An Expression of Elastic-Plastic Constitutive Law Incorporating Vertex Formation and Kinematic Hardening

A phenomenological corner theory was proposed for elastic-plastic materials by the authors in the previous paper (Goya and Ito, 1980). The theory was developed by introducing two transition parameters, μ (α) and β (α), which, respectively, denote the normalized magnitude and direction angle of plastic strain increments, and both monotonously vary with the direction angle of stress increments. The purpose of this report is to incorporate the Bauschinger effect into the above theory. This is achieved by the introduction of Ziegler’s kinematic hardening rule. To demonstrate the validity and applicability of a newly developed theory, we analyze the bilinear strain-path problem using the developed equation, in which, after some linear loading, the path is abruptly changed to various directions. In the calculation, specific functions, such as μ (α) = Cos (.5πα/αmax) and β (α) = (αmax- .5π) α/αmax, are chosen for the transition parameters. As has been demonstrated by numerous experimental research on this problem, the results in this report also show a distinctive decrease of the effective stress just after the change of path direction. Discussions are also made on the uniqueness of the inversion of the constitutive equation, and sufficient conditions for such uniqueness are revealed in terms of μ(α), β(α) and some work-hardening coefficients.