|
Mechanics
During monocrystal destruction buckling of its atomic lattice occurs. In this case equilibrium states of an atomic lattice change qualitatively. In mathematical modeling quasi-static deformation of atomic lattices, both loss of Lyapunov stability of equilibrium states of these lattices and achievement of singular points on an integral curve of the equations of this deformation result to qualitative changes.
In the present work external force is considered to be dead (the vector of this force does not change a direction during deformation of a lattice). It is supposed that deformation of a lattice is initiated from its natural state (in this state forces of atomic interaction are equal to zero in all atomic pairs of a lattice). Singular points of two types of integral curves are considered: turning points (corresponding to the maximum loads) and bifurcation points of solutions of a quasi-static deformation problem. The assumption that the singular point may be both a turning point and a bifurcation point simultaneously is admitted. A loss of stability of solutions of the equilibrium equations on atomic lattices is investigated. Stability criteria of equilibrium states with respect to dynamic perturbation introduced into the lattice through specifying the initial velocity vector are obtained. It is shown that unstable, according to Lyapunov, equilibrium equation solutions arise under quasi-static deformation of an atomic lattice just after the singular points occur on the integral curve.
Note. Abstracts are published in author's edition
Last update: 06-Jul-2012 (11:52:45)