LAUSR

Abstract Developments in microscopic imaging techniques for soft biological tissues have greatly improved understanding of their underlying microstructures, notably the three-dimensional orientation and dispersion of fibrous constituents. In structural constitutive modelling, assuming that the collagenous and muscle fibres in soft tissues are perfectly aligned along a prescribed orientation can limit the ability to accurately predict the experimentally detected stress-strain response of biological samples. The objective of this paper is to extend the representation of hyperelasticity for anisotropic bodies using fourth-order structural tensors (FOSTs) to incorporate the effects of fibre dispersion according to the generalized structural tensor (GST) approach. Dispersion within a family of reinforcing collagen fibres is a common phenomenon in soft tissues which alters their overall mechanical behaviour. The FOST-based representation of the strain energy density function (SEF) separates the constitutive properties of the continuum from the nonlinear descriptions of geometric deformations; with each of these being described by different fourth-order tensors. The constant-valued material and structural properties of the continuum reside within fourth-order material tensors referred to as the anisotropic Lame tensors. Nonlinearity in the model is then solely applied to the components of the displacement gradient tensor in fourth-order strain measures. The framework provided leads to a unique set of fourteen generalised FOSTs for two-direction preferred hyperelasticity including fibre families which are dispersed according to normalised distributions. In the absence of dispersion, the model collapses to the conventional FOST-based model. Models for the hyperelastic response of arterial wall and passive ventricular myocardium tissues are postulated and show good agreement with experimental data using minimal ground-state material constants.