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In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.
The main aim of this paper is to analyze numerically the model behaviour of a granular material during loading and unloading. The model was originally proposed by D. Kolymbas and afterward modified by E. Bauer. For our purposes the constitutive equation was transformed into a rate independent form by introducing a dimensionless time parameter. By this transformation we were able to derive explicit formulas for the strain-stress trajectories during loading-unloading cycles and compare the results...
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