Generalisations of the strain-energy function of linear elasticity to model biological soft tissue

Abstract

Publication informationInternational Journal of Non-Linear Mechanics, 47 (2): 268-272Publisher Elsevier Item record/more information http://hdl.handle.net/10197/4602 Publisher's statementThis is the author's version of a work that was accepted for publication in International Journal of Non-Linear Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Non-Linear Mechanics (47, 2, (2012) ABSTRACT Strain measures consistent with the classical, infinitesimal form of the strain-energy function are obtained within the context of isotropic, homogeneous, compressible, non-linear elasticity. It will be shown that there are two distinct families of such measures. One family has already been much studied in the literature, the most important member being the strains whose principal values are a function only of the corresponding principal stretches. The second family of strains appears new. The motivation for studying such strains is the intuitive expectation that, for at least moderate deformations, a good fit with experimental data from material characterisation tests will be obtained with the corresponding strain-energy functions. In particular, there is the expectation that such models could prove useful for the modelling of biological soft tissue, whose physiological response is characterised by moderate strains. It will be shown that this is indeed the case for simple tension tests on porcine brain tissue.

Elimination of Pseudo Initial Stress for Proposed Invariants based Hyper elastic Strain Energy

“…Mansouri and Darijani [4] utilized this test data for proofing of robustness of the invariants model and showed the invariants model fitted both of the pure shear and uniaxial tension loading. The silicone rubber is common material in biomechanical applications because of its unique properties and excellent biocompatibility [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].The material constants of the porcine liver tissue and unfilled silicone rubber can be seen in Table 1.…”

“…Where, Modify W is the modified strain energy function that consists of the invariants model terms and the zero initial stress constraint. Moreover, the initial energy yet is zero and as Ogden et al has mentioned it is one of the methods to impose a constraint on the hyper elastic strain energy [23][24][25][26]. Regarding Eqs.…”

Conjugated kinetic and kinematic measures for constitutive modeling of the thermoelastic continua

“…However, the pioneering work in this context is as early as 1915 by Armanni [29]. This problem is still of interest, for example, we can refer to the recent works of Batra [30,31], Nader [32], Chiskis and Parnes [33], Murphy [34], Darijani et al [25] and Gilchrist et al [35].…”

A Natural Generalization of Linear Isotropic Relations with Seth-Hill Strain Tensors to Transversely Isotropic Materials at Finite Strains

“…Some general results for linear isotropic relations in finite hyperelasticity are suggested by Murphy [11]. Further, Gilchrist and his coworkers [12] investigated the generalization of the linear isotropic elasticity to model biological soft tissue undergoing moderate strains. They experimentally proved that when a proper strain tensor is chosen, such generalizations of the structures of the linear theory to the nonlinear regime might provide an efficient method to model the mechanical behaviors of such materials at moderate deformations.…”

“…The Seth-Hill strain tensors are widely used not only in anisotropic finite elasticity, but also in anisotropic finite elastoplasticity [25][26][27]. The present paper focuses on the cases of finite elasticity and adopts the first approach, similar to isotropic cases [1][2][3][4][5][6][7][8][9][10][11][12][13], to generalizing the structures of the classical anisotropic linear theory to moderate deformation cases. The intuitive expectation for doing so is that, given the excellent agreement of the classical model with experimental data, such generalizations can provide simple and accurate models of nonlinear elastic media undergoing moderate deformations [12].…”