In the field of computational modeling of material failure mechanisms, a classical brittle damage model commonly leads to an ill-posed system of equations in numerical realizations, and further yields a divergent numerical solution. An established gradient enhanced approach has been demonstrated to be a powerful and efficient tool to address the issue of localized singularities. The work at hand formulates a brittle damage model based on a gradient micromorphic regularization approach, which, in particular, incorporates a novel Representative Crack Element (RCE) framework to address physically reasonable crack kinematics in the damaged zone. The deformations in the micro cracks within the macro damage zone, which include crack opening, closing (stiff contact), shearing as well as mixed aforementioned deformations, can be comprehensively captured. Thus, the work at hand attempts to resolve the strong-discontinuity problem (within cracks) based on a regularized damage model in a numerically robust manner. The present constitutive model of the gradient damage coupled problem is derived based on a thermodynamic consistent algorithm. In the meantime, a minimization algorithm of the RCE virtual power is employed for the solution of the unknown crack deformations. The formulation is implemented into the context of the conventional Finite Element Method framework. Several representative and meaningful numerical examples are studied to demonstrate the capability of the present model.

在材料失效机制的计算建模领域，经典的脆性损伤模型通常会导致数值实现中的不适定方程组，并进一步产生发散的数值解。已证明已建立的梯度增强方法是解决局部奇点问题的强大且有效的工具。手头的工作制定了基于梯度微形态正则化方法的脆性损伤模型，特别是结合了一种新颖的代表性裂纹元素（RCE）框架来解决损坏区域中物理上合理的裂纹运动学。可以全面捕捉宏观损伤区内的微裂纹变形，包括裂纹的张开、闭合（刚性接触）、剪切以及上述混合变形。因此，手头的工作试图以数值稳健的方式基于正则化损伤模型解决强不连续问题（裂缝内）。目前梯度损伤耦合问题的本构模型是基于热力学一致算法推导出来的。同时，采用RCE虚功率最小化算法求解未知裂纹变形。该公式是在传统有限元方法的背景下实施的框架。研究了几个有代表性和有意义的数值例子来证明本模型的能力。