Hyperelasticity Modeling for Incompressible Passive Biological Tissues

Abstract

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.

Intraluminal Ultrasonic Palpation Imaging Technique Revisited for Anisotropic Characterization of Healthy and Atherosclerotic Coronary Arteries: A Feasibility Study

“…The fibrotic plaque medium and the healthy coronary arterial wall were considered as orthotropic and quasi-incompressible media (Appendix I), with initial mechanical properties coming from measurements (Chagnon et al 2017;Holzapfel et al 2005) of the pathologic coronary thick intima layer and the adventitia layer, respectively. The mechanical properties of the dense fibrosis and soft necrotic cores were considered as isotropic and quasi-incompressible (Lee et al 1991;Loree et al 1994).…”

A Review on Damage and Rupture Modelling for Soft Tissues

“…Soft tissue consists of cells, elastin, collagen, and a non-mineralized ground matrix. Collagen fibres are of high stiffness compared to the rest of the constituents of the tissue, and they majorly contribute towards the overall stiffness of the tissue [ 20 , 21 ]. Based on their constituents and structure, soft tissues exhibit non-linear, anisotropic, hyperelastic, and viscoelastic behaviour [ 21 ].…”

“…Collagen fibres are of high stiffness compared to the rest of the constituents of the tissue, and they majorly contribute towards the overall stiffness of the tissue [ 20 , 21 ]. Based on their constituents and structure, soft tissues exhibit non-linear, anisotropic, hyperelastic, and viscoelastic behaviour [ 21 ]. Constitutive behaviour varies from tissue to tissue, depending on the collagen fibre distribution and orientation inside the tissue.…”

“…For example, in connective tissues such as ligaments and tendons, the collagen fibre orientation is regular and unidirectional [ 22 , 23 ]. While in non-connective tissues, such as arterial walls, collagen fibres orientation is irregular and multi-directional [ 6 , 20 , 21 ]. In the arterial wall, collagen fibre distribution is arranged in a double-helical pattern [ 24 ].…”

An intelligent control system for robot massaging with uncertain skin characteristics

“…An environmental dynamics based on the Kelvin–Voigt model is described to control both force and position for robots that work on the human surface (Jones and Du, 2003; Koga et al , 2008). Living tissues like skin have biomechanical characteristics such as elasticity, viscoelasticity, non-linearity, and anisotropy, among which the non-linear characteristic of skin is markedly according to the relevant literatures (Chagnon et al , 2017; Seyfi et al , 2016). The environment dynamics in the above-mentioned studies only characterize linear elasticity of the material, which is unable to describe real skin dynamical characteristics.…”