Microstructures in phase-transitions of alloys are modeled by the energy minimization of a nonconvex energy density . Their time-evolution leads to a nonlinear wave equation with the non-monotone stress-strain relation plus proper boundary and initial conditions. This hyperbolic-elliptic initial-boundary value problem of changing types allows, in general, solely Young-measure solutions. This paper introduces a fully-numerical time-space discretization of this equation in a corresponding very weak sense. It is shown that discrete solutions exist and generate weakly convergent subsequences whose limit is a Young-measure solution. Numerical examples in one space dimension illustrate the time-evolving phase transitions and microstructures of a nonlinearly vibrating string.
@article{M2AN_2004__38_3_397_0, author = {Carstensen, Carsten and Rieger, Marc Oliver}, title = {Young-measure approximations for elastodynamics with non-monotone stress-strain relations}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {38}, year = {2004}, pages = {397-418}, doi = {10.1051/m2an:2004019}, mrnumber = {2075752}, zbl = {1130.74383}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_2004__38_3_397_0} }
Carstensen, Carsten; Rieger, Marc Oliver. Young-measure approximations for elastodynamics with non-monotone stress-strain relations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) pp. 397-418. doi : 10.1051/m2an:2004019. http://gdmltest.u-ga.fr/item/M2AN_2004__38_3_397_0/
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