A cell-centered Lagrangian method is developed for elastic-plastic flows governed by
the Wilkins hypoelastic model. Its numerical fluxes are obtained from HLLC-type approximate Rie
mann solvers: the one-dimensional solver retains the elastic and plastic wave structure, while the two
dimensional solver contains elastic longitudinal, elastic shear and contact waves. Based on the local
one-dimensional wave classification, the sound speed in the wall-heating viscosity is modified so that the
added dissipation is better matched with the elastic-plastic wave pattern. This treatment reduces the
wall-heating error while keeping the resolution of the main wave profiles. A third-order WENO recon
struction is also applied to two-dimensional unstructured Lagrangian quadrilateral meshes, together with
a vertex velocity construction based on local momentum balance. Numerical tests show that the method
attains the expected order of accuracy for smooth problems and captures the principal wave structures
in typical elastic-plastic examples.
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