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. ln the present paper, an isotropie local damage madel with symmetric tangent mat rix is presented. Two alternative nonlocal versions of the same madel are comparative/y discussed. ft is shawn how the symmetry of the tangent mat rix in the finite element approximation can be preserved formulating the nonlocal madel within the context of the thermodynamic nonlocal theory recent/y proposed by Borino et al. The computational implications of the adopted regularization technique are discussed by means of a simple onedimensional example.