson's ratio ). The in plane shear modulus is calculated through the stress analysis of the 45° specimen. Using the stress analysis of fibre reinforced composite material's [START_REF] Hyer | Stress analysis of fiber-reinforced composite materials[END_REF] a relation (see equation 1) between the shear modulus and the calculated Young's modulus and Poisson's ratio is established.

Where:

• : Young's modulus in the longitudinal direction • : Young's modulus in the transverse direction

• : In plan Poisson's ratio • °: Experimental Young's modulus of the 45° specimen
The out of plane Poisson's ratio ( : in the isotropy plane) cannot be identified using the available data. Here plane stress loadings are studied and has no influence on the in plane material behavior. Since it only affects the out of plane strain component. By analyzing the compliance matrix components for the transversely isotropic material is only activated when off plane shear loading is applied or by measuring the out of plane displacement. Therefore , for the numerical model, an average value between the Poisson's ratios calculated using the transverse specimen and the longitudinal specimen is used. It is important to consider the air gap (voids inside a 3D printed part) while calculating the Young's modulus since it influences directly the mechanical behavior of the material. Otherwise, getting an accurate estimation of the air gap is difficult. Therefore, in order to avoid such calculation that possibly adds another source of error and especially to keep the global dimensions of the part while creating the numerical model, the engineering stress was calculated using the effective measured section of the specimen. As previously announced, this work is part of developing a full numerical model of the pre-structured material that goes until fracture. Thus reaching the yielding point with the right stress and the right strain levels is crucial. Since an elastic non-linearity was observed, calculating Young's modulus as the slope of the tangent to the true stress-strain curve at low stress will lead to an under estimations of the strain at the yielding point. This is why another method for calculating Young's modulus was used. It consists of considering a linear elastic behavior until the yielding point calculated with an offset of 0.2 % strain.

Finite element model validation

In order to check the validity of the identified elastic constants, an oriented numerical model for each specimen will be created. The local references in mesh element assignment method described in [START_REF] Zouaoui | Numerical Prediction of 3D Printed Specimens Based on a Strengthening Method of Fracture Toughness[END_REF] will be used to reproduce the printing orientation inside the model. The numerical answer will be compared to collect data using the DIC analysis.

The cost function was formulated based on the Finite Element Model Updated widely used [START_REF] Robert | Identification of hardening parameters using finite element models and full-field measurements: some case studies[END_REF]- [START_REF] Sztefek | Tensile stiffness distribution in impacted composite laminates determined by an inverse method[END_REF] that represents an inverse method to identify the inputs of a numerical model. The validity of those inputs is related to their capacity the reproduce experimental results (fields measurement) with a low level of error. The objective here is to evaluate the difference between the numerical and experimental forces as well as the difference between the DIC and numerical strain fields while using the identified material's constants ( , , , ) ,except that was proved to have no influence on the formulated cost function.

Subsets and Integration points linking

A linking procedure was performed between the subsets of the reference snapshot and the integration points of the undeformed mesh. The density of subsets is higher than the integration points, so it was decided to reduce the experimental data size to fit the number of integration points by linking each one to the neighbor subsets within a radius less than half the used mesh seize. The following figure shows the reference snapshot localized on the undeformed finite element mesh of the tensile specimen.

Loading steps choice

Several loading steps were chosen from the start of the test until the yielding point. Such choice was mad to ensure the prediction accuracy of the mechanical behavior of the pre-structured material. After computing the cost function for each loading step it was decided to discard the steps at low levels of strain and load. Such choice was made knowing that low strain values are easily perturbed by the noise and the measured load values are affected by the loading phase (slip between the jaws).

Cost function formulation

The equation 2 represents the full cost function that can be divided into two components. A cost function for the strain fields comparison and the other one for the force comparison.

The experimental strain field ε . calculated for the snapshot i and overall the subsets s on the ROI will be compared with the numerical strain field ε . ! calculated for the simulation i (or snapshot i) over all the integration points n inside the ROI. As said before a procedure was performed in order to link every integration point n with the neighbor subsets"p $ … p & ' where an average value will be used for comparison. N presents the number of integration points inside the ROI. In addition, the numerical force F ! is compared to the experimental one F . The final cost function is a computation of this comparison over the M chosen loading steps.

For the strain field comparison only two components were used (the longitudinal and the transverse strains).

