近场动力学在断裂力学领域的研究进展

张恒; 张雄; 乔丕忠

doi:10.6052/1000-0992-22-023

近场动力学在断裂力学领域的研究进展

doi: 10.6052/1000-0992-22-023

张恒¹,
张雄^1, ,,
乔丕忠^2, ,

1.
清华大学航天航空学院, 北京 100084
2.
上海交通大学海洋工程国家重点实验室和船舶海洋与建筑工程学院, 上海 200240

基金项目: 国家自然科学基金 (12172192, 11972224, 12102226)、中国博士后科学基金 (2021M691798) 资助项目.

详细信息

作者简介:
张雄, 清华大学航天航空学院长聘教授, 主要从事强冲击载荷作用下材料与结构力学行为数值分析方法的研究. 2004年入选教育部首批新世纪优秀人才支持计划, 获北京市高等学校教学名师奖、教育部自然科学奖二等奖和一等奖、北京市教育创新标兵、钱令希计算力学成就奖、ICACM Computational Mechanics Award和Fellows Award等奖励. 兼任北京振动工程学会副理事长、《International Journal of Mechanics and Materials in Design》副主编和多本国内外期刊编委. 已出版专著4部、教材3部, 发表期刊论文150余篇, 自2015年连续入选爱思唯尔中国高被引学者榜单, 1篇论文入选2012年度中国百篇最具影响国内学术论文. 出版了国内首部《无网格法》专著、国际首部《物质点法》专著及其英文版, 研发了三维显式并行物质点法数值仿真软件MPM3D, 已成功应用于多个实际工程问题中

乔丕忠, 上海交通大学“致远”讲席教授, 国家特聘专家, 教育部长江学者特聘教授; 美国土木工程协会会士 (ASCE Fellow) 和工程力学院会士 (EMI Fellow). 主要从事先进结构材料与力学的研究, 尤其致力于复合、智能和高性能材料在航空航天和土木水利工程中的发展和应用. 首次提出双层梁剪切和界面变形理论 (被波音公司命名为“乔方法”), 拓展了断裂力学的适用空间; 创建了离散板理论及结构局部稳定显式解, 已被航空业成功用于结构分析; 创新地提出了以剪切变形角为变量参数的板壳结构后屈曲分析方法, 为复材结构非线性大变形分析提供了理论基础; 研究了智能材料用于结构健康监测的关键性基础问题并发展了损伤识别的新理论与方法; 提出了几种破坏模型, 提升了复合材料对传统结构加固和修复的理论研究水平; 给出了态基近场动力学临界伸长准则与断裂释放能表达式, 推动了计算断裂力学的发展; 建立了近场动力学临界歪斜 (critical skew) 准则, 为II型断裂和剪切变形提供了分析手段. 现任《Journal of Engineering Mechanics》《 Journal of Aerospace Engineering》和《Structural Health Monitoring-An International Journal》三个国际期刊副主编和《力学季刊》副主编

通讯作者:
qiao@sjtu.edu.cn

xzhang@tsinghua.edu.cn

中图分类号: O34
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出版历程
- 收稿日期: 2022-05-02
- 录用日期: 2022-07-11
- 网络出版日期: 2022-07-12
- 刊出日期: 2022-12-29

Advances of peridynamics in fracture mechanics

ZHANG Heng¹,
ZHANG Xiong^{1
, ,},
QIAO Pizhong^{2
, ,}

1.
School of Aerospace, Tsinghua University, Beijing 100084, China
2.
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

More Information

Corresponding author: qiao@sjtu.edu.cn; xzhang@tsinghua.edu.cn

摘要

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.
- 近场动力学 /
- 断裂力学 /
- 裂纹扩展 /
- 键失效
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.
- peridynamics /
- fracture mechanics /
- crack growth /
- bond failure.

HTML全文

图 1 常规态近场动力学模型.

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图 2 近场动力学虚拟裂纹闭合技术 (Zhang H & Qiao 2020c).

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图 3 近场动力学J积分 (Hu W K et al. 2012a).

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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.

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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.

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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).

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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).

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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.

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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.

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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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