Abstract
The object of this paper is the study of the moving boundary problem modeling the growth of a spherical solid inclusion in an infinite solid matrix. The displacement in bulk is assumed infinitesimal, while the phases are modeled as isotropic elastic bodies, and the interface structure is described by a constant surface tension. Existence of solutions is proved, and their asymptotic behavior in time is studied, with particular attention to the competition between surface tension and bulk deformation.
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R. Abeyaratne and J.K. Knowles, On the driving traction acting on a surface of strain discontinuity in a continuum.J. Mech. Phys. Solids 38 (1990) 345–360.
R. Abeyaratne and J.K. Knowles, Kinetic relations and the propagation of phase boundaries in solids.Arch. Rational Mech. Anal. 114 (1991) 119–154.
C.M. Dafermos, The entropy rate admissibility criterion for solutions of hyperbolic conservation laws.J. Diff. Eqs. 14 (1973) 202–212.
M.E. Gurtin, The dynamics of solid-solid phase transitions 1. Coherent interfaces.Arch. Rational Mech. Anal. 123 (1993) 305–335.
M.E. Gurtin, The characterization of configurational forces.Arch. Rational Mech. Anal. 126 (1994) 387–394.
M.E. Gurtin, The nature of configurational forces,Arch. Rational Mech. Anal. 131 (1995) 67–100.
M.E. Gurtin and A. Struthers, Multiphase termomechanics with interfacial structure 3. Evolving phase boundaries in the presence of bulk deformation.Arch. Rational Mech. Anal. 112 (1991) 97–160.
M.E. Gurtin and P.W. Voorhees, The continuum mechanics of two-phase systems with mass transport and stress.Proc. Roy. Soc. Lond. 440A (1993) 323–343.
R.D. James, The propagation of phase boundaries in elastic bars.Arch. Rational Mech. Anal. 73 (1980) 125–158.
R.V. Kohn, Relaxation of a double-well energy.Cont. Mech. Therm. 3 (1991) 193–236.
P.Le Floch, Propagating phase boundaries: formulation of the problem and existence via the Glimm method.Arch. Rational Mech. Anal. 127 (1993) 153–197.
A.C. Pipkin, Elastic materials with two preferred states.Q. J. Mech. appl. Math. 44/1 (1991) 1–15.
L. Truskinowsky, Dynamics of non-equilibrium phase boundaries in a heat conducting non-linearly elastic medium.P.M.M. U.S.S.R. 51/6 (1987) 777–784.
L. Truskinowsky, Kinks versus shocks. In R. Fosdick, E. Dunn and H. Slemrod (eds),Shock-Induced Transitions and Phase Structures in General Media. Springer-Verlag (1991).
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Cermelli, P. Effect of bulk deformation and surface tension on the growth of a coherent inclusion. J Elasticity 41, 77–106 (1995). https://doi.org/10.1007/BF00042509
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DOI: https://doi.org/10.1007/BF00042509