A class of variational strain-localization finite elements

We present a class of finite elements for capturing sub-grid localization processes such as shear bands and void sheets. The elements take the form of a double surface and deform in accordance with an arbitrary constitutive law. In particular they allow for the development of displacement and velocity jumps across volume element boundaries. The thickness of the localized zone is set by an additional field variable which is determined variationally. The localization elements are inserted, and become active, only when localized deformations become energetically favourable. The implementation presented in this work is three-dimensional and allows for finite deformations. The versatility and predictive ability of the method are demonstrated through a simple shear test and the simulation of the dynamic impact of a pre-notched C300 steel sample by a steel projectile