Modified G-L thermoelasticity theory for nonlinear longitudinal wave in a porous thermoelastic medium

This paper presents a nonlinear analysis of the transient response of a porous medium affected by external traction. The formulation is presented based on a new modified G-L theory of thermoelasticity while temperature and strain rate parameters are included in the governing equations. Based on the finite strain theory (FST), the Lagrangian strain–displacement equation and Second Piola-Kirchhoff stress are applied to express the generalized form of thermoelasticity equations including large deformation. Both mechanical and thermal shocks are applied and finally, the effects of loading rate on transient response are discussed. An updated finite element method and Newmark's numerical time integration method are employed to solve the nonlinear and time-dependent equations. It is determined that the modified G-L model is more powerful in predicting the wave propagation phenomenon. Furthermore, the findings indicate that the external surface shock induces compressive stresses, temperature raise, and volume fraction field increase in a porous medium. It is found compared to the classic model, the modified G-L model is superior in capturing the perceived wave propagation phenomenon.