Numerical solution for a nonlinear, one-dimensional problem of thermoelasticity

A numerical solution for a nonlinear, one-dimensional boundary-value problem of thermoelasticity for the elastic half-space is presented. The resulting equations are discussed and the numerical method is investigated for stability. Comparison with other existing numerical schemes is carried out. The obtained results clearly indicate the process of shock formation. The presented figures show the effects of different nonlinear coupling constants on the distributions of the mechanical displacement and temperature in the medium. A special case is briefly discussed.