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Several composite materials consisting of ceramic particles embedded in a 6061‐T6 aluminum matrix have been studied under conditions of shock‐wave compression and release, including spallation. The 6061‐T6 matrix represents a material for which high‐rate shock‐wave response has been extremely well characterized for thermoelastic‐plastic deformation. The ceramic particles (alumina and mullite) are also well characterized, particularly in the elastic regime. Experimental tests consist of quasistatic, uniaxial‐stress compression of both virgin and shock‐recovered samples as well as time‐resolved velocity interferometer measurements under conditions of flat‐plate impact. The latter tests were performed with lithium fluoride windows for transmitted wave studies and free surfaces for spallation measurement. Theoretical analysis of the data is carried out with a pseudodissipation model originated by Barker [J. Composite Mat. 5, 140 (1971)] for application to elastic deformation of layered composites and generalized here to include thermoelastic‐plastic properties of the constituents. For a pseudodissipative model to apply to composite material response, significant geometrical randomization must be present in the composite structure; this is something that all commercially produced composites naturally possess. Randomization produces mechanical energy traps, which convert some fraction of regular, directed motion into random elastic vibrations behind the shock front. Within a few microseconds (depending on the pinned dislocation segment density) this macroscale, continuum vibrational energy is converted to heat by means of the anelastic properties of the metal matrix. The use of pseudodissipation as a means of representing dispersive composite material behavior is thus placed on a more secure physical foundation.