The linear constitutive relations and the failure criteria of composite mat
erials made of thermoviscoelastic solids are presented. The post-failure ma
terial behavior is proposed and the dynamic finite element equations are fo
rmulated. However, a nonlinear term is kept in the energy equation because
it represents the effect of the second law of thermodynamics. A general pur
pose nonlinear three-dimensional dynamic finite element program COMPASS is
upgraded and employed in this work to investigate the interdependence among
stress wave propagation, stress concentration, failure progression and tem
perature elevation in composite materials. The consequence of truthfully in
corporating the second law of thermodynamics is clearly observed: it will a
lways cause temperature rise if there exists a dynamic mechanical process.