Simulations of the penetration of limestone targets using two-dimensional multimodal Fourier analysis

This paper is devoted to the presentation of a finite element based on a Fourier modal description of physical values on circumferences for a quasi-axisymmetric structure. The finite element detailed in this paper is an advanced version of the COMU element, developed by Combescure [Static and dynamic buckling of large thin shells: design procedure, computation tools, physical understanding of the mechanisms. Nucl Eng Des 1985; 92:339–54, Etude de la stabilité non linéaire géométrique et non linéaire matériau des coques minces. Application aux coques de révolution avec imperfections soumises à des chargements complexes. Habilitation à Diriger des Recherches, INSA Lyon, 1995], in order to extend it for simulating penetration of targets composed of geological materials by steel projectiles. A finite element code with COMU elements is coupled with analytical forcing functions based on the dynamic expansion of a spherical cavity to represent the target. This combined analytical and computational approach is employed to reproduce normal impact of ogive-nosed VAR 4340 steel projectiles striking limestone targets with small angles of pitch and yaw. Results obtained from the cost-effective approach with two-dimensional COMU elements are checked against experimental data [Frew DJ, Forrrestal MJ, Hanchak SJ. Penetration experiments with limestone targets and ogive-nose steel projectiles. J Appl Mech 2000; 67: 841–5] and results from an analogous combined approach using three-dimensional hexahedral continuum elements [Warren TL. Simulations of the penetration of limestone targets by ogive-nose 4340 steel projectiles. Int J Impact Eng 2002;27:475–96].