FINITE ELEMENT CALCULATION USING A PLASTIC CONSTITUTIVE EQUATION INCORPORATING STRESS INCREMENT DIRECTIONAL DEPENDENCY

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A constitutive theory of plastic deformation has been proposed by Goya and Ito, which can take into account the directional dependency of plastic strain increment on stress increment. The theory was developed through the introduction of two transiton parameters mu and beta, which denote the magnitude and the direction angle of plastic strain increment, respectively, and are defined to be functions of the direction angle, alpha , of the stress increment. The theory is different from the J2 corner theory proposed by Christoffersen and Hutchinson, that has been introduced in many numerical studies as an effective constitutive equation to make the localization emerge.In this research, Goya and Ito's rule and some other constitutive rules are used in the finite element analysis of a plane strain tensile test problem to investigate the effect of the stress increment directional dependency on the onset of the localzed necking.The numerical results show that shear band localization can not be observed even though the directional dependency of beta max = 30' is assumed, which is allowable for the Tresca type yield surface. The resulting deformation mode is of interesting since the past studies showed clear shear band formaiton for the material similar to the Tresca surface in terms of the acuteness of the corner.