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

Goya和Ito提出了塑性变形的本构理论，该理论考虑了塑性应变增量对应力增量的方向依赖性。该理论是通过引入两个过渡参数mu和beta来建立的，它们分别表示塑性应变增量的大小和方向角，并定义为应力增量方向角alpha的函数。该理论不同于Christoffersen和Hutchinson提出的J2角理论，后者在许多数值研究中作为有效的本构方程引入，使局部化出现。本文将Goya和Ito规则等本构规则应用于平面应变拉伸试验问题的有限元分析中，研究应力增量方向依赖性对局部颈缩发生的影响。数值结果表明，即使假设β max = 30'的方向依赖性，也不能观察到剪切带局部化，这对于Tresca型屈服面是允许的。由此产生的变形模式很有趣，因为过去的研究表明，在拐角的尖锐程度方面，材料的剪切带形成与Tresca表面相似。

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.