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首页> 外文期刊>International journal of computational methods >A General Approach to Derive Stress and Elasticity Tensors for Hyperelastic Isotropic and Anisotropic Biomaterials
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A General Approach to Derive Stress and Elasticity Tensors for Hyperelastic Isotropic and Anisotropic Biomaterials

机译：过度激动式各向异性和各向异性生物材料产生压力和弹性张力的一般方法

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摘要

Hyperelastic models are of particular interest in modeling biomaterials. In order to implement them, one must derive the stress and elasticity tensors from the given potential energy function explicitly. However, it is often cumbersome to do so because researchers in biomechanics may not be well-exposed to systematic approaches to derive the stress and elasticity tensors as it is vaguely addressed in literature. To resolve this, we present a framework of a general approach to derive the stress and elasticity tensors for hyperelastic models. Throughout the derivation we carefully elaborate the differences between formulas used in the displacement-based formulation and the displacement/pressure mixed formulation. Three, hyperelastic models, Mooney Rivlin, Yeoh and Holzapfel Gasser-Ogden models that span from first-order to higher order and from isotropic to anisotropic materials, are served as examples. These detailed derivations are validated with numerical experiments that. demonstrate excellent. agreements with analytical and other computational solutions. Following this framework, one could implement with ease any hyperelastic model as user-defined functions in software packages or develop as an original source code from scratch.
机译：超弹性模型对建模生物材料特别感兴趣。为了实现它们，必须明确地从给定的潜在能量函数中得出压力和弹性张量。然而，这样做往往很麻烦，因为生物力学的研究人员可能不会良好地暴露于系统的方法，以获得压力和弹性张力，因为它在文献中含糊不清。要解决此问题，我们介绍了一种普遍方法的框架来导出超弹性模型的应力和弹性张量。在整个推导过程中，我们仔细阐述了基于位移的配方和位移/压力混合制剂中使用的公式之间的差异。三，超级弹性模型，门尼逆流器，yeoh和holzapfel gasser-ogden型号，从一流到高阶和从各向同性的各向异性材料跨越，都是例子。这些详细的衍生经验证了数值实验。表现出优秀。与分析和其他计算解决方案的协议。在此框架之后，可以通过在软件包中的用户定义的函数轻松实现任何超弹性模型，也可以从头开始开发为原始源代码。

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