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On the elastic energy invariance of crystal twins
Arch. Mech. 62 (6), 441-464, 2010
Keywords: type 1; type 2; compound twinning; pseudoelasticity; nonconvex elastic energy; energy invariance
Abstract
An analysis by Zanzotto (1992, 1996) showed that, if crystal twinning is considered as a material symmetry operation, the symmetry groups of many crystals that form twins correspond to the unimodular group, which is the symmetry group of elastic fluids. It is therefore evident that an elastic modelling based on an elastic energy that includes any possible combination of twin system activation must fail. However, one may try to construct an elastic energy which includes only the stressfree configurations of the parent and the first order twins. It is known that, even under this restriction, many twinning modes exhibit an elastic energy invariance, which renders them indistinguishable in terms of the elastic energy. In this article, it is demonstrated that this energy invariance holds for all compound twins. The implications of the latter are discussed. It is suggested to distinguish between crystallographically equivalent and crystallographically distinct compound twins, since different implications regarding the elastic energy invariance emerge.