An incremental variational approach to coupled thermo-mechanical problems in anelastic solids. Application to shape-memory alloys
PEIGNEY ; SEGUIN
Type de document
ARTICLE A COMITE DE LECTURE REPERTORIE DANS BDI (ACL)
Langue
anglais
Auteur
PEIGNEY ; SEGUIN
Résumé / Abstract
We study the coupled thermo-mechanical problem that is obtained by combining generalized standard materials with Fourier's law for heat conduction. The analysis is conducted in the framework of nonsmooth mechanics in order to account for possible constraints on the state variables. This allows models of damage and phase-transformation to be included in the analysis. In view of performing numerical simulations, an incremental thermo-mechanical problem and corresponding variational principles are introduced. Conditions for existence of solutions to the incremental problem are discussed and compared with the isothermal case. The numerical implementation of the proposed approach is studied in detail. In particular, it is shown that the incremental thermo-mechanical problem can be recast as a concave maximization problem and ultimately amounts to solve a sequence of linear thermal problems and purely mechanical (i.e. at a prescribed temperature ?eld) problems. Therefore, using the proposed approach, thermo-mechanical coupling can be implemented with low additional complexity compared to the isothermal case, while still relying on a sound mathematical framework. As an application, thermo-mechanical coupling in shape memory alloys is studied. The in?uence of the loading strain-rate on the phase transformation and on the overall stress-strain response is investigated, as well as the in?uence of the thermal boundary conditions. The numerical results obtained by the proposed approach are compared with numerical and experimental results from the literature.
Source
International Journal of Solids and Structures, num. 24, pp. 4043-4054 p.
Editeur
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