Virtual element method for solving a viscoelastic contact problem with long memory

IF 1.7 4区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Mathematics and Mechanics of Solids Pub Date : 2024-08-14 DOI:10.1177/10812865241263039
Wenqiang Xiao, Min Ling
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Abstract

In this paper, we use the virtual element method to solve a history-dependent hemivariational inequality arising in contact problems. The contact problem concerns the deformation of a viscoelastic body with long memory, subjected to a contact condition with non-monotone normal compliance and unilateral constraints. A fully discrete scheme based on the trapezoidal rule for the discretization of the time integration and the virtual element method for the spatial discretization are analyzed. We provide a unified priori error analysis for both internal and external approximations. For the linear virtual element method, we obtain the optimal order error estimate. Finally, three numerical examples are reported, providing numerical evidence of the theoretically predicted optimal convergence orders.
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解决长记忆粘弹性接触问题的虚拟元素法
在本文中,我们使用虚拟元素法解决了接触问题中出现的与历史相关的半变量不等式。接触问题涉及具有长记忆的粘弹性体在非单调法向顺应性和单边约束的接触条件下的变形。我们分析了基于梯形法则的时间积分离散化完全离散方案和用于空间离散化的虚拟元素法。我们为内部和外部近似提供了统一的先验误差分析。对于线性虚拟元素法,我们获得了最优阶误差估计。最后,报告了三个数值示例,为理论预测的最佳收敛阶数提供了数值证据。
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来源期刊
Mathematics and Mechanics of Solids
Mathematics and Mechanics of Solids 工程技术-材料科学:综合
CiteScore
4.80
自引率
19.20%
发文量
159
审稿时长
1 months
期刊介绍: Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science. The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).
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