In this work, a new damage model for concrete is proposed with an extension of the stress decomposition (limited to biaxial cases), to capture shear damage due to the opposite signed principal stresses. To extract the pure shear stress, the assumption is made that one component of the shear stress is a minimum absolute of the two principal stresses. The opposite signed principal stresses are decomposed into shear stress and uniaxial tensile/compressive stress. A local model is implemented in Abaqus UMAT and it is further extended to a non-local model by utilization of the gradient theory. The concept of three length scales (tension, compression, and shear) is kept the same as the recently proposed nonlocal damage model by the authors. The nonlocal model is implemented in the Abaqus UEL-UMAT subroutine with an eight-node quadrilateral user-defined element, having five degrees of freedom at corner nodes (displacement in X/Y direction and tensile/compressive and shear nonlocal equivalent strain) and two degrees of freedom at internal nodes. Some examples of a local model including uniaxial and biaxial loading are addressed. Also, five examples of mixed crack mode and mode-I cracking are presented to comprehensively show the performance of this model.

在这项工作中，提出了一种新的混凝土损伤模型，其中扩展了应力分解（仅限于双轴情况），以捕获由于相反的正负主应力引起的剪切损伤。为了提取纯剪切应力，假定剪切应力的一个分量是两个主应力中的最小绝对值。相反的正负主应力分解为剪切应力和单轴拉伸/压缩应力。在Abaqus UMAT中实现了局部模型，并通过使用梯度理论将其进一步扩展为非局部模型。作者将三个长度尺度（拉伸，压缩和剪切）的概念与最近提出的非局部损伤模型保持相同。非局部模型是在Abaqus UEL-UMAT子例程中实现的，该例程具有八个节点的用户定义的四边形元素，在角节点处具有五个自由度（在X / Y方向上的位移以及拉伸/压缩和剪切非局部等效应变）和两个内部节点的自由度。解决了包括单轴和双轴载荷的局部模型的一些示例。另外，给出了混合裂纹模式和模式I裂纹的五个示例，以全面显示该模型的性能。