Constitutive equations at high rates of loading

The stress-strain-time dependence for some metals and alloys based on the idea of non-linear heredity is proposed. In particular the theory can be applied to the metals with delayed yielding (low carbon mild steels). It is shown that the phenomenon of yield delay affects the slope of stress-strain diagram. The proposed theory is applied to the analysis of the results of the tests for some metals under various loading and unloading rates and also to the creep and relaxation experimental data. Using some additional assumption the basic equation can be applied to the description of material behavior under repeated loading and to incremental elastic wave propagation. The problem of the longitudinal wave propagation in non-linear hereditary type medium has been solved using the Laplace transform technique. An asymptotic expansion of the solution in the vicinity of the wave front has been obtained.