Abstract Continuum models based on the combination of the theories of plasticity and damage mechanics pose a powerful framework for representing the highly nonlinear material behavior of cohesive-frictional materials. However, non-associated plastic flow rules for representing the inelastic volumetric expansion of such materials may result in unstable material behavior and, accordingly, strongly mesh-dependent results in finite element simulations. Regularization techniques such as the gradient-enhanced continuum or similar nonlocal approaches, which work well for regularizing mode I failure, are often not sufficient as a remedy. In contrast to the latter, the theory of the micropolar continuum represents a suitable framework for regularizing non-associated plastic flow and shear band dominated failure properly, but it fails to do so for mode I failure. Hence, in the present contribution, a combination of the theories of the micropolar continuum and the gradient-enhanced continuum for regularizing both shear band dominated failure and mode I failure is presented. By incorporating a 3D damage-plasticity model for concrete into the proposed framework, it is demonstrated that the proposed model constitutes a physically sound and numerically stable approach for modeling the nonlinear material behavior of concrete in both the pre-peak and the post-peak regime for a broad variety of loading conditions.

中文翻译：

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一种用于模拟粘性摩擦材料准脆性破坏的 3D 梯度增强微极损伤塑性方法

摘要 基于塑性和损伤力学理论相结合的连续介质模型为表征内聚摩擦材料的高度非线性材料行为提供了强有力的框架。然而，用于表示此类材料的非弹性体积膨胀的非关联塑性流动规则可能会导致不稳定的材料行为，因此，在有限元模拟中会产生强烈依赖于网格的结果。正则化技术，例如梯度增强连续体或类似的非局部方法，对于正则化模式 I 失败效果很好，但通常不足以作为补救措施。与后者相反，微极连续体理论代表了一个合适的框架，可以适当地规范非相关塑性流动和剪切带主导的失效，但对于模式 I 失败，它没有这样做。因此，在目前的贡献中，提出了微极连续体和梯度增强连续体理论的组合，用于规范剪切带主导的破坏和模式 I 破坏。通过将混凝土的 3D 损伤塑性模型结合到所提出的框架中，证明所提出的模型构成了一种物理上可靠且数值稳定的方法，用于模拟混凝土在峰值前和峰值后的非线性材料行为适用于各种负载条件。