基于非局部理论的一维损伤模型的有限元算法

为了解决损伤局部化问题的网格依赖性，采用非局部理论，从损伤本构关系中引入特征长度入手，建立非局部损伤本构模型。提出了一种新的单元，将位移、非局部应变和非局部应变梯度作为基本的未知量，引入了C-1连续的形函数，并推导了非局部损伤本构模型的有限元格式。在ABAQUS中进行了二次开发，嵌入了本文提出的单元和本构模型，并用ABAQUS软件分析了一维损伤结构的受力情况。计算结果表明，数值模拟与理论推导结果的总体趋势吻合得较好，证明了本文方法的正确性与可行性。

Finite Element Algorithm of One-dimensional Damage Model Based on Nonlocal Theory

In order to circumvent the mesh dependence of damage localization, the nonlocal theory is adopted. A nonlocal damage model is established by introducing a characteristic length into the damage constitutive equation. A new element is proposed and the basic unknown quantities in the equations are displacement, nonlocal strain, and nonlocal strain gradient. A finite element (FE) format of the nonlocal damage model is derived by introducing the C1 continuum shape function. A numerical example for a one-dimensio...