Summary
We propose here a new model to the problem of phase transformations which account for micro-structural effects and non-equilibrium phenomena. The model is obtained by incorporating higher-order strain gradients in the relaxation function of a Maxwell's rate-type constitutive equation. This approach can be included in Šilhavý's thermodynamical theory of non-simple bodies with internal variables. Explicit necessary and sufficient conditions are given such that the model be fully compatible with the unmodified Clausius-Duhem inequality and balance equations. We show that its elastic set has to be the closure of an open set in the strain-stress-higher strain gradients space, i.e., the model is a viscoplastic one in the sense of Sokolovskii-Malvern. Energy estimates for smooth solutions of strain controlled problems are given. The influence of the “viscous mechanism”, “softening mechanism” and of the “strain gradients effects” on the local behaviour of solutions is investigated. Critical wave lengths for the onset of instability and pattern formation are determined.
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Făciu, C., Molinari, A. A non-local rate-type viscoplastic approach to patterning of deformation. Acta Mechanica 126, 71–99 (1998). https://doi.org/10.1007/BF01172800
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DOI: https://doi.org/10.1007/BF01172800