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摘要:近场动力学采用非局部积分计算节点内力, 利用统一数学框架描述空间连续与非连续, 避免了非连续区局部空间导数引起的应力奇异, 数值上具有无网格属性, 可自然模拟材料结构的断裂问题. 本文概述了近场动力学的弹性本构力模型, 系统介绍了近场动力学临界伸长率、临界能量密度以及材料强度相关的键失效准则. 详细介绍了近场动力学在断裂力学领域的研究进展, 包括断裂参数能量释放率与应力强度因子的求解、J积分、混合型裂纹、弹塑性断裂、黏聚力模型、动态断裂、材料界面断裂以及疲劳裂纹扩展等. 最后讨论了断裂问题近场动力学研究的发展方向.Abstract:In peridynamics, nonlocal integrals are proposed to calculate the node internal forces, and a unified mathematical framework is utilized to describe spatial continuity and discontinuity, which thus avoid the stress singularity caused by the local spatial derivative in the discontinuous region. Numerical peridynamic models have meshfree property, which is naturally capable of analyzing the fracture problems. In this paper, the elastic peridynamic model is briefly introduced, and the critical stretch, critical energy density, and strength-based peridynamic bond failure criteria are successively presented. Then, the research advances of peridynamics in the field of fracture mechanics are systematically introduced, including the computations of energy release rate and stress intensity factor, J integral, mixed-mode crack fracture, elastoplastic fracture, cohesive zone model, dynamic fracture, hybrid material interface fracture, and fatigue crack growth. Finally, the prospects for further research of peridynamics in fracture mechanics is provided.
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Key words:
- peridynamics/
- fracture mechanics/
- crack growth/
- bond failure.
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图 2近场动力学虚拟裂纹闭合技术 (Zhang H & Qiao 2020c).
图 3近场动力学J积分 (Hu W K et al. 2012a).
图 4混合型裂纹的近场动力学模型 (Zhang H et al. 2021). (a) 各向同性材料, (b) 材料界面, (c) 应用展示.
图 5位移载荷下弹塑性材料断裂中的等效应力分布 (Madenci & Oterkus 2016). (a)u= 0.0025 m, (b)u= 0.003 m; (c)u= 0.0035 m, (d)u= 0.004 m.
图 6传统断裂力学和近场动力学粘聚力模型. (a) 传统断裂力学粘聚力模型, (b) 近场动力学粘聚力模型 (Yang et al. 2018).
图 7应力载荷σ= 23 MPa下不同时刻裂纹动态扩展和分叉以及应变能密度分布 (Ha & Bobaru 2011).
图 8双弹性材料界面的近场动力学模型 (Zhang H et al. 2022). (a) 材料界面非局部力传递, (b) 近场动力学跨界面键与母材内部键.
图 9近场动力学疲劳模型 (Silling & Askari 2014). (a) 裂纹尖端近场动力学键, (b) 近场动力学疲劳模型参数校正.
表 1不同维度下常规态近场动力学弹性本构力模型
问题维度 力密度函数t 体积膨胀量θ 弹性参数κ 弹性参数α 三维 $ 3\dfrac{{\underline {\omega x} }}{q}\kappa \theta + \alpha \underline {\omega e} $ $ 3\dfrac{{\underline {\omega x} \cdot \underline e }}{q} $ $ \dfrac{E}{{3\left( {1 - 2v} \right)}} - \dfrac{{5\mu }}{3} $ $ \dfrac{{15\mu }}{q} $ 平面应力 $ 2\dfrac{{\underline {\omega x} }}{q}\kappa \theta + \alpha \underline {\omega e} $ $ 2\dfrac{{\underline {\omega x} \cdot \underline e }}{q} $ $ \dfrac{E}{{2\left( {1 - v} \right)}} - 2\mu $ $ \dfrac{{8\mu }}{q} $ 平面应变 $ 2\dfrac{{\underline {\omega x} }}{q}\kappa \theta + \alpha \underline {\omega e} $ $ 2\dfrac{{\underline {\omega x} \cdot \underline e }}{q} $ $ \dfrac{E}{{2\left( {1 + v} \right)\left( {1 - 2v} \right)}} - 2\mu $ $ \dfrac{{8\mu }}{q} $ 一维 $ \alpha \underline {\omega e} $ $ \dfrac{{\underline {\omega x} \cdot \underline e }}{q} $ 0 $\dfrac{E}{q}$ 
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