On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.3934/mine.2023021

L. Placidi, E. Barchiesi, F. dell’Isola, V. Maksimov, A. Misra, N. Rezaei, Angelo Scrofani, D. Timofeev

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引用次数: 12

Abstract

We report a continuum theory for 2D strain gradient materials accounting for a class of dissipation phenomena. The continuum description is constructed by means of a (reversible) placement function and by (irreversible) damage and plastic functions. Besides, expressions of elastic and dissipation energies have been assumed as well as the postulation of a hemi-variational principle. No flow rules have been assumed and plastic deformation is also compatible, that means it can be derived by a placement function. Strain gradient Partial Differential Equations (PDEs), boundary conditions (BCs) and Karush-Kuhn-Tucker (KKT) type conditions are derived by a hemi variational principle. PDEs and BCs govern the evolution of the placement descriptor and KKT conditions that of damage and plastic variables. Numerical experiments for the investigated homogeneous cases do not need the use of Finite Element simulations and have been performed to show the applicability of the model. In particular, the induced anisotropy of the response has been investigated and the coupling between damage and plasticity evolution has been shown.

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二维颗粒状弹塑性损伤应变梯度固体的半变分公式

我们报告了二维应变梯度材料的连续统理论，该理论考虑了一类耗散现象。连续体描述是通过(可逆)放置函数和(不可逆)损伤和塑性函数来构建的。此外，还假设了弹性能和耗散能的表达式以及半变分原理的假设。没有假定流动规律，塑性变形也是相容的，这意味着它可以由放置函数导出。利用半变分原理推导出应变梯度偏微分方程(PDEs)、边界条件(BCs)和Karush-Kuhn-Tucker (KKT)型条件。pde和BCs控制着放置描述符和KKT条件的演变，即损伤和塑性变量。所研究的均匀情况的数值实验不需要使用有限元模拟，并且已经进行了数值实验来证明该模型的适用性。特别地，研究了响应的诱导各向异性，并显示了损伤与塑性演化之间的耦合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.