Flat elasticity theory application for the description of stressed state and fracture of solids under phase transitions

The stress function is proved to be biharmonic for an elastically isotropic crystal undergoing phase transition which follows spontaneous dilatation. For an elastically anisotropic crystal which is neither improper nor proper ferroelastic, as well as for the improper ferroelastic, the stress function is proved to fulfil the Lehnitsky equation. The flat elasticity theory methods are extended to the case of crystals undergoing phase transitions. The stressed state, arising due to the phase transition in a crystal with a crack or with a rigid inclusion, is described. The spontaneous fracture conditions of crystals under phase transitions are obtained. 23 refs.