1 Introduction
Experiments indicate that granular solids harden when compacted
due to an irreversible increase in their effective density.
Consequently, the behavior of these solids is compaction
history dependent and can be characterized by their solid volume
fraction in the initial stress-free state.This history dependence
can result in complex dynamic loading behavior for
heterogeneous materials that have been either intentionally
or accidentally preconditioned. Examples of preconditioned
materials include layered or graded granular composites,
whose mechanical properties have been spatially tuned by
controlling the granular solid density distribution, and heterogeneous
energetic solids that have been damaged due to
aging and/or mechanical and thermal insult. These heterogeneous
materials usually consist of solid grains (grain size
≈ 0.1–250μm) embedded within a plastic or epoxy-like
binder phase. The granular solid volume fraction is large, often
exceeding 70%; thus, the granular solid may be regarded
as the main load bearing constituent, particularly in compression,
due to the occurrence of significant stress bridging
between grains as the material is volumetrically compacted.
The analysis of granular solids can provide leading order estimates
for the dynamic loading behavior of composite materials,
and will enable the effects of a binder phase to be clearly
isolated and subsequently investigated. The impact response
of granular solids is further complicated due to the nonlinear
influence of fine scale phenomena on their bulk behavior.This
influence is perhaps nomore severe than that exhibited by the
violent combustion of heterogeneous explosives originating
from the formation of intense temperature fluctuations in the
vicinity of intergranular contact surfaces referred to as “hotspots”
[14,15]. A comprehensive description of bulk material
behavior often requires the development of submodels
that accurately account for the influence of such grain scale
phenomena.
In this article, we give numerical predictions for timedependent
hyperbolic wave interactions induced by dynamic
compaction of a granular energetic solid having spatially
varying initial porosity.Unlike detailedmeso-scalemodeling