A transversely isotropic visco-hyperelastic constitutive model for soft tissues

Abstract

A transversely isotropic visco-hyperelastic constitutive model is provided for soft tissues, which accounts for large deformations, high strain rates, and short-term memory effects. In the first part, a constitutive model for quasi-static deformations of soft tissues is presented, in which a soft tissue is simulated as a transversely isotropic hyperelastic material composed of a matrix and reinforcing fibers. The strain energy density function for the soft tissue is additively decomposed into two terms: a neo-Hookean function for the base matrix, and a polyconvex polynomial function of four invariants for the fibers. A comparison with existing experimental data for porcine brain tissues and bovine pericardium shows that this new model can well represent the quasi-static mechanical behavior of soft tissues. In the second part, a viscous potential is proposed to describe the rate-dependent short-term memory effects, resulting in a visco-hyperelastic constitutive model. This model is tested for a range of strain rates from 0.1 /s to 90 /s and for multiple loading scenarios based on available experimental data for porcine and human brain tissues. The model can be applied to other soft tissues by using different values of material and fitting parameters.

Characterizing white matter tissue in large strain via asymmetric indentation and inverse finite element modeling

“…In this study, we aimed at exploring the capability of using a single asymmetric indentation test (Bischoff, 2004) to characterize white matter. Brain white matter, with its aligned axonal fiber bundles, is typically idealized as a fiber-reinforced material and the tissue's mechanical responses are commonly modeled by a transversely isotropic material (Kulkarni et al, 2014; Ning et al, 2006; Velardi et al, 2006), which is the simplest, yet the most representative anisotropic form in many soft biological tissues (Liu et al, 2014; Thomopoulos and Genin, 2012). In a previous study, a minimal form of a transversely isotropic material model was used to explain the experimental observations of mechanical anisotropy of white matter in both shear and indentation tests in the small-strain regime (Feng et al, 2013).…”

A computational study of invariant I5 in a nearly incompressible transversely isotropic model for white matter

“…Many strain energy functional (SEF) forms have been studied analytically in the hyperelasticity framework (Criscione et al, 2001; Destrade et al, 2014; Holzapfel and Ogden, 2009; Horgan and Murphy, 2014; Horgan and Saccomandi, 2005; Kulkarni et al, 2016; Lu and Zhang, 2005; Merodio and Ogden, 2005; Schröder et al, 2005; Taber, 2004). For the white matter, most of the SEF forms utilize only the fourth invariant ( I 4 ) (Ning et al, 2006; Velardi et al, 2006).…”

A visco-hyperelastic constitutive model and its application in bovine tongue tissue

“…In general, for a transversely isotropic material, 12 invariants ( , , … , ) of ̇ have been defined (Boehler 1987). Among them, and are the most popular invariants in the proposed viscoelastic CLs for isotropic and transversely isotropic materials, respectively (Pioletti et al 1998, Limbert et al 2004, Zhurov et al 2007, Lu et al 2010, Kulkarni et al 2016and Ahsanizadeh and LePing 2015:…”

“…To show the accuracy of the proposed models in predicting the rate dependent behavior, they are compared with one of the most popular transversely isotropic visco-hyperelastic CLs for soft tissues (Limbert et al 2004, Lu et al 2010and Kulkarni et al 2016, originally proposed by Limbert et al (2004)…”

“…Soft tissues envelope, bind, and connect other parts of the body (Kulkarni et al 2016). From a mechanical point of view, soft tissues exhibit nonlinear stress-strain behavior, strain rate sensitivity, hysteresis, viscoelastic responses (relaxation and creep), and permanent strains.…”