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The nature of configurational forces

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References

  • [1878] Gibbs, J. W., On the equilibrium of hetrogeneous substances, Trans. Connecticut Acad. 3, 108–248. Reprinted in: The Scientific Papers of J. Willard Gibbs, vol. 1, Dover, New York (1961).

    Google Scholar 

  • [1892] Burton, C. V., A theory concerning the constitution of matter, Phil. Mag. (Series 5) 33, 191–203.

    Google Scholar 

  • [1951] Eshelby, J. D., The force on an elastic singularity, Phil. Trans. A244, 87–112.

    Google Scholar 

  • [1951] Herring, C., Surface tension as a motivation for sintering, The Physics of Powder Metallurgy (ed. W. E. Kingston), McGraw-Hill, New York.

    Google Scholar 

  • [1952] Burke, J. E. & D. Turnbull, Recrystallization and grain growth, Progress in Metal Physics 3, 220–292.

    Google Scholar 

  • [1956] Mullins, W. W., Two-dimensional motion of idealized grain boundaries, J. Appl. Phys., 27, 900–904.

    Google Scholar 

  • [1958] Frank, F. C., On the kinematic theory of crystal growth and dissolution processes, Growth and Perfection of Crystals (eds. R. H. Doremus, B. W. Roberts, D. Turnbull), John Wiley, New York.

    Google Scholar 

  • [1960] Mullins, W. W., Grain boundary grooving by volume diffusion, Trans. Met. Soc. AIME, 218, 354–361.

    Google Scholar 

  • [1963] Chernov, A. A., Crystal growth forms and their kinetic stability [in Russian], Kristallografiya 8, 87–93 (1963). English Transl. Sov. Phys. Crystall. 8, 63–67 (1963).

    Google Scholar 

  • [1963] Coleman, B. D. & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178.

    Google Scholar 

  • [1963] Mullins, W. W. & R. F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 34, 323–329.

    Google Scholar 

  • [1964] Chernov, A. A., Application of the method of characteristics to the theory of the growth forms of crystals [in Russian], Kristallografiya 8, 499–505. English Transl. Sov. Phys. Crystall. 8, 401–405 (1964).

    Google Scholar 

  • [1964] Mullins, W. W. & R. F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys. 35, 444–451.

    Google Scholar 

  • [1964] Voronkov, V. V., Conditions for formation of mosaic structure on a crystallization front [in Russian], Fizika Tverdogo Tela 6, 2984–2988. English Transl. Sov. Phys. Solid State 6, 2378–2381 (1965).

    Google Scholar 

  • [1965] Truesdell, C. A. & W. Noll, The non-linear field theories of mechanics, Handbuch der Physik, III/3 (ed. S. Flügge), Springer-Verlag, Berlin.

    Google Scholar 

  • [1966] Truesdell, C. A., Method and taste in natural philosophy, Six Lectures on Modern Natural Philosophy, Springer Verlag, New York.

    Google Scholar 

  • [1970] Eshelby, J. D., Energy relations and the energy-momentum tensor in continuum mechanics, Inelastic Behavior of Solids (ed. M. Kanninen, W. Adler, A. Rosen-Field & R. Jaffee), 77–115, McGraw-Hill, New York.

    Google Scholar 

  • [1970] Sherman, B., A general one-phase Stefan problem, Quart. Appl. Math. 28, 377–382 (1970).

    Google Scholar 

  • [1972] Hoffman, D. W. & J. W. Cahn, A vector thermodynamics for anisotropic surfaces. 1. Fundamentals and applications to plane surface junctions, Surface Sci. 31, 368–388.

    Google Scholar 

  • [1974] Cahn, J. W. & D. W. Hoffman, A vector thermodynamics for anisotropic surfaces. 2. Curved and faceted surfaces, Act. Metall. 22, 1205–1214.

