The complete exact Riemann solution for one-dimensional elastic–perfectly plastic Riemann problem

Xiao, Li; Zhai, Jiayin; Shen, Zhijun

doi:10.1016/j.cma.2021.114346

Cited by 4 publications

(1 citation statement)

References 19 publications

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“…Aided with a high-order and pressure oscillating-free scheme, Eulerian description of conservation laws as well as a hyper-elastic framework were also used to understanding multi-material elastic-plastic flow [33,34]. Similar elastic-plastic wave propagation problems were also investigated with slightly different form of conservation laws, transport equation, or constitutive models in Eulerian frame [35][36][37]. Based on multi-material diffuse interface method, Wallis et al [38] studied elasto-plastic-rigid body interaction using Eulerian conservation laws for solid-fluid interaction which were derived by Barton [39].…”

Section: Introductionmentioning

confidence: 99%

Simulation of Wave in Hypo-Elastic-Plastic Solids Modeled by Eulerian Conservation Laws

Yang¹,

Lowe²

2023

Preprint

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This paper reports a theoretical and numerical framework to model nonlinear waves in elastic-plastic solids. Formulated in the Eulerian frame, the governing equations employed include the continuity equation, the momentum equation, and an elastic-plastic constitutive relation. The complete governing equations are a set of first-order, fully coupled partial differential equations with source terms. The primary unknowns are velocities and deviatoric stresses. By casting the governing equations into a vector-matrix form, we derive the eigenvalues of the Jacobian matrix to show the wave speeds. The eigenvalues are also used to calculate the Courant number for numerical stability. The model equations are solved using the Space-Time Conservation Element and Solution Element (CESE) method. The approach is validated by comparing our numerical results to an analytical solution for the special case of longitudinal wave motion.

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