The high strength, light weight, and flexibility of fabric protection systems makes them an effective impact mitigation solution in some important engineering applications. Examples include body armor, fan blade containment systems, and orbital debris shielding. Most soft armor protection systems employ a plain weave fabric, suitable for use in flat or slightly curved geometries. However, future fabric protection system designs may employ nonplain weaves to protect highly curved surfaces (such as personnel extremities) or to optimize the performance of protection systems composed of a nonhomogeneous fabric stack. In recent research, the authors developed an improved hybrid particle-element method to simulate the ballistic impact performance of fabric protection systems. The new formulation is the first to address the full range of modeling issues (including penalty-based contact-impact, excessive yarn bending stiffness, and mass or energy discard) that have limited the effectiveness of legacy finite element-based fabric modeling methods for over two decades. Validation simulations modeled three-dimensional perforation dynamics in multilayer fabric stacks, and showed good agreement with new ballistic experiments conducted at three different target-layer counts for two different projectile types and four different weaves.
Nomenclature= second Euler parameter coefficient matrix g = generalized nonconservative torque, N · m g e = contact-impact torque, N · m g v = viscous torque, N · m H = semiaxis scaling matrix, m −2 H = transformed semiaxis scaling matrix, m −2 i = vector component i i = particle or element i i; j = particle combination i, j J = moment of inertia matrix, kg · m 2 m = particle mass, kg m p = projectile mass, kg N = number of connected neighbor particles n = number of particles n w = number of particles spanning a yarn P = pressure, Pa q d = generalized nonconservative force, J q p = generalized nonconservative force, J q U = generalized nonconservative force R = rotation matrix r o = element reference length, m s = element length, m s o = element length in the reference configuration, m T = kinetic coenergy, J t = fabric thickness, m U = internal energy, J u = internal energy per unit mass, J · kg −1 u s = step function V = potential energy, J= generic vector in the fixed framê v = generic vector in the corotating frame w = yarn width, m Y = yield stress, Pa Y o = reference yield stress, Pa α = particle semiaxis scaling factor β t = transition particle stretch factor Γ d = damage strain energy release rate, J Γ p = plastic strain energy release rate, J γ = first Euler angle δ ij = Kronecker delta ϵ = total strain ϵ p f = plastic failure strain ϵ e = elastic strain ϵ p = plastic strain ζ = ellipsoidal coordinate ζ R = reference ellipsoidal coordinate η = heat transfer coefficient, J · s −1 · K −1 η p = thermal softening coefficient, K −1 θ = third Euler angle (without superscript) θ = temperature (with superscript), K θ m = melt temperature, K θ o = reference temperature, K θ H = homologous temperat...