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.
© 2004 John Wiley & Sons. Received 6 February 2004. Revised 3 June 2004. Accepted 6 July 2004. Published online 15 November 2004. MO and AM gratefully acknowledge the support of the Department of Energy through Caltech's ASCI/ASAP Center for Simulating the Dynamic Response of Materials. We are also grateful for support provided by Caltech's NSF/MRSEC Center for the Science and Engineering of Materials, and DARPA's Structural Amorphous Metals program through Caltech's Center for Structural Amorphous Metals.