Shocks and induced discontinuities in materials with internal state variables ? Applications to finite linear viscoelasticity

Abstract

In this paper, we derive the coupled governing differential equations of shock amplitudes and induced discontinuities in materials with internal state variables. For the special case of finite linear viscoelasticity and weak shocks and under physically reasonable conditions, two examples of the solutions of the coupled equations are given. In the first example, the solutions of the shock and the induced discontinuity approach finite nonzero values in an oscillatory manner, very much akin to the forced vibrations of springmass-damper systems. In the second example, both solutions decay monotonically to zero.