Growth of Pre-Existing Micro-Void in Infinite Elastoplastic Body Under Remote Thermal and Mechanical Loads

Growth of pre-existing micro-void in infinite elastoplastic body under remote thermal and mechanical loads is analyzed. A geometrical nonlinear mathematic model based on the Hooke elastic law and the ideally Mises yield criterion is constructed. The stress and the displacement distributions near the micro-void are presented by the elastoplastic analysis in this paper. The critical temperature and mechanical loads of cavitation can be calculated by the limiting case of a micro-void. The radius of the micro-void and the radius of the plastic zone increase rapidly when the remote temperature and mechanical load increase and close to the critical value from the numeric computation. It is shown that the unlimited micro-void growth under the critical thermal and mechanical load is referred to as an unstable cavitation.

AN EVOLUTIONARY ELASTOPLASTIC PLATE MODEL DERIVED VIA Γ-CONVERGENCE

This paper is devoted to dimension reduction for linearized elastoplasticity in the rate-independent case. The reference configuration of the three-dimensional elastoplastic body has a two-dimensional middle surface and a positive but small thickness. Under suitable scalings we derive a limiting model for the case in which the thickness of the plate tends to 0. This model contains membrane and plate deformations (linear Kirchhoff–Love plate), which are coupled via plastic strains. We establish strong convergence of the solutions in the natural energy space. The analysis uses an abstract Γ-convergence theory for rate-independent evolutionary systems that is based on the notion of energetic solutions. This concept is formulated via an energy-storage functional and a dissipation functional, such that energetic solutions are defined in terms of a stability condition and an energy balance. The Mosco convergence of the quadratic energy-storage functional follows the arguments of the elastic case. To handle the evolutionary situation the interplay with the dissipation functional is controlled by cancellation properties for Mosco-convergent quadratic energies.