梯度增强的弹塑性损伤非局部本构模型研究

简要介绍了几种主要的梯度增强非局部模型．基于“能量耗散梯度依赖”原则，在连续介质热力学框架内推导了梯度增强损伤与塑性耦合的本构关系，同时给出了一个基于塑性的损伤模型的梯度依赖本构的具体形式．在数值计算方面，结合移动最小二乘法和泰勒级数展开方法，建立了损伤场（有限元高斯积分点上）的Laplace值的近似求解格式，分别给出了二维和三维情况下的相关公式．给出的二维的韧性断裂的梯度依赖损伤塑性的数值应用，表明了格式的有效性和实用性．还讨论了内部长度的意义及取值问题．

Investigation on Gradient-Dependent Nonlocal Constitutive Models for Elasto-Plasticity Coupled With Damage

Firstly, typical gradient-dependent nonlocal inelastic models were briefly reviewed. Secondly, based on the principle of 'gradient-dependent energy dissipation', a gradient-dependent constitutive model for plasticity coupled with isotropic damage was presented in the framework of continuum thermodynamics. Numerical scheme for calculation of Laplacian term of damage field with the numerical results obtained by FEM calculation was proposed. Equations have been presented on the basis of Taylor series for both 2-dimensional and 3-dimensional cases respectively. Numerical results have indicated the validity of the proposed gradient-dependent model and corresponding numerical scheme.