论文标题
关于各向异性弹性以及有关其有限元的实现的问题
On anisotropic elasticity and questions concerning its Finite Element implementation
论文作者
论文摘要
我们给出了非线性各向异性超弹性材料的应变能功能的条件，该材料可确保与各向异性弹性的经典线性理论兼容。我们发现与所使用的应变能的体积偏离分离相关的局限性，例如在许多有限元（Fe）代码中，因为它不能完全代表线性方案中各向异性材料的行为。该限制有重要的后果。我们表明，在小的变形方案中，基于体积依从性分离假设的Fe代码预测，在静水压力载荷下而不是预期的椭圆形下，由可压缩各向异性材料制成的球会变形为另一个球体。对于有限的变形，通常在当前的FE代码中错误地实现了纤维不能支持压缩的通常假设，并导致非物理结果，即在静水张力下，可压缩各向异性材料的球体变形为较大的球体。
We give conditions on the strain-energy function of nonlinear anisotropic hyperelastic materials that ensure compatibility with the classical linear theories of anisotropic elasticity. We uncover the limitations associated with the volumetric deviatoric separation of the strain energy used, for example, in many Finite Element (FE) codes in that it does not fully represent the behavior of anisotropic materials in the linear regime. This limitation has important consequences. We show that, in the small deformation regime, a FE code based on the volumetric-deviatoric separation assumption predicts that a sphere made of a compressible anisotropic material deforms into another sphere under hydrostatic pressure loading, instead of the expected ellipsoid. For finite deformations, the commonly adopted assumption that fibres cannot support compression is incorrectly implemented in current FE codes and leads to the unphysical result that under hydrostatic tension a sphere of compressible anisotropic material deforms into a larger sphere.
