Numerical Calculations Models for Physical-Mechanical Systems

Numerical Modeling Of Solid-State Phase Transformations With Surface Tension In Case Of Finite Strains

K. M. Zingerman^a, V. A. Levin^b, Freyman Yevgeniy Igorevich<sup>c

a</sup> Tver State University
^b Department of Computational Mechanics, Faculty of Mechanics and Mathematics, Moscow State University. M.V. Lomonosov
^c FIDESIS LLC

Abstract: An approach for the modelling of stress-induced solid-state phase transformations is developed using the apparatus of solid body mechanics and the kinetic model of phase transformations which is based on the theory of Landau and Ginzburg. This approach permits one to investigate phase transformations in bodies with nano-sized holes and inclusions of diverse shapes undergoing finite deformations, including the case of their superposition. The computations are performed using the finite-element technique. The model plane problems of phase transformations in bodies made of Ni$_{65}$Al$_{35}$ with holes are solved with account for surface tension. The impact of geometrical nonlinearity and surface tension on the state of stress and strain, and on the phase state is investigated.

Keywords: Phase transformation, mathematical model, nonlinear elasticity, finite strains, holes, surface tension, finite element method.

UDC: 539.3

Received: 23.05.2013
Revised: 30.05.2013