Archive of Applied Mechanics

, Volume 87, Issue 6, pp 1019–1036 | Cite as

Stiff phase nucleation in a phase-transforming bar due to the collision of non-stationary waves

  • Ekaterina V. Shishkina
  • Serge N. GavrilovEmail author


We deal with a new phase nucleation in a phase-transforming bar caused by a collision of two non-stationary waves. We consider an initial stage of dynamical process in the finite bar before the moment of time when the waves emerged due to new phase nucleation reach the ends of the bar. The model of a phase-transforming bar with trilinear stress–strain relation is used. The problem is formulated as a scale-invariant initial value problem with additional restrictions in the form of several inequalities involving the problem parameters. We consider the particular limiting case where the stiffness of a new phase inclusion is much greater than the stiffness of the initial phase and obtain the asymptotic solution in the explicit form. In particular, the domains of existence of the solution in the parameter space are constructed.


Phase transitions 1D elastodynamics Asymptotics 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute for Problems in Mechanical Engineering RASSt. PetersburgRussia
  2. 2.Peter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia

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