Nonlocal formulation of the evolution of damage in a one-dimensional configuration

The constitutive modelling of distributed damage evolution with strain-softening effects causes serious problems when local concepts are employed: numerical approximations obtained by finite element techniques show unlimited localization of deformation and energy dissipation decreases to unrealistic values when element meshes are refined. To overcome these problems nonlocal formulations have been introduced; a particular continuum damage example is presented which allows an analytical elaboration in the one-dimensional case. For a bar in uniaxial tension the exact solution is derived and the physical implications are examined