A variational formulation of rate-independent phase transformations using an extremum principle
UNSPECIFIED. (2002) A variational formulation of rate-independent phase transformations using an extremum principle. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 162 (2). pp. 137-177. ISSN 0003-9527Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s002050200194
We propose a rate-independent, mesoscopic model for the hysteretic evolution of phase transformations in shape-memory alloys. The model uses the deformation and phase-indicator function as basic unknowns and the potentials for the elastic energy and for the dissipation as constitutive laws. Using the associated functionals, admissible processes are defined to be the ones which are stable at all times and which satisfy the energy inequality.
This concept leads to a natural time-incremental method which consists in a minimization problem. The mesoscopic model is obtained by a relaxation procedure. It leads to new functionals involving the cross-quasiconvexification of the elastic stored-energy density. For a special case involving two phases of linearized elastic materials we show that the incremental problem provides existence of admissible processes for the time-continuous problem, if we let the time-step go to 0.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
|Journal or Publication Title:||ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS|
|Official Date:||April 2002|
|Number of Pages:||41|
|Page Range:||pp. 137-177|
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