各向异性弹塑性有限变形的无网格SPH计算方法

doi:10.3901/JME.2021.18.153

机械工程学报 ›› 2021, Vol. 57 ›› Issue (18): 153-163.doi: 10.3901/JME.2021.18.153

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各向异性弹塑性有限变形的无网格SPH计算方法

李姣^1,2, 富芳艳³, 王广春¹, 管延锦^1,2, 赵国群¹, 林军¹

1. 山东大学材料液固结构演变与加工教育部重点实验室济南 250061;
2. 山东大学苏州研究院苏州 215123;
3. 上海航天设备制造总厂有限公司上海 200245

收稿日期:2021-03-11 修回日期:2021-06-21 出版日期:2021-09-20 发布日期:2021-11-30
通讯作者: 林军(通信作者),男,1986年出生,博士,副教授,博士研究生导师。主要研究方向为塑性成形新工艺及其装备,塑性成形CAE。E-mail:linjun@sdu.edu.cn
作者简介:李姣,女,1987年出生,博士研究生。主要研究方向为塑性成形新工艺及其装备。E-mail:lijiao_87@163.com
基金资助:
国家自然科学基金资助项目（52005299，51705291）。

Meshless SPH Method for Anisotropic Elasto-plastic Analysis

LI Jiao^1,2, FU Fangyan³, WANG Guangchun¹, GUAN Yanjin^1,2, ZHAO Guoqun¹, LIN Jun¹

1. Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials, Ministry of Education, Shandong University, Jinan 250061;
2. Suzhou Institute of Shandong University, Shandong University, Suzhou 215123;
3. Shanghai Aerospace Equipments Manufacturer Limited Company, Shanghai 200245

Received:2021-03-11 Revised:2021-06-21 Online:2021-09-20 Published:2021-11-30

摘要/Abstract

摘要： 基于无网格光滑粒子动力学方法（Smoothed particle hydrodynamics，SPH）方法，建立了各向异性弹塑性变形分析模型。首先利用移动最小二乘函数构建了SPH近似函数，提高了SPH方法计算精度；通过完全拉格朗日框架下的SPH形式不仅节约了计算时间，同时消除了传统SPH方法中的拉伸失稳现象。通过分析零能模式产生原因，引入了惩罚力来减小沙漏现象，提高了SPH方法的稳定性。利用上述修正的SPH方法离散了质量、动量及能量守恒方程，并采用一般的图形返回算法建立了基于Hill48屈服准则和Swift等向强化材料模型的各向异性本构关系，从而建立了各向异性弹塑性SPH分析模型。利用该模型进行各向异性材料的弹塑性变形分析，将获得的应力应变与有限元计算结果进行对比，验证了本文数值模拟模型稳定性和可靠性。

关键词: 光滑粒子动力学方法, 各向异性, 弹塑性, 移动最小二乘, 沙漏控制

Abstract: The meshless Smoothed Particle Hydrodynamics (SPH) method is extended for the anisotropic elasto-plastic analysis. The moving least square function is firstly introduced to construct the SPH approximation function to improve the computational precision. The total Lagrangian SPH formulation is applied to reduce the computational effort, as well as eliminated the tensile unstability problem in the conventional SPH method. The inherent zero-energy problem is suppressed by exerting an hour-glass control mechanism. The mass, momentum and energy conservation functions are constructed by the corrected SPH method, where the anisotropic stress-strain relationship is established by the mapping return algorithm based on the Hill48 yield criterion and Swift isotropic hardening model. Finally, several numerical examples are solved by the proposed anisotropic elasto-plastic SPH model, of which the stability and the effectiveness are verified by comparing the results with ones obtained from finite element analysis.

Key words: smoothed particle hydrodynamics, anisotropic, elasto-plastic, moving least square, hourglass control

中图分类号:

TG301

李姣, 富芳艳, 王广春, 管延锦, 赵国群, 林军. 各向异性弹塑性有限变形的无网格SPH计算方法[J]. 机械工程学报, 2021, 57(18): 153-163.

LI Jiao, FU Fangyan, WANG Guangchun, GUAN Yanjin, ZHAO Guoqun, LIN Jun. Meshless SPH Method for Anisotropic Elasto-plastic Analysis[J]. Journal of Mechanical Engineering, 2021, 57(18): 153-163.

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各向异性弹塑性有限变形的无网格SPH计算方法

Meshless SPH Method for Anisotropic Elasto-plastic Analysis

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