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 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 model of an 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.

发展有限应变各向异性粘弹性介质理论的主要理论问题之一是对材料对称群及其随时间演化的正确定义。在本文中，通过引入与结构框架无差异原理兼容的新型各向异性重塑方程，对该问题进行了详尽的讨论和解决，该要求是基于变形梯度的乘法分解的每个非弹性理论都必须遵守的要求。耗散过程的演化规律完全由两个标量函数决定，即弹性应变能和耗散密度。耗散功能的正确选择，使我们能够提出的模型降低各向异性流体模型，当变形足够慢，或各向异性的超弹性实体以快速变形。最后，讨论了一些原型示例，以突出弛豫时间在本构响应中的作用。