微极连续介质内聚断裂的相场模型
A phase field model for cohesive fracture in micropolar continua
摘要：
虽然可以通过变分或基于材料力的相场断裂模型预测脆性或准脆性区域中的裂纹成核和扩展，但这些模型通常假设材料的基本弹性响应是非极性的，并且必须引入长度尺度参数以使尖锐裂纹由正则化隐函数表示。然而，许多材料的内部微观结构，包含表面张力，微裂纹，微断裂，夹杂物，空腔或那些颗粒的性质往往表现出尺寸依赖的行为，在路径无关和路径依赖的制度。本文旨在介绍一个统一的处理，捕捉在弹性和损伤状态下的材料的尺寸效应。通过引入内聚微极相场断裂理论，结合计算模型和验证实验，我们探讨了复杂微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，我们引入了独特的退化功能的力-应力-应变和耦合应力-微旋转能量共轭对一个给定的正则化配置文件，使宏观尺寸依赖的响应的微极连续是不敏感的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泛函出发导出控制方程。数值算例表明，正确的方法来识别材料参数和能力的新配方模拟复杂的裂纹图案在准静态政权。
英文摘要：
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 non-polar and yet a length scale parameter must be introduced to enable the sharp cracks 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 is 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.
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