Thermomechanical evolution of a microstructure

Authors:
Karl-Heinz Hoffmann and Tomáš Roubíček

Journal:
Quart. Appl. Math. **52** (1994), 721-737

MSC:
Primary 73B30; Secondary 35Q72, 73F15, 73S10, 73V25

DOI:
https://doi.org/10.1090/qam/1306046

MathSciNet review:
MR1306046

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Abstract | References | Similar Articles | Additional Information

Abstract: A nonisothermal microstructure evolution model, governed by a Helmholtz free energy which need not be convex as a function of deformations, is formulated by using a convexified geometry proposed already in [13]. A multidimensional but scalar case is treated. It is shown that, as a special case, this model includes the usual nonlinear thermo-visco-elasticity. In the case of an actual appearance of a microstructure, the existence of a weak solution to a partial linearized model is shown by a semi-implicit time discretization.

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DOI:
https://doi.org/10.1090/qam/1306046

Article copyright:
© Copyright 1994
American Mathematical Society