Modeling of Shock Propagation and Attenuation in Viscoelastic Components

Abstract

Protection from the potentially damaging effects of shock loading is a common design requirement for diverse mechanical structures ranging from shock accelerometers to spacecraft. High damping viscoelastic materials are employed in the design of geometrically complex, impact-absorbent components. Since shock transients are characterized by a broad frequency spectrum, it is imperative to properly model frequency dependence of material behavior over a wide frequency range. The Anelastic Displacement Fields (ADF) method is employed herein to model frequency-dependence within a time-domain finite element framework. Axisymmetric, ADF finite elements are developed and then used to model shock propagation and absorption through viscoelastic structures. The model predictions are verified against longitudinal wave propagation experimental data and theory.

Frequency-dependent mechanical damping in alloys

“…Power-law scaling holds for about two decades of frequency for glass, and for about four decades in frequency for random and ordered alloys. This is consistent with a large a large body of work on sound attenuation [36][37][38][39] and propagation of shock waves in viscoelastic materials [40] and damping in nanomechanical resonators [10], where a power-law scaling with respect to frequency (with an exponent ranging between 0 and 2) is observed. Indeed, widely disparate mechanisms are responsible for loss and attenuation in various viscoelastic media [36,41], and the precise mechanisms for the frequency dependence of our damping results would require separate attention.…”

<title>Investigations of viscoelastic structure behavior using a three dimensional anelastic displacement field finite element</title>

“…Similar equations are obtained for the other nodes j, m and p. By substituting the shape functions, the strain matrix is obtained as a function of the displacements and the anelastic displacement vector A : The element damping-matrix is found using similar considerations [13] …”

“…Govindswamy [12] used ADF rod elements to study longitudinal wave propagation along a viscoelastic bar. Rusovici et al developed planestress and axisymmetric ADF-based finite elements [13].…”

“…In the ADF model, stress-strain relationships are written in tensor form as [10] A kl kl ijkl E kl ijkl ij E E (13) where A are the anelastic strains. The anelastic stresses are…”

“…Solid, tetrahedral, four-node ADF finite elements are developed, using References [10,13,14]. Each node has three degrees of freedom (DOF) corresponding to the total displacements and three degrees of freedom corresponding to the anelastic displacements.…”