https://hal-enpc.archives-ouvertes.fr/hal-00813543Peigney, MichaëlMichaëlPeigneynavier umr 8205 - Laboratoire Navier - IFSTTAR - Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche ScientifiqueOn the energy-minimizing strains in martensitic microstructures-Part 1: Geometrically nonlinear theoryHAL CCSD2013Tranformations finiesBornes non linéairesTransformation de phaseRelaxation[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph][SPI.MECA.SOLID] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]Peigney, Michael2015-09-18 16:04:452022-01-15 03:49:122015-09-18 17:15:59enJournal articleshttps://hal-enpc.archives-ouvertes.fr/hal-00813543/document10.1016/j.jmps.2012.12.009application/pdf1This paper addresses the theoretical prediction of the quasiconvex hull of energy-minimizing strains that can be realized by martensitic microstructures. Polyconvexification and related notions are used to derive some upper bounds (in the sense of inclusion). Lower bounds are constructed by lamination techniques. The geometrically nonlinear theory (finite strains) is considered in the present Part 1. Analytical expressions are obtained for a three-well problem which encompasses the cubic to tetragonal transformation as a special case. Twelve-well problems related to cubic to monoclinic transformations are also studied. In that case, sufficient conditions are derived for the microstructure to be restricted to only two of the 12 wells