This article presents a localizing gradient damage model with evolving micromorphic stress‐based anisotropic nonlocal interactions. The objective is to model mesh independent fracture behavior of quasi‐brittle materials, and to avoid the issues associated with the existing gradient‐enhanced damage models. In the proposed model, an evolving anisotropic nonlocal interaction domain governs the spatial diffusive behavior, which helps to maintain a localized damage bandwidth during the final stages of loading. The anisotropy in nonlocal interactions is captured through an anisotropic gradient tensor, which defines the orientation of the diffusive interaction domain based on the principal stresses at a given material point. In this article, a smooth micromorphic stress tensor is utilized for the determination of principal stress states, to enforce a properly oriented interaction across the bandwidth of the damage process zone throughout the loading process. The proposed approach also enables the usage of low order finite elements without any oscillatory micromorphic or nonlocal equivalent strain response in the later stages of deformation. The accuracy and performance of the proposed model are demonstrated numerically in plane strain/stress for mode‐I, mode‐II, and mixed‐mode loading conditions.

中文翻译：

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基于微晶应力的各向异性非局部相互作用的局部梯度损伤增强

本文提出了一种基于演化的基于微观形态应力的各向异性非局部相互作用的局部梯度损伤模型。目的是对准脆性材料的独立于网格的断裂行为进行建模，并避免与现有的梯度增强损伤模型相关的问题。在提出的模型中，不断发展的各向异性非局部相互作用域控制着空间的扩散行为，这有助于在载荷的最后阶段保持局部损伤带宽。通过各向异性梯度张量捕获非局部相互作用中的各向异性，该各向异性张量基于给定材料点上的主应力定义扩散相互作用域的方向。在本文中，使用光滑的微晶应力张量确定主应力状态，在整个加载过程中，在损坏过程区域的整个带宽上实施正确定向的交互。所提出的方法还使得能够在变形的后期使用低阶有限元而没有任何振荡微晶或非局部等效应变响应。在模式I，模式II和混合模式加载条件下，在平面应变/应力下以数值方式证明了所提出模型的准确性和性能。