摘要
应变梯度工程塑性(简称CMSG)理论是一种低阶应变梯度塑性理论。它保持了经典塑性理论的基本结构,不需要非经典的附加边界条件,因此容易应用于数值分析。该文建立了在混合硬化情况下CMSG理论的本构关系,并采用非线性偏微分方程中的特征线方法研究其适定性。对于无限长固体层承受剪切的问题,确定了在不同的混合硬化情况下CMSG理论的"定解域"。在"定解域"内特征线方法的解与混合差分方法的解吻合得很好,但在"定解域"之外解有可能不唯一,因此需要非经典的附加边界条件才能使其解成为适定。随着外加剪切应力的增加,"定解域"逐渐收缩并最终消失。
The Conventional Theory of Mechanism-based Strain Gradient Plasticity （CMSG） is of lower-order strain gradient that retains the essential structure of classical plasticity theory. It does not require additional non-classical boundary conditions, thus it can be easily applied in numerical analysis. The constitutive relations of CMSG theory for mixed hardening are established, and its well-posedness is studied by the method of characteristics. For an infinite layer in shear, the ＂domain of determinacy＂ for CMSG theory at different mixed hardening states is determined. Within the ＂domain of determinacy＂, the presented results agree well with the numerical solution obtained by the finite difference method. Outside the ＂domain of determinacy＂, the solution may not be unique, in that case, the additional, non-classical boundary conditions are needed for the well-posedness of CMSG theory. As the applied shear stress increases, the ＂domain of determinacy＂ shrinks and eventually vanishes.
出处
《工程力学》
EI
CSCD
北大核心
2009年第9期176-185,共10页
Engineering Mechanics
基金
国家自然科学基金项目(10121202)
教育部博士点专项科研基金项目(20020003023)
教育部重点专项基金项目(0306)
关键词
特征线方法
应变梯度
CMSG理论
混合硬化
定解域
method of characteristics
strain gradient plasticity
CMSG theory
mixed hardening
domain of determinacy
