Predictions are made based on an analysis of a new nonlinear theory of martensitic transformations introduced by the authors. The crystal is modelled as a nonlinear elastic material, with a free-energy function that is invariant with respect to both rigid-body rotations and the appropriate crystallographic symmetries. The predictions concern primarily the two-well problem , that of determining all possible energy-minimizing deformations that can be obtained with two coherent and macroscopically unstressed variants of martensite. The set of possible macroscopic deformations obtained is completely determined by the lattice parameters of the material. For certain boundary conditions the total free energy does not attain a minimum , and the finer and finer oscillations of minimizing sequences are interpreted as corresponding to microstructure. The predictions are am enable to experimental tests. The proposed tests involve the comparison of the theoretical predictions with the mechanical response of properly oriented plates subject to simple shear.

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Magnetic coercivity is often viewed to be lower in alloys with negligible (or zero) values of the anisotropy constant. However, this explains little about the dramatic drop in coercivity in FeNi alloys at a non-zero anisotropy value. Here, we develop a theoretical and computational tool to investigate the fundamental interplay between material constants that govern coercivity in bulk magnetic alloys. The two distinguishing features of our coercivity tool are that: (a) we introduce a large localized disturbance, such as a spike-like magnetic domain, that provides a nucleation barrier for magnetization reversal; and (b) we account for magneto-elastic energy-however small-in addition to the anisotropy and magnetostatic energy terms. We apply this coercivity tool to show that the interactions between local instabilities and material constants, such as anisotropy and magnetostriction constants, are key factors that govern magnetic coercivity in bulk alloys. Using our model, we show that coercivity is minimum at the permalloy composition (Fe21.5Ni78.5) at which the alloy's anisotropy constant is not zero. We systematically vary the values of the anisotropy and magnetostriction constants, around the permalloy composition, and identify new combinations of material constants at which coercivity is small. More broadly, our coercivity tool provides a theoretical framework to potentially discover novel magnetic materials with low coercivity.

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