FINITE ELEMENT MODELLING OF IMPACT DAMAGE ON CONCRETE BY SMALL HARD PROJECTILES

Abstract

A finite element program, DYNA3D is used to model the response of both low and high strength concrete subjected to high velocity impact by small hard projectiles. Experimental results from both perforation and penetration tests [1] were used to verify the numerical results. An initial assessment of the existing concrete model in DYNA3D showed that it exhibited unacceptable strain-localization and hence predicted incorrectly, an insufficient amount of energy absorbed by the concrete. Previous research has shown that strain-localization is caused by material strain softening in finite element modelling. To solve this problem, a mathematical device called a localization limiter must be introduced to prevent strain from localizing into a zone of diminishing volume. A nonlocal yield limit degradation approach [2], which treats elastic strains as local but which considers as nonlocal the inelastic strain that corresponds to strain-softening, was incorporated into DYNA3D. A detailed study of the DYNA3D program structure was conducted and the functions of some major subroutines identified. The vectorized programming in the code, developed to save CPU time, presented some difficulties in implementation of the nonlocal continuum method, since calculation of nonlocal plastic strains required that the local plastic strains from surrounding elements be immediately known. To solve this problem, two programming loops were implemented. In the first loop, plastic strains were calculated and stored in a global array. These values were then passed to the second loop to calculate nonlocal plastic strains and to update stresses, energies and nodal forces. A comparison of numerical results from the modified concrete model with experiments showed good correlation of residual velocities and energy absorbed. In addition, cracking and scabbing effects were simulated by the numerical model. The perforation hole size and scabbing zone predicted using the modified concrete model were also found to agree well with that in experiments. However, the modified concrete model is not able to simulate cratering which is caused by spalling on the impact face and poor comparisons with experiments were obtained for penetration tests. This is probably due to the crushing failure criterion adopted. Nevertheless, the modified concrete model does improve the predicted energy absorption of concrete to an appropriate level compared with the original model found in DYNA3D.