Transient response of an elastic plate on crushable material striking a rigid boundary

Transient response of an elastic plate on crushable material striking a rigid boundary is analyzed. The crushable material is approximated by a discrete chain of masses and non-linear springs with properties from the non-linear constitutive law of the crushable material. Plate elasticity and crushable material response are uncoupled. Deceleration from impact assumes a rigid but massive plate. The pressure from deceleration is then applied to the elastic plate to evaluate its response. Prior to arrest, when plate and crushable material strike a rigid boundary, a temporary drop in deceleration response is observed depending on relative density ρ˜=ρf/ρs where ρf and ρs are crushable and parent material densities. This drop is absent when the plate strikes crushable material at rest. Measured deceleration response of an elastic plate on crushable material is modulated by oscillations from plate response with amplitude depending on the obliquity angle of the setup as it strikes the rigid boundary. The difference between “moving-crushable” and “fixed-crushable” configurations is substantial in form and magnitude. A 2D model of a strip with intermediate flexible supports models response of a thin electronic board from deceleration transmitted to its boundaries by a frame mounted on crushable material.