A finite strain, finite band method for modeling ductile fracture

We present a finite deformation generalization of the finite thickness embedded discontinuity formulation presented in our previous paper A.E. Huespe, A. Needleman, J. Oliver, P.J. Sánchez, A finite thickness band method for ductile fracture analysis, Int. J. Plasticity 25 (2009) 2349-2365]. In this framework the transition from a weak discontinuity to a strong discontinuity can occur using a single constitutive relation which is of importance in a range of applications, in particular ductile fracture, where localization typically precedes the creation of new free surface. An embedded weak discontinuity is introduced when the loss of ellipticity condition is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. The methodology is illustrated through several example problems emphasizing finite deformation effects including the development of a cup-cone failure in round bar tension.