论文标题
各向异性粘性材料的结构框架诱导模型
A structurally frame-indifferent model for anisotropic visco-hyperelastic materials
论文作者
论文摘要
在有限菌株中开发各向异性粘弹性介质理论的主要理论问题之一在于材料对称群体的适当定义及其随着时间的推移的演变。在本文中，对问题进行了彻底讨论，并通过引入一种新型各向异性重塑方程与结构框架无关的原理兼容，这一要求要求每个基于变形梯度的多重分解的无弹性理论都必须遵守。耗散过程的进化定律是通过引入新颖（重塑）平衡方程来获得的，该方程完全由两个标量函数，弹性应变能和耗散密度确定。当变形足够缓慢或对各向异性超弹性固体以进行快速变形时，耗散函数的正确选择使我们能够将所提出的模型减少到埃里克森各向异性流体。最后，讨论了一些原型示例，以强调弛豫时间在本构响应中的作用。
One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed thoroughly and addressed by introducing a novel anisotropic remodelling equation compatible with the principle of structural frame indifference, a requirement that every inelastic theory based on the multiplicative decomposition of the deformation gradient must obey to. The evolution laws of the dissipative process are %obtained by introducing a novel (remodelling) balance equation which is completely determined by two scalar functions, the elastic strain energy and the dissipation densities. The proper choice of the dissipation function allows us to reduce the proposed model to the Ericksen anisotropic fluid, when deformation is sufficiently slow, or to the anisotropic hyperelastic solid for fast deformations. Finally, a few prototype examples are discussed to highlight the role of the relaxation times in the constitutive response.
