INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2002; 54:365–398 (DOI: 10.1002/nme.427) Modelling of failure mode transition in ballistic penetration with a continuum model describing microcracking and ow of pulverized media Benjamin A. Gailly 1 and Horacio D. Espinosa 2; ∗; † 1 D el egation G en erale pour l’Armement=Etablissement Technique de Bourges; Route de Guerry; 18015 Bourges C edex; France 2 Department of Mechanical Engineering; Northwestern University; 2145 Sheridan Road; Evanston; IL 60208-3111; U.S.A. SUMMARY A new continuum model to describe damage, fragmentation and large deformation of pulverized brittle materials is presented. The multiple-plane-microcracking (MPM) model, developed by Espinosa, has been modied to track microcracking on 13 orientations under high pressure, high strain rate and high deformation. This model provides the elastic and inelastic response of the material before massive crack coalescence. When pulverization occurs, the constitutive response is modelled by means of a visco- plastic model for granular material, which is a generalization to three dimensions of the double-sliding theory augmented by a consolidation mechanism. The initialization of the granular model is governed by a yield surface at the onset of massive crack coalescence. This is accomplished by examining a representative volume element, modelled using the MPM model, in compression-shear. The main advantage of this approach is to keep a continuum model at all stages of the deformation process and thus avoid the diculties of crack representation in a discrete nite element code. This model has been implemented in LS-DYNA and used to examine interface defeat of long rod penetrators by a conned ceramic plate. The numerical simulations are compared to experiments in order to identify failure modes. The model parameters were obtained independently by simulating plate and rod impact experiments. The proposed model captures most of the physical observations as well as failure mode transition, from interface defeat to full penetration, with increasing impact velocity. Copyright ? 2002 John Wiley & Sons, Ltd. KEY WORDS: granular materials; brittle materials; constitutive modelling; impact; ballistic penetration; damage; visco-plasticity ∗ Correspondence to: Horacio D. Espinosa, Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A. † E-mail: espinosa@nwu.edu Contract=grant sponsor: Army Research Oce; contract=grant number: DAAH04-96-1-0331 Contract=grant sponsor: Delegation Generale pour L’Armement; contract=grant number: 21132=DGA=DSP=D Received 9 July 2000 Copyright ? 2002 John Wiley & Sons, Ltd. Revised 10 May 2001