Ground states of simple bodies that may undergo brittle fractures

Equilibrium states of elastic–brittle solids that may suffer nucleation of cracks in finite deformation setting are analyzed. Crack patterns are described in terms of appropriate Radon measures, namely curvature varifolds with boundary. A new form of the energy is presented: it includes terms associated with the curvature of margins and tips of possible cracks. Existence of minima of the energy is established in classes of pairs of deformation and families of varifolds. Configurational balances in weak form are determined with reference to generic curvature varifolds with boundary. They include non-standard terms associated with the curvatures involved in the energy. Pointwise balances of configurational actions are also evaluated in a special case: new pointwise balances at the tips and along the margins of the crack pattern emerge.