有限弹塑性变形的几何模型

A GEOMETRICAL MODEL FOR FINITE ELASTIC-PLASTIC DEFORMATION

以连续介质力学内变量理论为基础，建立了一个以材料内部微结构变量为底流形。材料外部变形状态为对应纤维的材料状态纤维丛模型，使材料的力学特性与模型的几何性质自然对应起来．在模型上讨论和分析了有限弹塑性变形中变形梯度的Ｌｅｅ和Ｃｌｉｆｔｏｎ的分解和联系，并证明了塑性变形为沿内变量演化在纤维丛的水平空间的运动由此获得了塑性变形随内变量演化的变化方程和塑性速率梯度与内变演化的协调关系．

in this paper, based on theory of internal state variables in continuum mechanics,a fibre bundle model of material states are presented. First of all, the states of material aredivided into the internal microstructural states and the external deformation states. Assumingthat the plastic deformation of material can be given by the internal states of material and theirevolution laws, a principal fibre bundle structure and the correspondent relationships between thegeometrical characterization and the mechanical properties of the structure are obtained. In thestructure the states of material internal microstructure are taken as the base manifold and thestates of the material deformation as the fibres over the base. Then the Lee's and the Clifton'sdecomposition for finite elasto-plastic deformation are described and discussed on the model. Itis shown that elastic deformation is a vertical motion over the same fiber and the plastic one is akind of level motion along the direction of evolution of internal variables on the bundle. Finally,the equation of the level motion is given on the model.