Abstract While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the material is not size-dependent. Yet, a length scale parameter must be introduced to these models to enable sharp cracks properly represented by a regularized implicit function. However, many materials with internal microstructures that contain surface tension, micro-cracks, micro-fracture, inclusion, cavity or those of particulate nature often exhibit size-dependent behaviors in both the path-independent and path-dependent regimes. This paper is intended to introduce a unified treatment that captures the size effect of the materials in both elastic and damaged states. By introducing a cohesive micropolar phase field fracture theory, along with the computational model and validation exercises, we explore the interacting size-dependent elastic deformation and fracture mechanisms exhibits in materials of complex microstructures. To achieve this goal, we introduce the distinctive degradation functions of the force-stress–strain and couple-stress-micro-rotation energy-conjugated pairs for a given regularization profile such that the macroscopic size-dependent responses of the micropolar continua are insensitive to the length scale parameter of the regularized interface. Then, we apply the variational principle to derive governing equations from the micropolar stored energy and dissipative functionals. Numerical examples are introduced to demonstrate the proper way to identify material parameters and the capacity of the new formulation to simulate complex crack patterns in the quasi-static regime.

中文翻译：

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微极连续区内聚断裂的相场模型

摘要 虽然脆性或准脆性状态下的裂纹成核和扩展可以通过基于变分或基于材料力的相场断裂模型进行预测，但这些模型通常假设材料的潜在弹性响应与尺寸无关。然而，必须在这些模型中引入长度尺度参数，以使尖锐的裂纹能够由正则化的隐函数正确表示。然而，许多内部微观结构包含表面张力、微裂纹、微断裂、夹杂物、空腔或颗粒性质的材料通常在路径无关和路径依赖状态下都表现出与尺寸相关的行为。本文旨在介绍一种统一的处理方法，以捕捉材料在弹性和损坏状态下的尺寸效应。通过引入内聚微极相场断裂理论，以及计算模型和验证练习，我们探索了复杂微观结构材料中相互作用的尺寸相关弹性变形和断裂机制。为了实现这一目标，我们针对给定的正则化曲线引入了力-应力-应变和耦合-应力-微-旋转能量-共轭对的独特退化函数，使得微极连续体的宏观尺寸相关响应对正则化接口的长度尺度参数。然后，我们应用变分原理从微极储能和耗散函数推导出控制方程。