A thermodynamically nonlocal damage model using a surface-residual-based nonlocal stress

IF 1.5 4区 工程技术 Q3 MECHANICS Journal of Mechanics Pub Date : 2021-07-21 DOI:10.1093/jom/ufab017
Liyang Huang, Yin Yao
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引用次数: 2

Abstract

In this research, a surface-residual-based nonlocal stress was introduced into nonlocal damage theory to describe the long-range actions among microstructures that were excluded in the definition of Cauchy stress. By using the surface-residual-based nonlocal stress tensor, a thermodynamically consistent nonlocal integral damage model was established to simulate the strain localization behavior for elastic-brittle damage problems. In this model, both the strain and the damage were taken as nonlocal variables in the free energy function, and the integral-type damage constitutive relationships and the evolution equation were derived via thermodynamic laws in order to ensure the self-consistency within the thermodynamic framework. Based on the nonlocal damage formulations using a real nonlocal stress concept, we simulated the strain localization phenomenon in an elastic bar subjected to uniaxial tension. The results showed clear localizing and softening features of strain in the damage zone, and the boundary effects arising from the nonlocal surface residual were illuminated. Furthermore, the strain localization behaviors for different internal characteristic lengths were simulated, through which we found that the characteristic length was comparable to the size of the strain localization zone.
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基于表面残余的非局部应力的热力学非局部损伤模型
本研究将基于表面残余的非局部应力引入非局部损伤理论,以描述柯西应力定义中不包括的微观结构之间的远程作用。利用基于表面残馀的非局部应力张量,建立了一种热力学一致的非局部积分损伤模型,模拟弹脆损伤问题的应变局部化行为。该模型将应变和损伤均作为自由能函数中的非局部变量,根据热力学规律推导出积分型损伤本构关系和演化方程,以保证在热力学框架内的自洽性。基于非局部损伤公式,采用真实非局部应力概念,模拟了弹性杆在单轴拉伸作用下的应变局部化现象。结果表明,损伤区应变具有明显的局部化和软化特征,揭示了非局部表面残余引起的边界效应。此外,模拟了不同内部特征长度下的应变局部化行为,发现特征长度与应变局部化区大小相当。
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来源期刊
Journal of Mechanics
Journal of Mechanics 物理-力学
CiteScore
3.20
自引率
11.80%
发文量
20
审稿时长
6 months
期刊介绍: The objective of the Journal of Mechanics is to provide an international forum to foster exchange of ideas among mechanics communities in different parts of world. The Journal of Mechanics publishes original research in all fields of theoretical and applied mechanics. The Journal especially welcomes papers that are related to recent technological advances. The contributions, which may be analytical, experimental or numerical, should be of significance to the progress of mechanics. Papers which are merely illustrations of established principles and procedures will generally not be accepted. Reports that are of technical interest are published as short articles. Review articles are published only by invitation.
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