非局部模型与变形局部化数值模拟

基于非线性身体场论，建立了材料非局部连续模型、变分方程及相应的实时拖带系大变形有限元数值模型，设计了这一模型的数值卷积算法，由于广义函数弱收敛定理和卷积理论，证明所提出的非局部连续模型具备收敛性和稳定性。并阐明了材料特征尺度数学物理意义，统计加权函数的选择原则，数值结果表明非局部模型描述变形局部化问题是适当的。

NONLOCAL CONTINUUM MODEL AND ITS NUMERICAL SIMULATION FOR LOCALIZATION PROBLEM

A non local continuum model for strain softening with plastic strain or damage variable taken as a nonlocal variable is derived by using the Stokes Chen additive decomposition principle of finite deformation gradient. At the same time, variational equations, their finite element formulations and numerical convolved integration algorithm of the model in current configuration usually called co moving coordinate system are given. Stability and convergence of the model are proven by means of the weak convergence theorem of generalized function and the convolved integration theory. Mathematical and physical properties of the characteristic size for material or structure are accounted for within the context of a statistical weigthted or kernel function, and the way how to determine the kernel function is investigated. Numerical simulations show that this model is rational to analyse problems with deformation localization.