Numerical aspects of nonlocal damage analyses

ABSTRACT Constitutive models based on nonlocal variables provide an effective and mechanically sound solution to the ill-posedness of the boundary value problem in the presence of damage induced softening. However, the averaging of constitutive variables entails other computational problems like the lack of symmetry of the tangent operator in a finite element approximation. In the present paper, an isotropic local damage model with symmetric tangent matrix is presented. Two alternative nonlocal versions of the same model are comparatively discussed. It is shown how the symmetry of the tangent matrix in the finite element approximation can be preserved formulating the nonlocal model within the context of the thermodynamic nonlocal theory recently proposed by Borirlo et al. The computational implications of the adopted regularization technique are discussed by means of a simple one-dimensional example.