具有非局部库仑摩擦的非线性henky型材料热-电-机械耦合系统的分析与数值方法

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-05-19 DOI:10.1080/01630563.2023.2212496
El‐Hassan Benkhira, R. Fakhar, Y. Mandyly
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引用次数: 0

摘要

讨论了含温场对压电体与具有导热性和导电性的刚性基础接触过程的影响。假定材料的本构关系为热-电弹性关系,涉及非线性弹性本构henky定律。摩擦接触用sigorini条件、正则化库仑定律和正则化电导和导热条件进行建模。所得到的热-机电模型包括温度场作为一个额外的状态变量,以考虑热效应和压电效应。利用Schauder不动点定理,结合涉及非线性强单调Lipschitz连续算子的变分不等式理论的论证,证明了该问题弱解的存在性。提出了一种逐次迭代的数值求解方法,并证明了该方法的收敛性。增广拉格朗日的一种变体,即所谓的乘数交替方向法(ADMM),它将原问题分解为两个子问题,依次求解,并在每次迭代时更新对偶变量。通过图解说明了热边界条件对接触力和电势行为的影响。
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Analysis and Numerical Approach of a Coupled Thermo-Electro-Mechanical System for Nonlinear Hencky-Type Materials with Nonlocal Coulomb’s Friction
Abstract The effects of an included temperature field in the contact process between a piezoelectric body and a rigid foundation with thermal and electrical conductivity are discussed. The constitutive relation of the material is assumed to be thermo-electro-elastic and involves the nonlinear elastic constitutive Hencky’s law. The frictional contact is modeled with Signorini’s conditions, the regularized Coulomb law, and the regularized electrical and thermal conductivity conditions. The resulting thermo-electromechanical model includes the temperature field as an additional state variable to take into account thermal effects alongside with those of the piezoelectric. The existence of the unique weak solution to the problem is established by using Schauder’s fixed point theorem combined with arguments from the theory of variational inequalities involving nonlinear strongly monotone Lipschitz continuous operators. A successive iteration technique to solve the problem numerically is proposed, and its convergence is established. A variant of the Augmented Lagrangian, the so-called Alternating Direction Method of multipliers (ADMM), is used to decompose the original problem into two sub-problems, solve them sequentially and update the dual variables at each iteration. The influence of the thermal boundary condition on the behavior of contact forces and electrical potential is shown through graphical illustrations.
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来源期刊
Accounts of Chemical Research
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.
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