Abstract:

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 C-1 continuum shape function. A numerical example for a one-dimensional damage structure is analyzed in ABAQUS through the user subroutine UEL. The result shows that the trend of the numerical solution coincides with the analytical solution and the method can be used to analyze damage localization.

Key words: nonlocal theory, localization, mesh dependency, C-1 continuum element, ABAQUS, finite element method