A comparison of hyperelastic constitutive models applicable to brain and fat tissues

Abstract

In some soft biological structures such as brain and fat tissues, strong experimental evidence suggests that the shear modulus increases significantly under increasing compressive strain, but not under tensile strain, whereas the apparent Young's elastic modulus increases or remains almost constant when compressive strain increases. These tissues also exhibit a predominantly isotropic, incompressible behaviour. Our aim is to capture these seemingly contradictory mechanical behaviours, both qualitatively and quantitatively, within the framework of finite elasticity, by modelling a soft tissue as a homogeneous, isotropic, incompressible, hyperelastic material and comparing our results with available experimental data. Our analysis reveals that the Fung and Gent models, which are typically used to model soft tissues, are inadequate for the modelling of brain or fat under combined stretch and shear, and so are the classical neo-Hookean and Mooney–Rivlin models used for elastomers. However, a subclass of Ogden hyperelastic models are found to be in excellent agreement with the experiments. Our findings provide explicit models suitable for integration in large-scale finite-element computations.

Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

“…(iii) Non-polyconvexity: For a general theoretical framework that is nevertheless consistent with the observed mechanical behaviour of many materials operating in large strain deformation [18,19,[45][46][47][48], restriction to the class of polyconvex strain-energy functions is not required [49][50][51]. The non-polyconvexity allows for more general a priori bounds on the random hyperelastic parameters to be chosen during the calibration process.…”

“…For natural and engineered materials, uncertainties in the experimental observations typically arise from the inherent micro-structural inhomogeneity [13,14], sample-to-sample intrinsic variability, or when elastic data are extracted from viscoelastic mechanical tests [15][16][17][18][19]. For these materials, hyperelastic models based on mean data values constitute a starting point for the development of more complex models.…”

Non-contact experimental methods to characterise the response of a hyper-elastic membrane

“…Hyper-elastic membrane models are presented in other applications including the behaviour of biological materials and tissues (Chagnon et al 2015;Mihai et al 2015;Rashid et al 2012). Chakravarty (2013) modelled the wings of micro air vehicles as hyper-elastic membranes to investigate their modal parameters.…”

Guaranteed Upper and Lower Bounds on the Uniform Load of Contact Problems in Elasticity

“…In materials analysis and design, contact problems in elasticity are central to the modeling and investigation of many structural systems. In particular, the analysis of soft tissue biomechanics and the design of bioinspired synthetic structures involve nonlinear hyperelastic models for which the mathematical and numerical treatment poses many physical, theoretical, and computational challenges [2,17,29,31,32,33,39].Hyperelastic materials are the class of material models described by a strain energy density function [1,14,15,35,40]. For these materials, boundary value problems are often equivalent to variational problems, which provide powerful methods for obtaining approximate solutions.…”

“…In materials analysis and design, contact problems in elasticity are central to the modeling and investigation of many structural systems. In particular, the analysis of soft tissue biomechanics and the design of bioinspired synthetic structures involve nonlinear hyperelastic models for which the mathematical and numerical treatment poses many physical, theoretical, and computational challenges [2,17,29,31,32,33,39].…”