Numerical Modeling Of Fabric Impact

A numerical code has been developed to model the complex behavior of woven fabric panels subjected to ballistic impact. The code has the ability to model multiple-layer fabric panels, multiple projectile geometries, and fabric imperfections such as yarn slippage at crossovers and also at clamps. A discussion of the numerical methodology is presented, along with the results of numerical simulations of impact on single and multiple-layer fabrics, with and without resin impregnation. METHOD OF ANALYSIS The numerical algorithms used in our impact code are basically finite difference approximations of simple physical laws, as will be outlined below. This approach, sometimes called “direct analysis” in light of its simplicity, was first suggested by Mehta and Davids (1966) and their coworkers for a variety of dynamics simulations, and was adapted by Roylance and coworkers (1973, 1981) to the study of impact on woven textile panels. The codes based on the method appear to be well suited for flexible armor analysis and design: it is relatively simple to understand and implement, yet seems to capture the important physics of the impact event with good accuracy. The general nature of our impact algorithm will be outlined here briefly; the reader is referred to a report by Roylance and Houghton (1989) for further detail. In our simulations, the fabric reinforcement panel is idealized as an assemblage of pin-jointed, massless fiber elements. The fabric crossover points, or “nodes”, are assigned a mass that makes the areal density of the idealized mesh equal to that of the panel being simulated. The density of crossovers in the numerical model need not necessarily be the same as that in the actual panel. The code is currently restricted to zero-obliquity impact of a square-symmetric panel, though these limitations could be relaxed at the expense of code complexity. The initial projectile velocity is imposed on the node at the impact point, which causes a strain to develop in the adjacent elements. The tension resulting from this strain is computed from a material “constitutive” (stress-strain) relation, and this tension is used to calculate an acceleration of the neighboring nodes. The computer proceeds outward from the impact point, successively using a momentum-impulse balance, a strain-displacement condition, and a constitutive equation to compute for each element the current values of tension, strain, velocity, position, and such ancillary but important quantities as strain energy and kinetic energy. At the end of these calculations, a new projectile velocity is computed from the tensions exerted on the projectile by the fibers, and the process is repeated for a new increment of time. The masses of the fiber elements are taken to be lumped at the nodal crossover points, so that each node incorporates half the mass of the four fiber elements meeting at that node: