Evolution of Phase Transitions: A Continuum Theory by Abeyaratne R., Knowles J.K.

By Abeyaratne R., Knowles J.K.

This 2006 paintings started with the author's exploration of the applicability of the finite deformation conception of elasticity whilst quite a few typical assumptions akin to convexity of varied energies or ellipticity of the sector equations of equilibrium are relinquished. The finite deformation idea of elasticity seems to be a average motor vehicle for the examine of section transitions in solids the place thermal results should be overlooked. this article will be of curiosity to these attracted to the improvement and alertness of continuum-mechanical types that describe the macroscopic reaction of fabrics in a position to present process rigidity- or temperature-induced transitions among reliable levels. the point of interest is at the evolution of section transitions that could be both dynamic or quasi-static, managed through a kinetic relation which within the framework of classical thermomechanics represents info that's supplementary to the standard stability ideas and constitutive legislation of traditional thought

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1205–21. [5] R. K. Knowles, On the propagation of maximally dissipative phase boundaries in solids. Quarterly of Applied Mathematics, 50 (1992), pp. 149–72. K. Knowles, A note on the driving traction acting on a propagating interface: adiabatic and non-adiabatic processes of a continuum. ASME Journal of Applied Mechanics, 67 (2000), pp. 829–31. [7] R. Abeyaratne and S. Vedantam, A lattice-based model of the kinetics of twin boundary motion. Journal of the Mechanics and Physics of Solids, 51 (2003), pp.

131–58. K. Knowles and E. Sternberg, On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics. Journal of Elasticity, 8 (1978), pp. 329–79. V. C. Brown, Pseudo-elasticity and the strain–memory effect in an Ag-45 at. pct. Cd alloy. Metallurgical Transactions A, 4 (1973), pp. 423–9. [33] P. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, Regional Conference Series in Applied Mathematics, No. 11. SIAM, Philadelphia, PA, 1973.

Local minima of P(·, σ ) are identified with material phases, and so, if, for example, P has n energy wells at some stress σ , we say that the material may exist in n phases at that stress. The three quantities P, W , and σ have certain characteristic properties when associated with a two-phase material, that is, a material that can exist in either of two phases for some range of stress. Since the potential energy for such a material must have two local minima for stress in the appropriate range, we shall see that W must be nonconvex and the stress must be a nonmonotonic function of strain.

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