TITLE:
Wave Propagation in Compressible Polymeric Solids: Shock Physics
AUTHORS:
Karan S. Surana, Elie Abboud
KEYWORDS:
Shock Physics, Finite Strain, Finite Deformation, Rheology, Dissipation, Stress and Density Shocks, Finite Element Method, Space-Time Coupled
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.15 No.3,
September
23,
2025
ABSTRACT: In the work presented here, we investigate wave physics in compressible polymeric solids. The nonlinear system of partial differential equations is derived using classical continuum mechanics with appropriate strain and stress measures. Constitutive theories are derived using the representation theorem incorporating ordered rate damping and memory. The complete mathematical model is thermodynamically and mathematically consistent. The solutions of the initial value problems (IVPs) described by the mathematical model are obtained using a space-time coupled finite element method. Model problems and their solutions illustrate the nonlinear physics of wave propagation and shock formation. The research presented here on wave propagation in compressible polymeric solids for compressive loading is not available in the published works.