0392444 20240103202549.520130611235959.9 000319665800003 10.3934/nhm.2013.8.481 19 s. P cav_un_epca*00825371556-180182 (2013)481-499 hysteresis shape memory cav_un_auth*0291738 DeSimone A. IT cav_un_auth*0101142 Kružík Martin Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory 50 Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2013/MTR/kruzik-domain patterns and hysteresis in phase-transforming solids analysis and numerical simulations of a sharp interface dissipative model via phase-field approximation.pdf GAP201/12/0671 GA ČR CZ cav_un_auth*0289475 We propose a sharp-interface model which describes rate-independent hysteresis in phase-transforming solids (such as shape memory alloys) by resolving explicitly domain patterns and their dissipative evolution. We show that the governing Gibbs' energy functional is the $/Gamma$-limit of a family of regularized Gibbs' energies obtained through a phase-field approximation. This leads to the convergence of the solution of the quasistatic evolution problem associated with the regularized energy to the one corresponding to the sharp interface model. Based on this convergence result, we propose a numerical scheme which allows us to simulate mechanical experiments for both spatially homogeneous and heterogeneous samples. We use the latter to assess the role that impurities and defects may have in determining the response exhibited by real samples. In particular, our numerical results indicate that small heterogeneities are essential in order to obtain spatially localized nucleation of a new martensitic variant from a pre-existing one in stress-controlled experiments. 2014 BA 2 RVO:67985556 http://hdl.handle.net/11104/0221747 MATHEMATICSINTERDISCIPLINARYAPPLICATIONS 0.995 0.065 4.IX 0.00242 0.734 311 46 0.731 ScienceCitationIndexExpanded Q1 79.572 40.526 Q1 Q2 2013 000319665800003 WOS cav_un_epca*0082537 Networks and Heterogeneous Media 1556-1801 1556-181X Roč. 8 č. 2 2013 481 499