An anisotropic nonlinear elasticity model for tearing of fibrous soft biomaterials

Abstract

The application of nonlinear elasticity concepts to the mechanical modeling of soft biomaterials is currently the subject of intense investigation. For fibrous soft biomaterials, some specific strain-energy density models for anisotropic hyperelastic materials have been proposed in the literature that are particularly useful as they reflect the typical J-shaped stress–stretch stiffening response due to collagen fibers that is observed experimentally. These models have the feature of incorporating the increased stiffness of the collagen fibers with deformation and involve a maximum fiber stretch (or locking stretch). Here we apply such models to the analysis of the fracture or tearing of fibrous soft biomaterials. Attention is focused on a particular fracture test namely the trousers test where two legs of a cut specimen are pulled horizontally apart out of the plane of the test piece. It is shown that, in general, the location of the cut in the specimen plays a key role in the fracture analysis, and that the effect of the cut position depends crucially on the degree of strain–stiffening. This dependence is characterized explicitly for the specific strain–stiffening constitutive models considered. The effects of anisotropy and strain–stiffening on the fracture toughness (resistance to tearing) are also examined.

Constitutive Modeling of multi-stimuli-responsive shape memory polymers with multi-functional capabilities

“…Here, by adopting the Neo-Hookean model for the purely mechanical hyperelastic property of the material, and based on the research works done in [28,48,50,53,54], a version of the nominal Helmholtz free energy density function for transversely isotropic electro-magneto-hyperelastic materials by ignoring the matric-fiber interaction is considered as: (23) in which 𝐶 1 , 𝐶 3 , 𝐶 4 , 𝐶 6 and 𝐶 7 are materials constants. q is a positive non-dimensional parameter that measures the rapidly increasing stiffness of the fibers with increasing stretch [55], and 𝐸 ̅ is a positive material modulus that measures the degree of anisotropy.…”