On formation of evolutional constitutive equations for finite elasto-plastic strains.

R.S.Novokshanov, A.A.Rogovoy

Institute of Continuous Media Mechanics, Ural, Russia

Large strains emergence characterizes the majority of technological processes of material processing. In this case the use of linear theories leads to unsatisfactory results. Therefore it appears necessary to apply a theory that would take into account finite character of the strains. Relaxational type materials being considered, to construct the constitutive equations we have to determine the objective derivative type correctly, so that material independence principle would be satisfied. There is no generally accepted approach to this problem. Different authors adduce different arguments defending the preferred type of the derivative. Usually their arguments have no thorough mathematical or mechanical basis. In the first part of our work we propose an approach that enables to determine the type of involved objective derivative unambiguously. It is based on the principle of material independence and links between different forms of the stress tensor. In our opinion this approach is the most general and mathematically substantiated one.

The second part of the work is devoted to constitutive equations construction in the case of finite elastic-plastic strains. Using the idea of small and finite strain superposition the famous Lee decomposition describing kinematics of elastoplastic deformation is transformed. The following three configurations are under consideration: the initial configuration, the current configuration and the intermediate configuration that hardly differs from the second one. The general form of constitutive equations for arbitrary elastic and plastic law is obtained. Choice of the objective derivative is done using the proposed approach and is the unambiguous one.

On the basis of the obtained general form the constitutive equations for Signiorini law and Prandtle-Reusse flow theory is constructed. The numerical analysis of the obtained equations was implemented for the simple shear problem.

Keywords : finite strain, objective derivative, evolutional constitutive equation, elastic-plastic deformation