arrow
Volume 14, Issue 3
A Cell-Centered Lagrangian Scheme with an Elastic-Perfectly Plastic Solid Riemann Solver for Wave Propagations in Solids

Qian Chen, Li Li, Jin Qi, Zhiqiang Zeng, Baolin Tian & Tiegang Liu

Adv. Appl. Math. Mech., 14 (2022), pp. 703-724.

Published online: 2022-02

Export citation
  • Abstract

A cell-centered Lagrangian scheme is developed for the numerical simulation of wave propagations in one dimensional (1D) elastic-plastic flow. The classical elastic-plastic material model initially proposed by Wilkins is adopted. The linear elastic model (Hooke’s Law), perfectly plastic model and von Mises yield criterion are used to describe the constitutive relationship of elastic-plastic solid. The second-order extension of this scheme is achieved by a linear reconstruction method. Various numerical tests are simulated to check the capability of this scheme in capturing nonlinear elastic-plastic waves. Compared with the well-developed operator splitting method used in simulating elastic-plastic flow, this scheme is more accurate due to the consideration of a list of 64 different types of the nonlinear elastic-plastic waves when constructing the elastic-perfectly plastic Riemann solver. The numerical simulations of typical examples show competitive results.

  • Keywords

Elastic-plastic flow, cell-centered Lagrangian scheme, elastic-perfectly solid Riemann problem, wave propagation.

  • AMS Subject Headings

35Q74, 74B10, 74C05, 74M20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-14-703, author = {Chen , QianLi , LiQi , JinZeng , ZhiqiangTian , Baolin and Liu , Tiegang}, title = {A Cell-Centered Lagrangian Scheme with an Elastic-Perfectly Plastic Solid Riemann Solver for Wave Propagations in Solids}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {3}, pages = {703--724}, abstract = {

A cell-centered Lagrangian scheme is developed for the numerical simulation of wave propagations in one dimensional (1D) elastic-plastic flow. The classical elastic-plastic material model initially proposed by Wilkins is adopted. The linear elastic model (Hooke’s Law), perfectly plastic model and von Mises yield criterion are used to describe the constitutive relationship of elastic-plastic solid. The second-order extension of this scheme is achieved by a linear reconstruction method. Various numerical tests are simulated to check the capability of this scheme in capturing nonlinear elastic-plastic waves. Compared with the well-developed operator splitting method used in simulating elastic-plastic flow, this scheme is more accurate due to the consideration of a list of 64 different types of the nonlinear elastic-plastic waves when constructing the elastic-perfectly plastic Riemann solver. The numerical simulations of typical examples show competitive results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0344}, url = {http://global-sci.org/intro/article_detail/aamm/20281.html} }
TY - JOUR T1 - A Cell-Centered Lagrangian Scheme with an Elastic-Perfectly Plastic Solid Riemann Solver for Wave Propagations in Solids AU - Chen , Qian AU - Li , Li AU - Qi , Jin AU - Zeng , Zhiqiang AU - Tian , Baolin AU - Liu , Tiegang JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 703 EP - 724 PY - 2022 DA - 2022/02 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0344 UR - https://global-sci.org/intro/article_detail/aamm/20281.html KW - Elastic-plastic flow, cell-centered Lagrangian scheme, elastic-perfectly solid Riemann problem, wave propagation. AB -

A cell-centered Lagrangian scheme is developed for the numerical simulation of wave propagations in one dimensional (1D) elastic-plastic flow. The classical elastic-plastic material model initially proposed by Wilkins is adopted. The linear elastic model (Hooke’s Law), perfectly plastic model and von Mises yield criterion are used to describe the constitutive relationship of elastic-plastic solid. The second-order extension of this scheme is achieved by a linear reconstruction method. Various numerical tests are simulated to check the capability of this scheme in capturing nonlinear elastic-plastic waves. Compared with the well-developed operator splitting method used in simulating elastic-plastic flow, this scheme is more accurate due to the consideration of a list of 64 different types of the nonlinear elastic-plastic waves when constructing the elastic-perfectly plastic Riemann solver. The numerical simulations of typical examples show competitive results.

Qian Chen, Li Li, Jin Qi, Zhiqiang Zeng, Baolin Tian & Tiegang Liu. (2022). A Cell-Centered Lagrangian Scheme with an Elastic-Perfectly Plastic Solid Riemann Solver for Wave Propagations in Solids. Advances in Applied Mathematics and Mechanics. 14 (3). 703-724. doi:10.4208/aamm.OA-2020-0344
Copy to clipboard
The citation has been copied to your clipboard