The idea of the paper is to apply the well established structural tensors approach to complex inelastic material modeling in the finite strain regime. Using this concept, a very general and new anisotropic damage model is derived which is the major novel contribution of the paper. In this framework, a second order damage tensor plays the role of a structural tensor. The damage model is coupled to finite elasto-plasticity such that its first purpose is to model damage-induced anisotropy in ductile materials, in particular metals. Further structural tensors could be introduced to represent initial anisotropy of materials such as soft tissues, composites or thermoplastics. The main results of the derivation are the suitable choice of the Helmholtz free energy function, the development of yield and damage potentials as well as the formulation of physically reasonable evolution equations for the plastic deformation, the damage tensor as well as plastic and damage hardening. It is important to mention that all tensorial internal variables are symmetric and referred to the undeformed configuration. To the knowledge of the authors, the interpretation of a structural tensor of the undeformed configuration as damage tensor is new. Two-point tensors such as the plastic part of the deformation gradient show up in the theoretical derivation but are never computed. The plastic spin remains undetermined which has the advantage that a statement about its evolution is not needed. Further, the evolution equation for the plastic deformation includes only six non-linear scalar equations instead of nine. The numerical implementation of the model is straightforward. The number of material parameters remains moderate. A strategy to identify them by means of standard experiments is discussed. Nevertheless, the validation of the model by means of own experiments or experimental results from the literature is left for further work.

本文的想法是将建立良好的结构张量方法应用于有限应变状态下的复杂非弹性材料建模。利用这一概念，得出了一个非常通用的新型各向异性损伤模型，这是本文的主要新颖贡献。在此框架中，二阶损伤张量起结构张量的作用。损伤模型与有限弹塑性耦合，这样它的第一个目的就是为可延展材料（尤其是金属）中的损伤引起的各向异性建模。可以引入其他结构张量来表示材料（例如软组织，复合材料或热塑性塑料）的初始各向异性。推导的主要结果是亥姆霍兹自由能量函数的合适的选择，屈服和破坏潜能的发展，以及为塑性变形，破坏张量以及塑性和破坏硬化建立物理上合理的演化方程。值得一提的是，所有张量内部变量都是对称的，并指向未变形的配置。据作者所知，将未变形构造的结构张量解释为损伤张量是新的。两点张量（例如，变形梯度的塑性部分）在理论推导中显示，但从未计算过。塑料纺丝仍未确定，其优点是不需要关于其演变的陈述。此外，塑性变形的演化方程只包括六个非线性标量方程，而不是九个。该模型的数值实现很简单。材料参数的数量保持适中。讨论了通过标准实验识别它们的策略。然而，通过自己的实验或文献中的实验结果对模型进行验证尚需进一步工作。