EFFECT OF STRESS-STRAIN CURVE OF MATERIAL ON SOLUTION OF PLANE-STRESS PROBLEMS WITH LARGE PLSTIC DEFORMATION

A brief review of author's previous work on the plastie plane stress problems with axial symmetry is first made. Results obtained for two of such problems, which show that the effeets of τ(γ) of the material and of loading on the distributions of the proportionate strains and of the ratios of principal stresses are very samll, are summmarized. An analysis of the equations is then made and the preceding ersults are explained. Equations of equilibrium in terms of the principal stresses and of the principal strains are derived for the two-dimensional plane stress problems without body force but considering finite strains. An analysis of these equations leads to the surmise that the effects of τ(γ) of the material on the distributions of the proportionate strains and of the ratios of the principal stresses are samll, provided that the proportionate strains and the ratios of the principal stresses at the boundary remain the same at different loads. On the other hand, the effects of τ(γ) of the material and of the load on the distributions of proportionate stresses are large. A simple approximate method of solution is obtained by using these results. The results obtained in this paper are compared with Ilyushin's theory of small elastic-plastic deformation.