Pragmatic analysis of material instability under strain control loading

In the present paper, the uniaxial idealized micro-mechanical model is adopted to consider the damage and softening of the materials. According to this model, structural element can be idealized as a sequence of micro-elements jointed in parallel and the elements are linked with rigid plate on the ends so that they are subjected to uniform deformation during the entire loading process. The individual elements represent the microscopic properties of the material. Then the system represents the macro or structural response. The bridge between the two scales is the probability distribution which describes the mechanical properties of the micro-elements. On the other hand, the instability under strain controlling is induced by the suddenly release of the elastic energy. Hence a major elastic element is linked to the parallel bundle. By analyzing the hierarchy system, the criterion for the instability of the system is finally obtained.