Abstract
This paper deals with the possibility to model phase transitions by using a Maxwell's rate-type viscoelastic constitutive equation. Piecewise linear constitutive equations for elastic and viscoelastic cases are used in order to study the qualitative behaviour of phase transition phenomena. The discontinuous elastic solutions (of Goursat and Riemann problems), steady wave solutions and numerical solutions of the corresponding viscoelastic problems are compared and the viscoelastic solutions are found to approach the elastic solutions when the Maxwell's type viscosity coefficient increases. The viscoelastic model incorporates instabilities appropriate to describe phase transitions. The numerical method of characteristics used here to compute the viscoelastic solutions may lead to numerical instabilities. The way to isolate the numerical instabilities is also studied in this paper.
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