A generalised structure tensor model for the mixed invariant I8. (December 2018)

• Record Type: Journal Article
• Authors: Melnik, Andrey V.; Luo, Xiaoyu; Ogden, Ray W.
• Is Part Of: International journal of non-linear mechanics. Volume 107(2018)
• Page Start: 137
• Page End: 148
• Publication Date: 2018-12
• Subjects: Soft tissue constitutive modelling -- Fibre dispersion -- Generalised structure tensor -- Deformation invariants -- Myocardium -- Anisotropic elasticity; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2018.08.018
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: Generalised Structure Tensors (GSTs) are used to formulate constitutive models for anisotropic fibre-reinforced materials in which fibres are dispersed. The GST approach has been applied so far to models based on invariants I 4 and I 5 ( I 6 and I 7 ). These anisotropic invariants capture the effect of deformation on each fibre family in isolation, unlike the invariant I 8, which couples two fibre families. We extend the GST approach to models based on the invariant I 8 . We consider two different formulations and for each model derive expressions for stress and elasticity tensors in both the general case and for axisymmetric distributions. We apply the proposed formulation to the hyperelastic Holzapfel–Ogden model for myocardium and obtain a modified model, in which fibre dispersion is consistently accounted for in every term of the strain-energy function. We demonstrate that when accounting for fibre dispersion in the coupling term, the effect on the predicted material response can be significant and may also reduce material symmetry. Highlights: Generalised structure tensor (GST) expressions derived for the coupling invariant I 8 . The GST approach is thereby extended to a complete set of anisotropic invariants. Orientation dispersion of fibres can be consistently included into a general model. The proposed approach is applied to the Holzapfel–Ogden (HO) model for myocardium. Fibre splay in I 8 may soften the response and reduce material symmetry.