{"title":"弹塑性固体接触问题的异步变量积分器","authors":"Zongwu Niu, Zixiao Wang, Yongxing Shen","doi":"10.1007/s10338-023-00456-2","DOIUrl":null,"url":null,"abstract":"<div><p>Simulations of contact problems involving at least one plastic solid may be costly due to their strong nonlinearity and requirements of stability. In this work, we develop an explicit asynchronous variational integrator (AVI) for inelastic non-frictional contact problems involving a plastic solid. The AVI assigns each element in the mesh an independent time step and updates the solution at the elements and nodes asynchronously. This asynchrony makes the AVI highly efficient in solving such bi-material problems. Taking advantage of the AVI, the constitutive update is locally performed in one element at a time, and contact constraints are also enforced on only one element. The time step of the contact element is subdivided into multiple segments, and the fields are updated accordingly. During a contact event, only one element involving a few degrees of freedom is considered, leading to high efficiency. The proposed formulation is first verified with a pure elastodynamics benchmark and further applied to a contact problem involving an elastoplastic solid with non-associative volumetric hardening. The numerical results indicate that the AVI exhibits excellent energy behaviors and has high computational efficiency.</p></div>","PeriodicalId":50892,"journal":{"name":"Acta Mechanica Solida Sinica","volume":"37 2","pages":"305 - 315"},"PeriodicalIF":2.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Asynchronous Variational Integrator for Contact Problems Involving Elastoplastic Solids\",\"authors\":\"Zongwu Niu, Zixiao Wang, Yongxing Shen\",\"doi\":\"10.1007/s10338-023-00456-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Simulations of contact problems involving at least one plastic solid may be costly due to their strong nonlinearity and requirements of stability. In this work, we develop an explicit asynchronous variational integrator (AVI) for inelastic non-frictional contact problems involving a plastic solid. The AVI assigns each element in the mesh an independent time step and updates the solution at the elements and nodes asynchronously. This asynchrony makes the AVI highly efficient in solving such bi-material problems. Taking advantage of the AVI, the constitutive update is locally performed in one element at a time, and contact constraints are also enforced on only one element. The time step of the contact element is subdivided into multiple segments, and the fields are updated accordingly. During a contact event, only one element involving a few degrees of freedom is considered, leading to high efficiency. The proposed formulation is first verified with a pure elastodynamics benchmark and further applied to a contact problem involving an elastoplastic solid with non-associative volumetric hardening. The numerical results indicate that the AVI exhibits excellent energy behaviors and has high computational efficiency.</p></div>\",\"PeriodicalId\":50892,\"journal\":{\"name\":\"Acta Mechanica Solida Sinica\",\"volume\":\"37 2\",\"pages\":\"305 - 315\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mechanica Solida Sinica\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10338-023-00456-2\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica Solida Sinica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10338-023-00456-2","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
摘要 由于接触问题具有很强的非线性和稳定性要求,对至少涉及一个塑性固体的接触问题进行模拟的成本可能很高。在这项工作中,我们为涉及塑性固体的非弹性非摩擦接触问题开发了一种显式异步变分积分器(AVI)。AVI 为网格中的每个元素分配一个独立的时间步长,并异步更新元素和节点的解。这种异步性使得 AVI 在解决此类双材料问题时非常高效。利用 AVI 的优势,构成更新每次只在一个元素上局部执行,接触约束也只在一个元素上执行。接触元素的时间步长被细分为多个部分,并相应地更新字段。在一个接触事件中,只考虑一个涉及几个自由度的元素,因此效率很高。我们首先用纯弹性动力学基准验证了所提出的计算方法,然后将其进一步应用于涉及具有非关联体积硬化的弹塑性固体的接触问题。数值结果表明,AVI 具有出色的能量表现和较高的计算效率。
An Asynchronous Variational Integrator for Contact Problems Involving Elastoplastic Solids
Simulations of contact problems involving at least one plastic solid may be costly due to their strong nonlinearity and requirements of stability. In this work, we develop an explicit asynchronous variational integrator (AVI) for inelastic non-frictional contact problems involving a plastic solid. The AVI assigns each element in the mesh an independent time step and updates the solution at the elements and nodes asynchronously. This asynchrony makes the AVI highly efficient in solving such bi-material problems. Taking advantage of the AVI, the constitutive update is locally performed in one element at a time, and contact constraints are also enforced on only one element. The time step of the contact element is subdivided into multiple segments, and the fields are updated accordingly. During a contact event, only one element involving a few degrees of freedom is considered, leading to high efficiency. The proposed formulation is first verified with a pure elastodynamics benchmark and further applied to a contact problem involving an elastoplastic solid with non-associative volumetric hardening. The numerical results indicate that the AVI exhibits excellent energy behaviors and has high computational efficiency.
期刊介绍:
Acta Mechanica Solida Sinica aims to become the best journal of solid mechanics in China and a worldwide well-known one in the field of mechanics, by providing original, perspective and even breakthrough theories and methods for the research on solid mechanics.
The Journal is devoted to the publication of research papers in English in all fields of solid-state mechanics and its related disciplines in science, technology and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. Articles, Short Communications, Discussions on previously published papers, and invitation-based Reviews are published bimonthly. The maximum length of an article is 30 pages, including equations, figures and tables