弹塑性有限变形的拟流动理论

QUASI-FLOW THEORY OF ELASTIC PLASTIC FINITE DEFORMATION

本文提出一种弹塑性有限变形的拟流动理论。该理论从正交性法则出发，通过引入“拟弹性模量”和模量衰减函数并改进应变率的弹塑性分解，实现了由有限变形Ｐｒａｎｄｔｌ－Ｒｅｕｓｓ流动理论（Ｊ２Ｆ）向基于非正交法则的率形式形变理论（Ｊ２Ｄ）的合理的光滑过渡；并适用于初始及后继各向异性变形分析。在特殊条件下，可退化为Ｊ２Ｆ、Ｊ２Ｄ理论以及由任意各向异性屈服函数描述的流动理论。将该理论用于韧性金属平面应力／应变拉伸失稳与变形局部化的有限元模拟，并与理论分析及实验结果相比较，表明了本文理论的正确性。

A Quasi-Flow Theory of elastic plastic finite deformation is proposed. Thetheory originates from the classical normality law. By introducing a weak function withrespect to elastic modulus into the constitutive equations and by improving the commondecomposition scheme of elastic and plaistic strain rates, the Quasi-Flow Theory achieves asmooth and continuous transition from the fiuite deformation Prandtl-Reuss equation (J2F)based on the norrnality law to the rate form of the hypoelastic J2 deformation theory(J2D)baised on the non-normality law.In addition, the theory can be applied to the theoret icalanalysis and the numerical simulatio n of anisotropic metals from initial and subsequentplastic deformation up to localized shear fracture. Under special conditions,the J2F,theJ2D and the const it utivetheories described by arbitrary anisotropic yield funct ions andbalsed on the normality law can be included into the Quasi-Flow Theory. This t heory hasbeen introduced into the numerical simulation of the instability and the localized deformationof ductile metaIs under plane stress/strain tension. By comparing with theoretical analysisand experimental observation,the results demonstrate the usefulness of the theory