Transversely isotropic materials undergoing large deformations and application to modelling of soft tissues

International audienceMany soft tissues are naturally made of a matrix and fibres that present some privileged directions. They are known to support large reversible deformations. The mechanical behaviour of these tissues highlights different phenomena as hysteresis, stress softening or relaxation. A hyperelastic constitutive equation is typically the basis of the model that describes the behaviour of the material. The hyperelastic constitutive equation can be isotropic or anisotropic, it is generally expressed by means of strain components or strain invariants. This paper proposes a review of these constitutive equations

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“…The same type of formulation is also proposed using the other invariants. Two general equations are of the form [122]:…”

Section: Power Developmentmentioning

confidence: 99%

Hyperelastic Energy Densities for Soft Biological Tissues: A Review

Chagnon

Rebouah

Favier

2014

J Elast

226

136

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“…Humphrey et al [80] W " ř kl c km pI 1´3 q k`? I 4´1˘m Jemolio et al [81] W " ř klmn c klmn pI 1´3 q a k pI 2´3 q b l pI 4´1 q cm pI 5´1 q dn Jemolio et al [81] W " is often chosen. Fung and co-authors conducted several studies [59,60,61] using the following global form of SEDF W " c 2 pexp Q´1q.…”

Section: Green-lagrange Tensor Components To Describe Anisotropymentioning

confidence: 99%

Hyperelasticity Modeling for Incompressible Passive Biological Tissues

Chagnon

Ohayon

Martiel

et al. 2017

Biomechanics of Living Organs

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Soft tissues are mainly composed of organised biological media giving them an anisotropic mechanical behavior. Soft tissues also have the ability to undergo large elastic reversible deformations. Many constitutive models were developed to describe these phenomena. In this chapter, we discuss several varying models and their constitutive equations which are defined by means of strain components or strain invariants. The notion of tangent moduli will be plotted for two well-known constitutive equations, and, we will illustrate how to implement explicitly a structural kinematics constraint in a constitutive law to derive the resulting Cauchy stress tensor.

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“…Large elastic deformations are typical among others in mechanics of composite materials in which polymeric matrix is reinforced with different types of fibres and in biomechanics of soft tissues [1][2][3]. Therefore, in this work, the constitutive relations of these materials within the theory of hyper-elasticity are considered.…”

Section: Introductionmentioning

confidence: 99%

Constitutive modelling of fibre reinforced nonhomogenous hyperelastic materials

Jemioło

Gajewski

2017

MATEC Web Conf.

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Abstract. In the paper two classes of poly-convex stored energy functions for transversally isotropic hyper-elastic materials have been proposed. Within these classes, a simplified model of hyper-elastic materials with an isotropic matrix reinforced with fibre family was derived and implemented in finite element software ABAQUS/Standard. The two numerical examples proving correctness of the implementation and showing its positive physical features are presented.

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Transversely isotropic materials undergoing large deformations and application to modelling of soft tissues

Cited by 12 publications

References 17 publications

Hyperelastic Energy Densities for Soft Biological Tissues: A Review

Hyperelastic Energy Densities for Soft Biological Tissues: A Review

Hyperelasticity Modeling for Incompressible Passive Biological Tissues

Constitutive modelling of fibre reinforced nonhomogenous hyperelastic materials

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