3D Residual Stress Field in Arteries: Novel Inverse Method Based on Optical Full-field Measurements

Arterial tissue consists of multiple structurally important constituents that have individual material properties and associated stress-free configurations that evolve over time. This gives rise to residual stresses contributing to the homoeostatic state of stress in vivo as well as adaptations to perturbed loads, disease or injury. The existence of residual stresses in an intact but load-free excised arterial segment suggests compressive and tensile stresses, respectively, in the inner and outer walls. Accordingly, an artery ring springs open into a sector after a radial cut. The measurement of the opening angle is commonly used to deduce the residual stresses, which are the stresses required to close back the ring. The opening angle method provides an average estimate of circumferential residual stresses but it gives no information on local distributions through the thickness and along the axial direction. To address this lack, a new method is proposed in this article to derive maps of residual stresses using an approach based on the contour method. A piece of freshly excised tissue is carefully cut into the specimen, and the local distribution of residual strains and stresses is determined from whole-body digital image correlation measurements using an inverse approach based on a finite element model

Hyperelasticity of Soft Tissues and Related Inverse Problems

International audienceIn this chapter, we are interested in the constitutive equations used to model macroscopically the mechanical function of soft tissues. After reviewing some basics about nonlinear finite–strain constitutive relations, we present recent developments of experimental biomechanics and inverse methods aimed at quantifying consti-tutive parameters of soft tissues. A focus is given to in vitro characterization of hyperelastic parameters based on full-field data that can be collected with digital image correlation systems during the experimental tests. The specific use of these data for membrane-like tissues is first illustrated through the example of bulge inflation tests carried out onto pieces of aortic aneurysms. Then an inverse method, based on the principle of virtual power, is introduced to estimate regional variations of material parameters for more general applications

Inverse problems in the mechanical characterization of elastic arteries

International audienceThis article presents an overview of diverse material models used to represent the mechanical behavior of arteries and of the inverse problems posed by the identification of their constitutive parameters. After a brief introduction about the definition of inverse problems and about the general features of arteries, the article addresses three main questions involving inverse problems and arterial wall characterization: (1) macroscopic identification of the parameters of sophisticated constitutive models from traditional uniaxial and biaxial experiments; (2) mesoscopic identification of regional variations in the material parameters of arteries, tracking the effects of functional adaptation or lesions; (3) how constitutive models and inverse problems allow to obtain information on the arterial microstructure and how the structural constituents interact in the mechanical response. Finally, the article shows that a significant effort has been made so far to relate the complex mechanical behavior of arteries to their microstructure but a new class of inverse problems has recently appeared. It is related to the identification of mechanobiological parameters which are the parameters involved in the numerical models of growth and remodeling

Identification of material parameters through inverse finite element modelling

International audienceIn the past, the mechanical behaviour of soft tissues has not received the attention it deserves, because their highly nonlinear behaviour requires numerical simulations that were beyond the power of all but the most advanced computing facilities. However, with the rapid development of computers and imaging techniques such as MRI and digital image correlation, it is now possible to make real progress in soft tissue modelling and interest in this important field is growing rapidly. There are many exciting applications in medicine, in the design of products such as razors and in other areas such as animation and computer graphics. In addition, there are many fields such as dermatology and cosmetics where accurate measurements of tissue properties are needed. In general, it is difficult to measure the mechanical properties of these materials directly and some kind of inverse approach is needed, where an experiment is simulated and the material parameters are adjusted until the model matches the experiment

Anisotropic and hyperelastic identification of in vitro human arteries from full-field optical measurements

In this paper, we present a new approach for the bi-axial characterization of in vitro human arteries and we prove its feasibility on an example. The specificity of the approach is that it can handle heterogeneous strain and stress distributions in arterial segments. From the full-field experimental data obtained in inflation/extension tests, an inverse approach, called the virtual fields method (VFM), is used for deriving the material parameters of the tested arterial segment. The obtained results are promising and the approach can effectively provide relevant values for the anisotropic hyperelastic properties of the tested sample

Méthode inverse d'identification des propriétés mécaniques locales dans les anévrysmes aortiques

Les objectifs de cette étude sont : (1) de quantifier les propriétés mécaniques locales en différents sites d'anévrysmes en combinant, pour la première fois, un système panoramique de corrélation numérique d'images, des essais mécaniques biaxiaux de traction-gonflement, un système OCT, et une méthode inverse d'identification ; (2) d'établir des corrélations entre les propriétés mécaniques locales du site étudié et la fraction massique locale de constituants biologiques obtenue par histologie quantitative. Les résultats soulignent la nécessité de mieux comprendre les processus mécanobiologiques qui régissent l'équilibre entre la production et la dégradation de la matrice extracellulaire car finalement ce sont les modifications de cet équilibre homéostatique qui sont à l'origine des troubles cardiovasculaires tels que les anévrysmes

Extension of the virtual fields method to elasto-plastic material identification with cyclic loads and kinematic hardening

International audienceThe virtual fields method (VFM) has been specifically developed for solving inverse problems from dense full-field data. This paper explores recent improvements regarding the identification of elasto-plastic models. The procedure has been extended to cyclic loads and combined kinematic/isotropic hardening. A specific attention has also been given to the effect of noise in the data. Indeed, noise in experimental data may significantly affect the robustness of the VFM for solving such inverse problems. The concept of optimized virtual fields that minimize the noise effects, previously developed for linear elasticity, is extended to plasticity in this study. Numerical examples with models combining isotropic and kinematic hardening have been considered for the validation. Different load paths (tension, compression, notched specimen) have shown that this new procedure is robust when applied to elasto-plastic material identification. Finally, the procedure is validated on experimental data

Caractérisation des propriétés mécaniques d'un tronçon d'aorte par méthode inverse basée sur une mesure ex-vivo du champ de déformations

National audienceCette contribution a pour objectif de caractériser les propriétés hyperélastiques du tissu composant l'aorte humaine. Pour cela, un nouveau dispositif de mesures ex vivo du champ de déformations est employé en parallèle avec une méthode inverse reposant sur des simulations éléments finis