Numerical modelling of ceramics using LS-Dyna

Numerical modelling of ceramics is a challenging problem due to the brittle nature of the ceramic material. Most ceramics have low tensile and shear strength, but very high compressive strength even after failure, and are especially attractive for various types of protective ballistic applications as they are usually much lighter than conventional armour steel. Failure is a complex multi-scale process involving, e.g., grain size, porosity, micro-crack initiation and crack growth. Despite a lack of understanding of all the involved processes during failure, important characteristics are qualitatively well understood. Confined ceramics show increased resistance to penetration as comminuted fragments remain in the path of the projectile and compressive (pre-) stresses increases the strength and ductility of the ceramic, as well as hinders premature failure in tension. The goal of this report is to investigate the numerical capability of the commercial finite element code LS-Dyna to model ceramic behaviour in general and the effects of confinement and pre-stress in ceramics in particular. Three commonly used material models for ceramics are therefore described in detail and two of them are investigated using a series of impact examples. Numerical results in LS-Dyna show that it is capable of mimicking the increased strength when adding pre-stress and/or confinement to the ceramic. We found, however, that adding pre-stress in terms of a shrink-fitted tube did not yield the expected results. Using a method of overlapping surfaces and penalisation of the contact stiffness when applying the shrink-fit, LS-Dyna was not capable of more than minor increases in stiffness. Using a method of applying a thermal expansion coefficient to the confining material did result in a larger increase in stiffness. The latter method, however, did not match the resistance to penetration obtained when applying a constant radial pressure. It remains unclear why a lower resistance to penetration was found using any of the shrink-fit procedures than when applying a constant confining pressure, but we can conclude that the shrink-fit method is highly sensitive. We also investigate the influence of using SPH elements in ceramic ballistic applications by comparing a numerical example that uses a classical hexahedral mesh, a SPH particle mesh and a mesh that converts hexahedral elements to SPH particles at failure. It is concluded that the converted mesh yields a much stiffer response than the other two element formulations.