This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack level: damage is related to the growth of microcracks, while plasticity is related to the frictional sliding of closed microcracks. Consequently, the hardening/softening functions and parameters entering the free energy follow from the definition of a single degradation function and the elastic material properties. The evolution of opening microcracks in tension leads to brittle behavior and mode I fracture, while the evolution of closed microcracks under frictional sliding in compression/shear leads to ductile behavior and mode II fracture. Frictional sliding is endowed with a non-associative law, a crucial aspect of the model that considers the effect of dilation and allows for realistic material responses with non-vanishing frictional energy dissipation. Despite the non-associative law, a variationally consistent formulation is presented using notions of energy balance and stability, following the energetic formulation for rate-independent systems. The material response of the model is first described, followed by the numerical implementation procedure and several benchmark finite element simulations. The results highlight the ability of the model to describe tensile, shear, and mixed-mode fracture, as well as responses with brittle-to-ductile transition. A key result is that, by virtue of the micromechanical arguments, realistic failure modes can be captured, without resorting to the usual heuristic modifications considered in the phase-field literature. The numerical results are thoroughly discussed with reference to previous numerical studies, experimental evidence, and analytical fracture criteria.
翻译：本文提供了一个在不同装货条件下模拟准碎裂地质材料失败的模型框架。 提出了一个基于微观机械的模型, 将现场变量与微裂缝的物理机制联系起来: 损害与微裂缝的生长有关, 而塑料与封闭的微裂缝的摩擦滑动有关。 因此, 进入自由能量的硬化/ 软化功能和参数是从单一摩擦功能和弹性物质特性的定义中定义的单一摩擦性消退功能和弹性物质特性中得出的。 在紧张状态中打开微裂缝的演变导致易碎行为和模式I的分解, 而在压缩/ 听的摩擦滑动下封闭的微裂缝演变导致微裂缝行为和模式II的断裂。 调滑裂与非粘结微裂微裂的微裂变形法有关, 模型的变硬化功能和变异性反应可以通过非加速的摩擦性能量分解法来进行, 模型和模式- 模型- 模型- 和模式- 货币- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 和数值- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型- 模型-
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