On the energy-minimizing strains in martensitic microstructures-Part 2: Geometrically linear theory

Michaël Peigney (1)

1 navier umr 8205 - Laboratoire Navier

This paper addresses the theoretical prediction of the quasiconvex hull of energy-minimizing (or stress-free) strains that can be realized by martensitic microstructure. Polyconvexification and related notions are used to derive some upper bounds (in the sense of inclusion). Lower bounds are obtained from lamination techniques. The geometrically linear setting (infinitesimal strains) is considered in the present Part 2. Three-, four-, and twelve-well problems are considered. In particular, the structure of the set of energy-minimizing strains in cubic to monoclinic transformations is investigated in detail. That investigation is notably supported by three-dimensional vizualisations obtained by considering four-well restrictions.

Mots clés: Microstructures; Lamination; Transformation de phase; Alliages à Mémoire de Forme; Minimisation énergetique

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Michaël Peigney. On the energy-minimizing strains in martensitic microstructures-Part 2: Geometrically linear theory. Journal of the Mechanics and Physics of Solids, 2013, 61 (6), pp.1511-1530. ⟨10.1016/j.jmps.2012.12.011⟩. ⟨hal-00813545⟩