The paper puts forwards principal kinematic relations and constitutive equations, which can be applied in designing numerical methods of study of finite elasto-plastic strains. The medium kinematics ...is considered under the multiplicative decomposition of the total deformation gradient. The constitutive equations are deduced using the theory of flow and the second law of thermodynamics. As a result, we find the dependence of the stress tensor rate on the free energy function and on the yield function.
A generalized statement of the problem of determining the stress-strain state of sandwich plates with a transversally soft core in the presence of constraints is proposed. Its correctness is ...discussed. The generalized problem is stated as the problem of finding a saddle point of some functional. The existence and uniqueness of a solution is proved. An iterative method for solving the problem is proposed and its convergence is studied.
The article studies the way the Russian literature reflects the process of women’s emancipation originated and developed. The author considers the women’s issue to become imminent mostly due to the ...development of realism and its attention to social problems. Besides, the growth of women’s emancipation in Europe also had certain influence. The material for the research has become the magazine «Otechestvennye Zapiski» («Domestic notes»), which was one of the most advanced Russian editions of the 40s of the XIX century. As the analysis of the magazine showed the patriarchal picture of the world dominated in the Russian literature of that time. “The women’s issue” was discussed not in the social-political perspective, but rather in moral-ethical and spiritual ones. It is stated that in spite of the domination of negative attitude to the women’s emancipation in the Russian society the growth of interest to the fate of the fair sex testified the growing importance of a woman in the society.
The paper is devoted to the development of a calculation technique for elasto-plastic solids with regard to finite strains. The kinematics of elasto-plastic strains is based on the multiplicative ...decomposition of the total deformation gradient into elastic and inelastic (plastic) components. The stress state is described by the Cauchy stress tensor. Physical relations are obtained from the equation of the second law of thermodynamics supplemented with a free energy function. The free energy function is written in an invariant form of the left Cauchy–Green elastic strain tensor. An elasto-plasticity model with isotropic strain hardening is considered. Based on an analog of the associated rule of plastic flows and the von Mises yield criterion, we develop the method of stress projection onto the yield surface (known as the radial return method) with an iterative refinement of the current stress-strain state. The iterative procedure is based on the introduction of additional virtual stresses to the resolving power equation. The constitutive relations for the rates and increments of the true Cauchy stresses are constructed. In terms of the incremental loading method, the variational equation is obtained on the basis of the principle of possible virtual powers. Spatial discretization is based on the finite element method; an octanodal finite element is used.We present the solution to the problem of tension of a circular bar and give a comparison with results of other authors.
PDF
