The investigation of critical behaviour of the non-euclidean model of a solid

The aim of the work is investigation of the non-euclidean model of defected solid, presented in [5–7]. The defects are represented in the model by an additional thermodynamical parameter – the deformation curvature tensor, measuring the incompatibility of the elastic strain. The model equations are considered here in a simplified plain-strain form. It is shown that there exists a threshold value for the external load. Exceeding this value violates the stability conditions for the classical elasticity solution. As a result, the inelastic counterpart of deformation appears and the non-euclidity parameter becomes non-zero. Unlike the traditional plasticity theory this critical load depends not only on the material properties, but also on the size of the domain. To find the critical load intensity a special eigenvalue problem is stated and a numerical procedure is provided for its solution.