{"title":"An implicit material point method using a cell-based integration scheme for large deformation static problems","authors":"Jae-Uk Song, Hyun-Gyu Kim","doi":"10.1007/s40571-024-00720-3","DOIUrl":null,"url":null,"abstract":"<p>A novel implicit material point method (MPM) using a cell-based integration scheme is proposed to solve large deformation static problems. An incremental weak form based on the updated Lagrangian approach is formulated for the implicit MPM. The volume integrals of the incremental weak form are evaluated at the integration points of grid cells instead of material points, which eliminates the cell-crossing error and reduces the integration error in MPM computations. Grid cells are equally sub-divided into grid cell sub-domains. The centers and the particle volumes of the grid cell sub-domains are, respectively, taken as the integration points and corresponding weights for the numerical integration of the incremental weak form. Particle information is transferred through grid nodes to the integration points of grid cells by using grid shape functions. A volume-weighted nodal averaging scheme is used for transferring the deformation gradient from material particles to grid nodes to correctly consider the particle volumes associated with the deformation gradient. Numerical results show that the present implicit MPM can effectively and efficiently solve large deformation static problems.</p>","PeriodicalId":524,"journal":{"name":"Computational Particle Mechanics","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Particle Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s40571-024-00720-3","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
A novel implicit material point method (MPM) using a cell-based integration scheme is proposed to solve large deformation static problems. An incremental weak form based on the updated Lagrangian approach is formulated for the implicit MPM. The volume integrals of the incremental weak form are evaluated at the integration points of grid cells instead of material points, which eliminates the cell-crossing error and reduces the integration error in MPM computations. Grid cells are equally sub-divided into grid cell sub-domains. The centers and the particle volumes of the grid cell sub-domains are, respectively, taken as the integration points and corresponding weights for the numerical integration of the incremental weak form. Particle information is transferred through grid nodes to the integration points of grid cells by using grid shape functions. A volume-weighted nodal averaging scheme is used for transferring the deformation gradient from material particles to grid nodes to correctly consider the particle volumes associated with the deformation gradient. Numerical results show that the present implicit MPM can effectively and efficiently solve large deformation static problems.
期刊介绍:
GENERAL OBJECTIVES: Computational Particle Mechanics (CPM) is a quarterly journal with the goal of publishing full-length original articles addressing the modeling and simulation of systems involving particles and particle methods. The goal is to enhance communication among researchers in the applied sciences who use "particles'''' in one form or another in their research.
SPECIFIC OBJECTIVES: Particle-based materials and numerical methods have become wide-spread in the natural and applied sciences, engineering, biology. The term "particle methods/mechanics'''' has now come to imply several different things to researchers in the 21st century, including:
(a) Particles as a physical unit in granular media, particulate flows, plasmas, swarms, etc.,
(b) Particles representing material phases in continua at the meso-, micro-and nano-scale and
(c) Particles as a discretization unit in continua and discontinua in numerical methods such as
Discrete Element Methods (DEM), Particle Finite Element Methods (PFEM), Molecular Dynamics (MD), and Smoothed Particle Hydrodynamics (SPH), to name a few.