{"title":"基于节点的弹塑性固体均匀应变虚拟元素法","authors":"Rodrigo Silva-Valenzuela, Alejandro Ortiz-Bernardin, Edoardo Artioli","doi":"arxiv-2409.10808","DOIUrl":null,"url":null,"abstract":"A recently proposed node-based uniform strain virtual element method (NVEM)\nis here extended to small strain elastoplastic solids. In the proposed method,\nthe strain is averaged at the nodes from the strain of surrounding\nlinearly-precise virtual elements using a generalization to virtual elements of\nthe node-based uniform strain approach for finite elements. The averaged strain\nis then used to sample the weak form at the nodes of the mesh leading to a\nmethod in which all the field variables, including state and history-dependent\nvariables, are related to the nodes and thus they are tracked only at these\nlocations during the nonlinear computations. Through various elastoplastic\nbenchmark problems, we demonstrate that the NVEM is locking-free while enabling\nlinearly-precise virtual elements to solve elastoplastic solids with accuracy.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A node-based uniform strain virtual element method for elastoplastic solids\",\"authors\":\"Rodrigo Silva-Valenzuela, Alejandro Ortiz-Bernardin, Edoardo Artioli\",\"doi\":\"arxiv-2409.10808\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A recently proposed node-based uniform strain virtual element method (NVEM)\\nis here extended to small strain elastoplastic solids. In the proposed method,\\nthe strain is averaged at the nodes from the strain of surrounding\\nlinearly-precise virtual elements using a generalization to virtual elements of\\nthe node-based uniform strain approach for finite elements. The averaged strain\\nis then used to sample the weak form at the nodes of the mesh leading to a\\nmethod in which all the field variables, including state and history-dependent\\nvariables, are related to the nodes and thus they are tracked only at these\\nlocations during the nonlinear computations. Through various elastoplastic\\nbenchmark problems, we demonstrate that the NVEM is locking-free while enabling\\nlinearly-precise virtual elements to solve elastoplastic solids with accuracy.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10808\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10808","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A node-based uniform strain virtual element method for elastoplastic solids
A recently proposed node-based uniform strain virtual element method (NVEM)
is here extended to small strain elastoplastic solids. In the proposed method,
the strain is averaged at the nodes from the strain of surrounding
linearly-precise virtual elements using a generalization to virtual elements of
the node-based uniform strain approach for finite elements. The averaged strain
is then used to sample the weak form at the nodes of the mesh leading to a
method in which all the field variables, including state and history-dependent
variables, are related to the nodes and thus they are tracked only at these
locations during the nonlinear computations. Through various elastoplastic
benchmark problems, we demonstrate that the NVEM is locking-free while enabling
linearly-precise virtual elements to solve elastoplastic solids with accuracy.