Results and discussions

Experimental results

Table 2 presents the founding of the experimental identification compared to data collected from the literature. For comparison, an equivalent printing configuration is mandatory (flat configuration, layer thickness, temperature, used filament, etc…). Young's modulus as announced before was calculated via two methods. Results are coherent with the literature despite the differences in the elastic modulus, which can be related to some different parameters while printing the specimen or the used type of ABS filament. Unforeseen, the material seems to have an overall isotropic behavior because Young's modulus has a slight difference between each other. This means that welding lines are not affecting the material stiffness and the anisotropy was mainly observed at the yielding stress and the tensile strength.

For the isotropy plane Poisson's ratio, an experimental protocol is under development allowing us to measure the out of plane displacement and then identify its value.

Cost function evaluation

For the numerical model, a value =0.3416 will be used. The results are shown below (Table 3). Both used elastic sets of constants independently from the calculation method are giving an accurate estimation of strain fields. This proves that the model can predict transversally strain using the identified Poisson's ratio. High levels of error for the load cost function are explained by the non-linearity observed with the true tensile curves. By comparing the full cost functions, it is clear that the linear approach is more adequate to our study. Especially, knowing that the major goal of the project is to go later on until fracture.

Beam A specimen

The experimental results issued from reference [START_REF] Lanzillotti | Enhancement of fracture toughness under mixed mode loading of ABS specimens produced by 3D printing[END_REF] will be utilized to check the validity of the previously identified elastic constants. Beam A geometry defined by Li and al. [START_REF] Li | J-Mp based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading[END_REF] was printed using two different deposition methods, a classical specimen with ± 45° orientation and an optimized specimen where the reinforcement method is applied. As the graph presented in figure 4 both numerical models are giving similar predictions of the load although the optimized specimens are stiffer than the classical ones. The model is not yet able to highlight the difference of stiffness that could be explained because of the almost isotropic elastic behavior and a layer-by-layer orthogonally building process.

Conclusion

The mechanical behavior of the pre-structured material fabricated by FDM process was studied in the elastic domain. It was observed that stiffness wise the material has a globally isotropic behavior since both Young's modulus are slightly different. Another founding concerns the global answer of Beam A specimen that remained the same even with the optimized deposition method. This is directly related to the previous result announcing the elastic behavior as isotropic. Moreover, in such geometry the number of layers is very high with a layer alternation strategy where filaments are orthogonally deposited. On the other hand, the anisotropy was well highlighted while comparing the yielding points and the fracture stress. Therefore, a Hill criterion will be used to model this aspect.

The developed procedure of comparison using the formulated cost function can also be used to identify all four accessible elastic constants through an inverse method. The research orientation is to minimize the error between the experimental data and the numerical over pre-selected ROI where the local loading stress on the filaments is known.

Fig. 1 .

 1 Fig. 1. Regions of interest definition: (a) Upper ROI; (b) Lower ROI; (c) Total ROI

Fig. 2 .

 2 Fig. 2. Young's modulus calculation method; Red line: slope of the tangent method; Blue line: linear elastic behavior assumption

Fig. 3 .

 3 Fig. 3. Reference snapshot linked with the undeformed mesh

Fig. 5 .Fig. 4 .

 54 Fig. 5. Beam A bending tests compared to the numerical model

Table 1 .

 1 The elastic constants for the transversely isotropic material

	Elastic constant	designation
	Longitudinal Young's modulus
	Transverse Young's modulus
	In plane Poisson's ratio
	In plane shear modulus
	Out of plane Poisson's ratio

Table 2 .

 2 Results of the experimental identification

	Elastic constant ) * (MPa) ) + (MPa) , *+ -*+ (MPa) , ++	slope of the tangent method 1680 ± 71 1414 ± 133 0.3710 ± 0.032 545 -	linear elastic behavior assumption 1476 1309 0.3710 ± 0.032 478 -	Rodríguez and al. 2001 [16] 1921.6 ± 17 1621± 24 0.37 ± 0.014 672.5 -	Alaimo and al. 2017 [7] 2010 ± 153 1671 ± 57 0.32 ± 0,1 641 ± 47 -

Table 3 .

 3 Cost function calculation

	Input calculation method Cost function (%) L	K L"$…M'.NOPQ 11.34	slope of the tangent method K L"$…M'.RSTPLU K L"$…M'.PVW.XYNN 5.78 8.61	linear elastic behavior assumption K L"$…M'.NOPQ K L"$…M'.RSTPLU K L"$…M'.PVW.XYNN 5.51 5.43 4.47
	T	15.90	11.71	13.81	8.76	8.83	8.80
	45°	15.88	4.73	10.30	9.12	4.07	6.59

Acknowledgements

The authors gratefully acknowledge the Grand-Est region in France and the European Regional Development Fund (ERDF), University of Technology of Troyes and EPF Engineering School of Troyes for their financial support.