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Thermo-elastic aspects of dynamic nucleation. (English) Zbl 1022.74034
A general scenario of homogeneous nucleation in multiphase solids leading to an explosive decomposition of a metastable state is studied on the basis of one-dimensional model of thermo-elastic bar with non-convex energy function. The mathematical problem is reduced to the analysis of a degenerate Riemann problem with identical data on both sides of nucleation site. The non-uniqueness associated with nucleation is resolved through regularization, leading to more detailed description of the process at micro-level. The thermo-visco-capillary model is used for the regularization. The system of equations of adiabatic thermoelasticity is augmented by adding thermal conductivity, viscosity, and gradient elasticity. A particular material model with cubic stress-strain relation and maximally simplified temperature dependence is exploited. It is demonstrated numerically that a localized perturbation of the original metastable state can generate two distinct dynamic regimes: one describing explosive nucleation of a new phase, and the other exhibiting the decay of perturbation.

MSC:
74N20 Dynamics of phase boundaries in solids
74F05 Thermal effects in solid mechanics
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