Abstract
This communication is concerned with the theoretical prediction of the recoverable strains (i.e. the strains that can be recovered by the shape memory effect) in polycrystalline SMAs. The analysis is carried out in the finite strain setting, considering a nonlinear elasticity model of phase transformation. The main results are some rigorous upper bounds on the set of recoverable strains. Those bounds depend on the polycrystalline texture through the volume fractions of the different orientations. A two-orientation polycrystal of tetragonal martensite is studied as an illustration. In that case, analytical expressions of the upper bounds are derived and the results are compared with lower bounds obtained by considering laminate textures. The issue of applying the proposed method to complex polycrystalline textures is commented on.
Highlights
A possible route to study the formation of microstructures in SMAs is to adopt a nonlinear elasticity model of phase transformation [1]
We focus on upper bounds of the recoverable strains of martensitic polycrystals, in the geometrically non-linear setting
The issue is to determine which deformation gradients in K + are recoverable for some polycrystalline texture that is compatible with the prescribed statistics
Summary
A possible route to study the formation of microstructures in SMAs is to adopt a nonlinear elasticity model of phase transformation [1]. A general method has been introduced in [16] for generating upper bounds on the set of macroscopic recoverable strains, assuming that the set of recoverable strains of the constitutive single crystals (or at least an upper bound on it) is known. The approach used in [16] is based on the translation method [17,18,19], which has proved to be a powerful tool in various problems related to homogenization [20,21,22]. In this communication, we first present in Sect.
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