Quasilinear rate-type constitutive equations and incremental stress waves

The requirement that the leading edge of an incremental loading pulse superimposed on a preloading that has reached a constant state will propagate at the elastic wave speed imposes some restrictions on the material functions describing a quasilinear rate-type material. These restrictions are discussed, and it is shown that the incremental wave behavior implies the existence of at least one relaxation boundary, and that a natural continuous transition from the quasilinear equation to a semilinear equation occurs in the neighborhood of the relaxation boundary.How the knowledge of a relaxation boundary can be used in determining the material functions is also discussed.