On the Influence of Variations of Material Properties on Stress Wave Propagation Through Elastic Slabs

The influence of variation of elastic properties through a plate on the propagation of elastic waves through it has been studied, with a view to investigating its ability to withstand impact. The relative merit of properties changes in a series of steps (graded material) or continuous variation (gradient material) is investigated. For an elastic slab with elastic modulus varying continuously but otherwise arbitrarily with depth, the magnitude of the stress wave front associated with an applied step surface pressure varies in proportion to $ρ(x)c(x)$ where ρ is the density and c the elastic wave speed for dilatational waves. This magnitude grows indefinitely with increasing c(x). However, in the limit of a sudden change of properties as at an interface with a rigid body (c → ∞), the stress magnitude only doubles. This paradox is explained by noting a singular approach to the limit of the continuously varying case. A boundary layer consisting of a peak of high stress can occur for sharp changes of properties, which narrows as the gradient material approaches a graded one. The possible significance of this result to material damage under dynamic loading is discussed.