各向异性非线性弹性材料数值模型的缺陷
Deficiencies in numerical models of anisotropic nonlinearly elastic materials
摘要：
不可压缩的非线性超弹性材料在有限元数值实验中很少被模拟为完全不可压缩的，因为与全局满足此约束相关的数值困难。因此，大多数商业有限元软件包都假定材料是轻微可压缩的。然后进一步假设，相应的应变能函数可以分解为体积和偏量部分。我们表明，这种分解是不现实的物理，特别是各向异性材料，这是特别感兴趣的模拟生物软组织的机械响应。最突出的缺点是，这种分解，各向异性立方体在静水压力下变形成另一个立方体，而不是一个六面体与非平行面。此外，商业数字代码需要指定一个“压缩性参数”（或“惩罚因子”），这自然产生于有缺陷的应变能函数的加法分解。这个参数通常是链接到一个“体积模量”，虽然这个概念是没有意义的各向异性固体，我们表明，它基本上是一个任意的参数和无穷小的变化，它导致在预测的应力响应的显着变化。这说明了与双轴拉伸实验的动脉，其中的应力响应的大小被发现改变了几个数量级时，无穷小的变化在“泊松比”接近完美的不可压缩性限制的1/2的数值模拟。
英文摘要：
Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial Finite Element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a `compressibility parameter' (or `penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a `bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in `Poisson's ratio' close to the perfect incompressibility limit of 1/2 are made.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
