基于对数应变的大变形简单剪切问题应力响应

摘要

Large deformation elastic constitutive model was given by using logarithmic strain and the large deformation simple shear problem was analyzed by using the constitutive model obtained in the paper. Based on deformation rate and logarithmic strain, the responses of stress corresponding to five objective rates in large deformation elastic simple shear problem were derived respectively. The results show that there exists the most severe oscillation of stress when adopting Jaumann rate, and corresponding to various objective rates, normal stresses may maintain good monotonicity, but there always exists different degrees of oscillation in shear stress. The objective rate wasn't the only factor bringing about unreasonable stress response.%建立了由对数应变描述的弹性大变形本构关系,利用该本构关系分析了弹性大变形简单剪切问题.对应张量的五种客观率,分别给出了基于变形率和对数应变的简单剪切问题应力响应.结果表明:Jaumann率对应的应力响应具有最显著的振荡现象；对应各种客观率,正应力均能保持较好的单调性,剪应力则存在不同程度的振荡趋势；张量的客观率不是导致不合理应力响应的唯一因素.