We present a novel microcrack-damage theory for brittle solids under compression. Instead of using internal variables like zeroth, second or fourth rank damage tensors, the state of material damage is represented by an internal function that encapsulates the information of direction, density and size of microcracks. Just like other internal variables, the evolution of this state function must obey the second law of thermodynamics for arbitrary loading paths. This is done by casting the model in the framework of continuous hyperplasticity and enforcing a non-negative dissipation rate functional. The proposed framework offers predictions on the continuous evolution of microcrack density and the induced material anisotropy along with the macroscopic stress-strain curves. The use of continuous damage function grants the model significantly enhanced resolution in characterizing the direction-dependent response of cracked solids compared to classical models that are based on damage tensors. Two scenarios are considered in developing the theory, one assumes frictionless cracks and the other incorporates friction between crack surfaces. The results highlight that inelasticity, pressure dependence, and loading-unloading hysteresis exhibited by brittle solids are natural consequences of frictional microcracks. The proposed theory offers a generic and versatile framework to upscale micromechanical processes operating at individual crack scale to explain the macroscopic behavior of cracked solids.

中文翻译：

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基于连续超塑性的脆性固体定向微裂纹损伤理论

我们提出了一种新的压缩脆性固体微裂纹损伤理论。材料损伤状态不是使用零、二或四阶损伤张量等内部变量，而是由封装微裂纹方向、密度和大小信息的内部函数表示。就像其他内部变量一样，该状态函数的演化必须遵循热力学第二定律，适用于任意加载路径。这是通过在连续超塑性框架中铸造模型并强制执行非负耗散率函数来完成的。所提出的框架提供了对微裂纹密度和诱导材料各向异性以及宏观应力-应变曲线的连续演变的预测。与基于损伤张量的经典模型相比，连续损伤函数的使用使模型在表征裂纹固体的方向相关响应方面显着提高了分辨率。在发展该理论时考虑了两种情况，一种假设是无摩擦裂纹，另一种是裂纹表面之间的摩擦。结果强调，脆性固体表现出的非弹性、压力依赖性和加载-卸载滞后是摩擦微裂纹的自然结果。所提出的理论提供了一个通用和通用的框架，用于在单个裂纹尺度上运行的升级微机械过程，以解释裂纹固体的宏观行为。