Research On Several Problems Of Elasto-plastic Constitutive Theory

The purpose of plastic theory is to research the relationship of stress and strain in the body of plastic deformation which is independent of time. The main difference between plasticity and the other branches of continuum mechanics is how to describe the mechanical properties. The incremental constitutive relationship of plastic theory was established in this paper. Based on the present researches, and the fundamental assumption of continuum mechanics and plastic theory, in this paper we pay more attention to how to establish the constitutive relationship described by increment, and we deduct two kinds of incremental constitutive relationships coupled about general loading law materials, such as ideal elastoplastic materials, isotropically hardening materials, kinematic hardening materials and thermoelastoplastic materials, and also we establish two kinds of incremental constitutive relationships coupled in stress space about general loading law materials like ideal elastoplastic materials, isotropically hardening materials, mixed hardening materials.The description in principal space was turned to the description with the two principal invariables of deviatory stress of Mises yield condition Tresca yield condition and maximum deviatory stress yield criterion of isotropic hardening material. The incremental constitutive relationships were established of isotropic hardening material in complex stress condition. Furthermore, the coherence of constitutive relationships in certain case was studied between these two methods.The multidimensional incremental theory was obtained by tensor theory of general loading law in elastoplasticity coupled condition. The incremental constitutive relationships of the two dual forms were gained of general elastoplasticity materials, isotropic hardening materials and kinematic hardening materials both in stress and strain spaces, based on generalized orthogonal rule.