The influence of porosity on the elastic response of homogeneous and structural composite media

Continuum theories of composites are employed to analyze the influence of inclusions and porosity on the elastic response of both homogeneous and laminated composite media. The general model analyzed consists of a periodic array of two perfectly bonded laminates; one of which consists of an elastic homogeneous material while the other is made up of a periodic array of cylindrical elastic inclusions that are distributed in another elastic matrix material. Several specific models are deduced as special cases. In all cases, porosity is simulated in the limit as the properties of the inclusions identically vanish. It is demonstrated that porosity plays a major role in the geometric dispersion of such media; in particular, it increases the arrival and rise times (spreading) of a propagating transient pulse. For the special case of elastic inclusions in a homogeneous matrix media, the present results correlate very well with existing experimental data and other approximate analyses.