TITLE:
Tensile Shock Physics in Compressible Thermoviscoelastic Solids with Rheology
AUTHORS:
Karan S. Surana, Elie Abboud
KEYWORDS:
Tensile Shock Physics, Rheology, Thermoviscoelastic, Space-Time Coupled, Space-Time Residual Functional, Conservation and Balance Laws, Tensile Wave, Finite Element Method, Scalar Product Spaces
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.12,
December
19,
2024
ABSTRACT: The paper addresses tensile shock physics in compressible thermoviscoelastic solids with rheology i.e., in compressible polymeric solids. Polymeric solids have elasticity, dissipation mechanisms and relaxation phenomena due to the presence of long chain molecules in the viscous medium. Thus, the main focus of this investigation is to study how the presence of rheology influences tensile shock physics compared to the tensile shock physics in thermoelastic solids with same elasticity and dissipation but without rheology. A traveling stress wave in polymeric solids leaves nonzero stress signature behind it that naturally influences density. Complete relaxation of the nonzero signatures of stress and associated density change depends upon viscosity of the medium, Deborah number, strength of the stress or velocity wave etc. These aspects of the tensile shock physics in TVES with rheology are investigated in the paper. The mathematical model for finite deformation, finite strain is derived using CBL and CCM, and constitutive theories are derived using conjugate pairs in the entropy inequality and the representation theorem. This mathematical model is thermodynamically and mathematically consistent and has closure. The solution of the IVPs described by this mathematical model related to tensile shock physics in TVES with memory are obtained using space-time coupled finite element method based on space-time residual functional for a space-time strip with time marching. p-version hierarchical space-time local approximations with higher order global differentiability in hpk-scalar product spaces and use of minimally conforming spaces ensure that all space-time integrals over space-time discretization are Riemann. This facilitates more accurate description of the physics in the computational process. Model problem studies are presented to illustrate various aspects of tensile shock physics in compressible TVES with rheology.