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Computational investigation of the impact of assumption of affine deformation on constitutive models of soft tissues

机译：对仿射变形对软组织本构模型影响的计算调查

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All constitutive models proposed during the last decades for large strain composites with hyperelastic matrix usean intrinsic assumption of affine deformation between the matrix and reinforcing fibres. While for typical technicalcomposites the affinity of deformation between fibres and matrix till high loads is ensured by targeted creation oftheir chemical bonds, this need not to be the case with soft biological tissues. For instance, this assumption mightbe disputable for arterial tissues with their matrix consisting of very compliant gel-like proteoglycans. On the otherhand, no constitutive model proposed till now has been capable to give a reasonable fit of all mechanical tests ofsome pathological tissues with low initial stiffness, such as aortic aneurysm wall. Thus, a question occurs whetherthis discrepancy could not be caused by the intrinsic assumption of affine deformation used in all models. To testthe impact of this assumption on the simulated response in some mechanical tests, two finite element models ofspecimens of arterial tissues were created, both including matrix and fibres separately. The former model mimickedthe affine deformation of matrix and fibres by merging all the nodes of both components, while the deformation offibres was independent of the matrix in the latter model, with exception of both fibre ends. Differences in reactionforces 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 smallerthan typical inaccuracies of constitutive models when fitting aortic aneurysm tissues.
机译：所有本构模型提出，在过去几十年中提出的大应变复合材料具有超弹性矩阵useAn仿真变形的基质和增强纤维之间的内在假设。虽然对于典型的技术填充，通过靶向生成化学键确保纤维和基质之间变形的亲和力，直至高负荷，但这种情况不一定是软生物组织的情况。例如，这种假设可能对动脉组织具有令人争议的，其基质由非常柔顺的凝胶状蛋白多糖组成。另一方面，迄今为止，没有提出的本构模型能够合理地适应具有低初始刚度的病理组织的所有机械测试，例如主动脉瘤壁。因此，如果所有模型中使用的仿射变形的内在假设，则出现问题。为了测试这种假设对某些机械测试中的模拟响应的影响，产生了两个动脉组织的两种有限元模型，包括分别包括基质和纤维。前模型通过合并两个组分的所有节点来模仿基质和纤维的仿射变形，而变形偏见与后一个模型中的矩阵无关，两种光纤末端除外。关于纤维方向的各种应变状态和方向评估了标本的差异。具有仿射和非仿射变形的模型之间的评价差异显着但在拟合主动脉瘤组织时构成模型的典型不准确性。

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