A novel thermodynamic framework for the continuum mechanical response of nonlinear solids is described. Large deformations, nonlinear hyperelasticity, viscoelasticity, and property changes due to evolution of damage in the material are all encompassed by the general theory. The deformation gradient is decomposed in Gram–Schmidt fashion into the product of an orthogonal matrix and an upper triangular matrix, where the latter can be populated by six independent strain attributes. Strain attributes, in turn, are used as fundamental independent variables in the thermodynamic potentials, rather than the usual scalar invariants of deformation tensors as invoked in more conventional approaches. A complementary set of internal variables also enters the thermodynamic potentials to enable history and rate dependence, i.e., viscoelasticity, and irreversible stiffness degradation, i.e., damage. Governing equations and thermodynamic restrictions imposed by the entropy production inequality are derived. Mechanical, thermodynamic, and kinetic relations are presented for material symmetries that reduce to cubic or isotropic thermoelasticity in the small strain limit, restricted to isotropic damage. Representative models and example problems demonstrate utility and flexibility of this theory for depicting nonlinear hyperelasticity, viscoelasticity, and/or damage from cracks or voids, with physically measurable parameters.

中文翻译：

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基于 Gram-Schmidt 分解的有限粘弹性和损伤本构框架

描述了非线性固体连续机械响应的新型热力学框架。大变形、非线性超弹性、粘弹性和由于材料损伤演化引起的性能变化都包含在一般理论中。变形梯度以 Gram-Schmidt 方式分解为正交矩阵和上三角矩阵的乘积，后者可以由六个独立的应变属性填充。反过来，应变属性被用作热力学势中的基本自变量，而不是在更传统的方法中调用的变形张量的通常标量不变量。一组互补的内部变量也进入热力学势，以实现历史和速率依赖性，即粘弹性，和不可逆的刚度退化，即损坏。导出了熵产生不等式施加的控制方程和热力学限制。呈现了材料对称性的机械、热力学和动力学关系，这些关系在小应变极限内降低为立方或各向同性热弹性，仅限于各向同性损坏。代表性模型和示例问题证明了该理论的实用性和灵活性，用于描述非线性超弹性、粘弹性和/或裂缝或空隙的损坏，以及物理可测量的参数。对于在小应变极限内降低为立方或各向同性热弹性的材料对称性，提出了动力学关系和动力学关系，仅限于各向同性损伤。代表性模型和示例问题证明了该理论的实用性和灵活性，用于描述非线性超弹性、粘弹性和/或裂缝或空隙的损坏，以及物理可测量的参数。对于在小应变极限内降低为立方或各向同性热弹性的材料对称性，提出了动力学关系和动力学关系，仅限于各向同性损伤。代表性模型和示例问题证明了该理论的实用性和灵活性，用于描述非线性超弹性、粘弹性和/或裂缝或空隙的损坏，以及物理可测量的参数。