13 June 1997 Evolution of equilibrium microstructures in adaptive materials
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Uniaxial deformation of an adaptive material which can change its microstructure due to a phase transformation is considered. At fixed temperature and fixed surface displacement the phase transformation results in an equilibrium two-phase mixture. A typical equilibrium two- phase microstructure of an initial and a product phase is an alteration of the plane-parallel layers of the phases with a special crystallographic orientation of interfaces between layers. The relative fractions of the phases are determined by the external conditions. The two-phase free energy is a non-convex function of constrained strain. Therefore, the stress-strain relation at displacement controlled deformation of the transforming two-phase mixture is characterized by a negative Young's modulus. If deformation proceeds under stress control, a hysteretic stress-strain curve on loading and unloading should be observed instead of a negative stress-strain slope.
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Julia Slutsker, Julia Slutsker, Alexander L. Roytburd, Alexander L. Roytburd, } "Evolution of equilibrium microstructures in adaptive materials", Proc. SPIE 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, (13 June 1997); doi: 10.1117/12.276563; https://doi.org/10.1117/12.276563

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