We propose a new direction-dependent model for the unilateral constraint involved in the phase field approach to fracture and also in the continuous damage mechanics models. The construction of this phase field model is informed by micromechanical modeling through the homogenization theory, where the representative volume element (RVE) has a planar crack in the center. The proposed model is made closely match the response of the RVE, including the frictionless self-contact condition. This homogenization approach allows to identify a direction-dependent phase field model with the tension-compression split obtained from cracked microstructures. One important feature of the proposed model is that unlike most other models, the material degradation is consistently determined without artificial assumptions or ad hoc parameters with no physical interpretation, thus, a more realistic modeling is resulted. With standard tests such as uniaxial loadings, three-point bending, simple shear, and through-crack tests, the proposed model predicts reasonable crack paths. Moreover, with the RVE response as a benchmark, the proposed model gives rise to an accurate stress-strain curve under shear loads, more accurate than most existing models.

中文翻译：

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单边约束脆性断裂的微机械相场模型

我们提出了一种新的依赖于方向的模型，用于涉及断裂相场方法和连续损伤力学模型的单边约束。该相场模型的构建是通过均质化理论通过微机械建模获得的，其中代表性体积元 (RVE) 在中心具有平面裂纹。所提出的模型与 RVE 的响应非常匹配，包括无摩擦自接触条件。这种均质化方法允许使用从裂纹微观结构获得的拉伸-压缩分裂来识别与方向相关的相场模型。所提出模型的一个重要特征是，与大多数其他模型不同，材料退化是一致确定的，没有人为假设或没有物理解释的临时参数，因此，产生了更真实的建模。通过单轴加载、三点弯曲、简单剪切和贯穿裂纹测试等标准测试，所提出的模型预测了合理的裂纹路径。此外，以 RVE 响应为基准，所提出的模型在剪切载荷下产生准确的应力 - 应变曲线，比大多数现有模型更准确。