Geodesic
Evolution model for martensitic phase transformation in shape-memory alloys
Tomáš Roubíček1 orcid
1Charles University, Praha, Czech Republic
Interfaces and free boundaries, Tome 4 (2002) no. 2, pp. 111-136

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DOI

A mesoscopical-level model for the evolution of microstructure in simple-laminate martensite undergoing an isothermal phase-transformation process within the context of a uniaxial deformation is proposed using a Hamiltonian approach to a relaxed problem involving a Young-measure-valued deformation gradient and Hill's maximum-dissipation principle involving positive homogeneous dissipation potential which reflects the energy needed for (and dissipated by) a phase transformation. A regularization by adding a (modified) volume-fraction gradient, which can be understood as a limit Ericksen-Timoshenko beam-like construction, is considered to ensure existence of a weak solution for a slow-process model. A numerical algorithm and computational experiments are also presented.
DOI : 10.4171/ifb/55
Classification : 46-XX, 60-XX
Mots-clés : Twinning; martensite; quasiplasticity; nonconvex scalar variational problems; double-well problem; relaxation; Young measures; evolution; dissipation; activation

Tomáš Roubíček  1

1 Charles University, Praha, Czech Republic 
Tomáš Roubíček. Evolution model for martensitic phase transformation in shape-memory alloys. Interfaces and free boundaries, Tome 4 (2002) no. 2, pp. 111-136. doi: 10.4171/ifb/55
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     title = {Evolution model for martensitic phase transformation in shape-memory alloys},
     journal = {Interfaces and free boundaries},
     pages = {111--136},
     year = {2002},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/55/}
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