Abstract
Some models of phase equilibria as local minima of a Lagrangian functional are shown to allow configurations where macroscopic strain is generally discontinuous, but internal variables (and derivatives) vary smoothly across the ‘phases’. The stability properties of ‘regularizations’ of such equilibria are also investigated.
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References
Richman R.H.: The diversity of twinning in body-centred cubic structures, in Deformation Twinning, ed., R.E. Reed-Hill, J.P. Hirth and H.C. Rogers, Gordon and Breach Science Publishers Inc., New York, London (1964).
James R.D.: Finite deformation by mechanical twinning, Arch. Rational Mech. Anal. 77 (1981) 143–176.
Parry, G.P.: Coexistent austenitic and martensitic phases in elastic crystals, to appear in the proceedings of the 5th International Symposium on Continuum Models of Discrete Systems, ed., A.J.M. Spencer, A.A. Balkema, Rotterdam.
Coleman B.D. and Gurtin M.E.: Thermodynamics with internal state variables. J. Chem. Phys. 47 (1967) 597–613.
Pouget, J. and Maugin, G.A.: Solitons and electroacoustic interactions in ferroelectric crystals-I: Single solitons and domain walls, to appear.
Aifantis E.C.: A proposal for continuum with microstructure, Mech. Res. Comm. 5 (1978) 139–145.
Toupin R.A.: Theories of elasticity with couple-stress. Arch. Rational Mech. Anal. 17 (1964) 85–112.
Weinberger, H.F.: A simple system with a continuum of stable inhomogeneous steady states, Institute for Mathematics and its Applications Preprint Series #6, University of Minnesota (1982). To appear in the proceedings of the United States—Japan Seminar on Nonlinear Partial Differential Equations, ed., H. Fujita, Lecture Notes in Numerical and Applied Analysis, North Holland Publishing Co., Amsterdam and Kinokimiya Co., Tokyo.
Mimura M., Tabata M. and Hosono Y.: Multiple solutions of two point boundary value problems of Neumann Type with a small parameter, Siam. J. Math. Anal. 11 (1980) 613–631.
Carr, J., Gurtin, M.E. and Slemrod, M.: One dimensional structured phase transitions under prescribed loads, M.R.C. Technical Summary Report #2559, University of Wisconsin (1983). Also, J. Elasticity 15 (1985) 133–142.
Antman S.S.: Nonuniqueness of Equilibrium States for Bars in Tension, J. Math. Anal. Applications 44 (1973) 339–349.
Ericksen J.L.: Simple static problems in nonlinear theories of rods. Int. J. Solids Structures 6 (1970) 371–377.
Mimura M.: Stationary pattern of some density-dependent diffusion system with competitive dynamics. Hiroshima Math. J. 11 (1981) 621–535.
Fife P.C.: Boundary and interior transition layer phenomena for pairs of second-order differential equations. J. Math. Anal. Applications 54 (1976) 497–521.
Ericksen J.L.: Equilibrium of bars. J. Elasticity 5 (1975) 191–201.
Maddocks, J.H. and Parry, G.P.: A model for twinning. Institute for Mathematics and its Applications Preprint Series #125, University of Minnesota (1985). Also, J. Elasticity 16 (1986) 113–133.
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Parry, G.P. On internal variable models of phase transitions. J Elasticity 17, 63–70 (1987). https://doi.org/10.1007/BF00042448
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DOI: https://doi.org/10.1007/BF00042448