Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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: 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

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