TITLE:
Shock Physics and Entropy Generation in Compressible Solids
AUTHORS:
Karan S. Surana, Stacia D. Zahn
KEYWORDS:
Elastic, Viscoelastic, Dissipation, Rheology, Entropy Generation, Shock Physics, Space-Time Finite Elements, Variationally Consistent, Wave Physics, Classical Continuum Mechanics, Conservation and Balance Laws
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.8,
August
10,
2026
ABSTRACT: This paper considers shock physics, entropy generation and associated thermal physics in compressible elastic, and thermoviscoelastic solid medium with and without rheology. The mathematical model containing nonlinear partial differential equations consists of conservation of mass and balance of linear momenta and energy equation derived using contravariant second Piola-Kirchhoff stress tensor and covariant Green’s strain tensor. This mathematical model is augmented with constitutive theories for contravariant second Piola-Kirchhoff stress tensor, heat vector and equation of state, thermodynamic pressure. The dissipation and rheology mechanisms are incorporated using rates of Green’s strain tensor up to orders n and rates of second Piola-Kirchhoff stress tensor up to orders m. Hence, the mathematical model contains spectra of dissipation coefficients and relaxation times. The solution of the mathematical model is obtained using space-time coupled finite element method based on space-time residual functional in which space-time local approximations are p-version hierarchical in higher order scalar product spaces, thus permitting desired orders of global differentiability of the approximations in space and time. The evolution is computed using a space-time strip for an increment of time followed by time marching. The space-time integral form in this approach is space-time variationally consistent, hence unconditionally stable computations are ensured during the entire evolution. Model problem studies are presented for one-dimensional wave propagation. Besides unconditional stability, other meritorious features of this computational methodology used here are discussed in the paper. Monitoring complex entropy generation and associated thermal physics in the presence of shock waves is a significant feature of the work presented here.