A previous perfect visco‐plastic constitutive formulation of the Perzyna type incorporating the concepts of prescribed stress increments and m‐AGC tangent operator (m‐Assumed algorithmic generalized compliance tangent operator) is extended to the case of Hardening/Softening (H/S). This extension is possible thanks to the closed‐form solution developed for the evolution of the loading function during a visco‐plastic time step. The formulation is then applied to constitutive modeling of zero‐thickness interfaces on the basis of a well‐established fracture‐based elasto‐plastic formulation, which in this manner is extended to visco‐plasticity. The resulting model is implemented in the finite element (FE) and small‐strain context by using both a standard Newton Raphson scheme for physical visco‐plasticity in which visco‐plastic time corresponds to physical time, and a Visco‐Plastic Relaxation (VPR) scheme, in which time corresponds to a fictitious time governing the transition from the elastic to the inviscid elasto‐plastic response. The numerical implementation is verified satisfactorily for common loading cases at interfaces such as pure tension (mode I) opening and shear‐compression (mixed‐mode) cracking/sliding, showing that the visco‐plastic results match the predictions of the fracture mechanics inviscid model in the long term. In addition, it is also shown that the VPR strategy developed is capable of providing temporary stability while the equilibrium path is recovered during instability events such as a snap‐back in the load‐displacement curve. This feature opens the door to a number of potential advanced applications of the formulation developed in the geomechanical context.

中文翻译：

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具有硬化/软化功能的 m-AGC 切线粘塑性算子，以及使用基于裂缝的地质力学接口对稳定和不稳定问题进行粘塑性松弛分析的应用

Perzyna 类型的先前完美粘塑性本构公式结合了规定应力增量和m-AGC正切算子（m-假设算法广义柔量正切算子）扩展到硬化/软化（H/S）的情况。由于为粘塑性时间步长期间加载函数的演化而开发的封闭式解决方案，这种扩展成为可能。然后，在完善的基于断裂的弹塑性公式的基础上，将该公式应用于零厚度界面的本构建模，从而将其扩展到粘塑性。通过使用物理粘塑性的标准牛顿拉夫森方案（其中粘塑性时间对应于物理时间）和粘塑性松弛（VPR），在有限元（FE）和小应变环境中实现了所得模型方案，其中时间对应于控制从弹性到无粘弹塑性响应转变的虚拟时间。对于纯拉伸（I 型）张开和剪切压缩（混合模式）开裂/滑动等界面常见载荷情况，数值实现得到了令人满意的验证，表明粘塑性结果与断裂力学无粘模型的预测相匹配在长期。此外，研究还表明，所开发的 VPR 策略能够提供临时稳定性，同时在不稳定事件（例如载荷-位移曲线中的快速恢复）期间恢复平衡路径。这一功能为在地质力学背景下开发的配方的许多潜在高级应用打开了大门。