    Google Scholar 

  • [1974] Gurtin, M. E. & I. Murdoch, A continuum theory of elastic material surfaces, Arch. Rational Mech. Anal., 57, 291–323.

    Google Scholar 

  • [1974] Robin, P.-Y. F., Thermodynamic equilibrium across a coherent interface in a stressed crystal, Am. Min. 59, 1286–1298.

    Google Scholar 

  • [1977] Fasano, A. & M. Primicerio, General free boundary problems for the heat equation, J. Math. Anal. Appl., Part 1, 57, 694–723; Part 2, 58, 202–231; Part 3, 59, 1–14.

    Google Scholar 

  • [1978] Larché, F. C. & J. W. Cahn, Thermochemical equilibrium of multiphase solids under stress, Act. Metall. 26, 1579–1589.

    Google Scholar 

  • [1980] Cahn, J. W., Surface stress and the chemical equilibrium of small crystals. 1. The case of the isotropic surface, Act. Metall. 28, 1333–1338.

    Google Scholar 

  • [1981] Grinfel'd, M. A., On hetrogeneous equilibrium of nonlinear elastic phases and chemical potential tensors, Lett. Appl. Engng. Sci. 19, 1031–1039.

    Google Scholar 

  • [1981] Gurtin, M. E., An Introduction to Continuum Mechanics, Academic Press, New York.

    Google Scholar 

  • [1981] James, R., Finite deformation by mechanical twinning, Arch. Rational Mech. Anal. 77, 143–176.

    Google Scholar 

  • [1983] Gurtin, M. E., Two-phase deformations of elastic solids, Arch. Rational Mech. Anal. 84, 1–29.

    Google Scholar 

  • [1985] Alexander, J. I. D. & W. C. Johnson, Thermomechanical equilibrium in solid-fluid systems with curved interfaces, J. Appl. Phys. 58, 816–824.

    Google Scholar 

  • [1986] Gurtin, M. E., On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199–241.

    Google Scholar 

  • [1986] Johnson, W. C. & J. I. D. Alexander, Interfacial conditions for thermomechanical equilibrium in two-phase crystals, J. Appl. Phys. 59, 2735–2746.

    Google Scholar 

  • [1986] Petryk, H. & Z. Mroz, Time derivatives of integrals and functional defined on varying volume and surface domains, Arch. Mech. 38, 697–724.

    Google Scholar 

  • [1987] Truskinovsky, L., Dynamics of nonequilibrium phase boundaries in a heat conducting nonlinear elastic medium, J. Appl. Math. Mech. (PMM), 51, 777–784.

    Google Scholar 

  • [1987] Uwaha, M., Asymptotic growth shapes developed from two-dimensional nuclei, J. Crystal Growth 80, 84–90.

    Google Scholar 

  • [1988] Gurtin, M. E., Multiphase thermomechanics with interfacial structure. 1. Heat conduction and the capillary balance law, Arch. Rational Mech. Anal., 104, 185–221.

    Google Scholar 

  • [1988] Kaganova, I. M. & A. L. Roitburd, Equilibrium between elastically-interacting phases [in Russian], Zh. Eksp. Teor. Fiz. 94, 156–173. English Transl. Sov. Phys. JETP 67, 1173–1183 (1988).

    Google Scholar 

  • [1989] Angenent, S. & M. E. Gurtin, Multiphase thermomechanics with interfacial structure. 2. Evolution of an isothermal interface, Arch. Rational Mech. Anal. 108, 323–391.

    Google Scholar 

  • [1989] Fonseca, I., Interfacial energy and the Maxwell rule, Arch. Rational Mech. Anal., 106, 63–95.

    Google Scholar 

  • [1989] Gurtin, M. E., A. Struthers & W. O. Williams, A transport theorem for moving interfaces, Quart. Appl. Math. 47, 773–777.

    Google Scholar 

  • [1989] Leo, P. H. & R. F. Sekerka, The effect of surface stress on crystal-melt and crystal-crystal equilibrium, Act. Metall. 37, 3119–3138.

