Wave speeds, shear bands and the second-order work for incrementally nonlinear constitutive models

The paper discusses the consequences of the incremental nonlinearity of a constitutive model of a solid for the analyses of characteristic wave speeds, acceleration waves, the second-order work criterion and shear band formation. Incremental nonlinearity may entail qualitative changes in the results as compared to incrementally linear models. Certain well-known correlations cannot be established if the constitutive equation is assumed to be incrementally nonlinear. In particular, the spectra of the characteristic wave speeds and the acceleration wave speeds become continuous and are described by different equations. The second-order work criterion as a sufficient condition of uniqueness of the incremental boundary value problem loses its applicability in bifurcation analyses, unless the applicability can be proved for a particular type of nonlinearity. The singularity of the acoustic tensor in the general nonlinear case correlates neither with the vanishing of the second-order work nor with the shear band formation.