A finite volume method for numerical simulations of adiabatic shear bands formation

Muratov, R. V.; Kudryashov, Nikolay A.; Ryabov, Pavel N.

doi:10.1016/j.cnsns.2021.105858

Cited by 10 publications

(1 citation statement)

References 23 publications

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“…Liu et al [23] modeled one-dimensional multi-material elastic-plastic flow using a Riemann solver. By using finite volume method with stationary grids in Eulerian frame, conservation laws and modified hypoelastic Wilkins model were solved to find the cause of adiabatic shear bands formation [24]. To understand seismic wave propagation, Sripanich et al [25] studied third-order elasticity.…”

Section: Introductionmentioning

confidence: 99%

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

Yang¹,

Lowe²

2023

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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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Section: Introductionmentioning

confidence: 99%