    Google Scholar 

  • [1989] Nozieres, P., Shape and Growth of Crystals, Notes of lectures given at the Beg-Rohu summer school.

  • [1990] Abeyaratne, R. & J. K. Knowles, On the driving traction acting on a surface of strain discontinuity in a continuum, J. Mech. Phys. Solids, 38, 345–360.

    Google Scholar 

  • [1990] Gurtin, M. E. & A. Struthers, Multiphase thermomechanics with interfacial structure. 3. Evolving phase boundaries in the presence of bulk deformation, Arch. Rational Mech. Anal. 112, 97–160.

    Google Scholar 

  • [1991] Abeyaratne, R. & J. K. Knowles, Kinetic relations and the propagation of phase boundaries in elastic solids, Arch. Rational Mech. Anal., 114, 119–154.

    Google Scholar 

  • [1991] Angenent, S. B., Parabolic equations for curves on surfaces, Ann. Math. (2) 132, 451–483 (1990); 133, 171–215.

    Google Scholar 

  • [1991] Chen, Y.-G., Y. Giga & S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Diff. Geom. 33, 749–786.

    Google Scholar 

  • [1991] Estrada, R. & R. P. Kanwal, Non-classical derivation of the transport theorems for wave fronts, J. Math. Anal. Appl., 159, 290–297.

    Google Scholar 

  • [1991] Gurtin, M. E., On thermodynamical laws for the motion of a phase interface, Zeit. angew. Math. Phys., 42, 370–388.

    Google Scholar 

  • [1991] Jaric, J. P., On a transport theorem for moving interfaces, preprint.

  • [1991] Truskinovsky, L., Kinks versus shocks, in Shock Induced Transitions and Phase Structures in General Media (ed. R. Fosdick, E. Dunn & M. Slemrod), Springer-Verlag, Berlin (1991).

    Google Scholar 

  • [1992] Lusk, M., Martensitic phase transitions with surface effects, Tech. Rept. 8, Div. Eng. Appl. Sci., Caltech.

  • [1992] Taylor, J., Mean curvature and weighted mean curvature, Act. Metall. 40, 1475–1485.

    Google Scholar 

  • [1992] Taylor, J., J. W. Cahn & C. A. Handwerker, Geometric models of crystal growth, Act. Metall. 40, 1443–1474.

    Google Scholar 

  • [1993] Götz, I. G. & B. Zaltzman, Two-phase Stefan problem with supercooling, preprint.

  • [1993a] Gurtin, M. E., Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford University Press, Oxford.

    Google Scholar 

  • [1993b] Gurtin, M. E., The dynamics of solid-solid phase transitions. 1. Coherent interfaces, Arch. Rational Mech. Anal., 123, 305–335.

    Google Scholar 

  • [1993] Soner, H. M., Motion of a set by the curvature of its boundary, J. Diff. Eqs. 101, 313–372.

    Google Scholar 

  • [1994] Cermelli, P. & M. E. Gurtin, The dynamics of solid-solid phase transitions. 2. Incoherent interfaces, Arch. Rational Mech. Anal., 127, 41–99.

    Google Scholar 

  • [1994a] Gurtin, M. E., The characterization of configurational forces, Addendum to Gurtin [1993b], Arch. Rational Mech. Anal., 126, 387–394.

    Google Scholar 

  • [1994b] Gurtin, M. E., Thermodynamics and the supercritical Stefan equations with nucleations, Quart. Appl. Math. 52, 133–155.

    Google Scholar 

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  1. Department of Mathematics, Carnegie Mellon University, 15213, Pittsburgh, Pennsylvania

    Morton E. Gurtin

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Gurtin, M.E. The nature of configurational forces. Arch. Rational Mech. Anal. 131, 67–100 (1995). https://doi.org/10.1007/BF00386071

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