Year: 2020
Author: Ruo Li, Yanli Wang, Chengbao Yao
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 212–250
Abstract
We propose a robust approximate solver for the hydro-elastoplastic solid material, a general constitutive law extensively applied in explosion and high speed impact dynamics, and provide a natural transformation between the fluid and solid in the case of phase transitions. The hydrostatic components of the solid is described by a family of general Mie-Grüneisen equation of state (EOS), while the deviatoric component includes the elastic phase, linearly hardened plastic phase and fluid phase. The approximate solver provides the interface stress and normal velocity by an iterative method. The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state. The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds. Several numerical examples, including Riemann problems, shock-bubble interactions, implosions and high speed impact applications, are presented to validate the approximate solver.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0039
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 212–250
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 39
Keywords: Riemann solver Mie-Grüneisen hydro-elastoplastic solid multi-medium flow.
Author Details
-
Elastic Hugoniot curve of one-dimensional Wilkins model with general Grüneisen-type equation of state
Li, Xiao | Zhai, Jiayin | Shen, ZhijunJournal of Computational Physics, Vol. 464 (2022), Iss. P.111337
https://doi.org/10.1016/j.jcp.2022.111337 [Citations: 0] -
The complete exact Riemann solution for one-dimensional elastic–perfectly plastic Riemann problem
Li, Xiao | Zhai, Jiayin | Shen, ZhijunComputer Methods in Applied Mechanics and Engineering, Vol. 390 (2022), Iss. P.114346
https://doi.org/10.1016/j.cma.2021.114346 [Citations: 2] -
An HLLC-type approximate Riemann solver for two-dimensional elastic-perfectly plastic model
Li, Xiao | Zhai, Jiayin | Shen, ZhijunJournal of Computational Physics, Vol. 448 (2022), Iss. P.110675
https://doi.org/10.1016/j.jcp.2021.110675 [Citations: 3] -
Harten-Lax-van Leer-discontinuities with elastic waves (HLLD-e) approximate Riemann solver for two-dimensional elastic-plastic flows with slip/no-slip interface boundary conditions
Zhao, Fuyu | Wang, Cheng | Jia, Xiyu | Wang, WanliComputers & Fluids, Vol. 265 (2023), Iss. P.106015
https://doi.org/10.1016/j.compfluid.2023.106015 [Citations: 2]