Abstract
All constitutive models proposed during the last decades for large strain composites with hyperelastic matrix use an intrinsic assumption of affine deformation between the matrix and reinforcing fibres. While for typical technical composites the affinity of deformation between fibres and matrix till high loads is ensured by targeted creation of their chemical bonds, this need not to be the case with soft biological tissues. For instance, this assumption might be disputable for arterial tissues with their matrix consisting of very compliant gel-like proteoglycans. On the other hand, no constitutive model proposed till now has been capable to give a reasonable fit of all mechanical tests of some pathological tissues with low initial stiffness, such as aortic aneurysm wall. Thus, a question occurs whether this discrepancy could not be caused by the intrinsic assumption of affine deformation used in all models. To test the impact of this assumption on the simulated response in some mechanical tests, two finite element models of specimens of arterial tissues were created, both including matrix and fibres separately. The former model mimicked the affine deformation of matrix and fibres by merging all the nodes of both components, while the deformation of fibres was independent of the matrix in the latter model, with exception of both fibre ends. Differences in reaction forces of specimens were evaluated in various strain states and directions with respect to the orientation of fibres. The evaluated differences between models with affine and non-affine deformations were significant but smaller than typical inaccuracies of constitutive models when fitting aortic aneurysm tissues.
Highlights
Computational modelling becomes an important tool in all engineering analyses
While applicability of analytical calculations is rather limited in the field of non-linear mechanics, since the last decade of the 20th century finite element method (FEM) has enabled analyses of general bodies of materials showing large strains, both plastic and elastic
For the states with dominant load in Y direction, the angle with maximum difference is higher than 45◦, i.e. the maximum difference occurs for the fibres oriented more longitudinally, closer to the direction of the dominant load
Summary
Computational modelling becomes an important tool in all engineering analyses. While applicability of analytical calculations is rather limited in the field of non-linear (large displacements and large strain) mechanics, since the last decade of the 20th century finite element method (FEM) has enabled analyses of general bodies of materials showing large strains, both plastic and elastic. A number of isotropic constitutive models have been proposed in the 20th century (e.g. Mooney-Rivlin model [16, 21] and its simplified forms such as Yeoh [29], Arruda-Boyce [1], Ogden [17], etc.). These models have been applied for technical elastomers like rubber and for description of soft biological tissues, and nowadays constitutive models represent a challenging and important issue in biomechanics. The importance of constitutive models for prediction of stresses in aneurysm wall was
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