{"title":"软材料动态大变形分析的光滑总拉格朗日材料点法","authors":"Shun Zhang, Cunliang Pan, Zhijie Zhu, Wei Sun, Hongfei Ye, Yonggang Zheng","doi":"10.1002/nme.70132","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>A smoothed total Lagrangian material point method (STLMPM) is developed in this study to effectively simulate dynamic problems involving large deformation in nearly incompressible soft materials. In this method, the governing equations are spatially discretized within the framework of the total Lagrangian material point method (TLMPM) and temporally discretized using an explicit time integration scheme. To address the issue of decreased computational accuracy of the material point method (MPM) near physical domain boundaries, a Gaussian kernel function with kernel correction is employed to establish the interpolation formulas between particles and the background grid. Furthermore, to mitigate volumetric locking caused by the nearly incompressible nature of soft materials, the <b>F</b>-bar method is further developed within the framework of TLMPM. The accuracy and efficiency of the proposed STLMPM are demonstrated by several representative numerical examples, and the simulation results are compared with analytical solutions and other numerical methods.</p>\n </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 18","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Smoothed Total Lagrangian Material Point Method for Dynamic Large Deformation Analysis of Soft Materials\",\"authors\":\"Shun Zhang, Cunliang Pan, Zhijie Zhu, Wei Sun, Hongfei Ye, Yonggang Zheng\",\"doi\":\"10.1002/nme.70132\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>A smoothed total Lagrangian material point method (STLMPM) is developed in this study to effectively simulate dynamic problems involving large deformation in nearly incompressible soft materials. In this method, the governing equations are spatially discretized within the framework of the total Lagrangian material point method (TLMPM) and temporally discretized using an explicit time integration scheme. To address the issue of decreased computational accuracy of the material point method (MPM) near physical domain boundaries, a Gaussian kernel function with kernel correction is employed to establish the interpolation formulas between particles and the background grid. Furthermore, to mitigate volumetric locking caused by the nearly incompressible nature of soft materials, the <b>F</b>-bar method is further developed within the framework of TLMPM. The accuracy and efficiency of the proposed STLMPM are demonstrated by several representative numerical examples, and the simulation results are compared with analytical solutions and other numerical methods.</p>\\n </div>\",\"PeriodicalId\":13699,\"journal\":{\"name\":\"International Journal for Numerical Methods in Engineering\",\"volume\":\"126 18\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2025-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal for Numerical Methods in Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/nme.70132\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nme.70132","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
Smoothed Total Lagrangian Material Point Method for Dynamic Large Deformation Analysis of Soft Materials
A smoothed total Lagrangian material point method (STLMPM) is developed in this study to effectively simulate dynamic problems involving large deformation in nearly incompressible soft materials. In this method, the governing equations are spatially discretized within the framework of the total Lagrangian material point method (TLMPM) and temporally discretized using an explicit time integration scheme. To address the issue of decreased computational accuracy of the material point method (MPM) near physical domain boundaries, a Gaussian kernel function with kernel correction is employed to establish the interpolation formulas between particles and the background grid. Furthermore, to mitigate volumetric locking caused by the nearly incompressible nature of soft materials, the F-bar method is further developed within the framework of TLMPM. The accuracy and efficiency of the proposed STLMPM are demonstrated by several representative numerical examples, and the simulation results are compared with analytical solutions and other numerical methods.
期刊介绍:
The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems.
The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.