Constitutive dynamic-order model for nonlinear contact phenomena

A dynamic integro-differential operator of variable order is suggested for a mode adequate description of processes, which involve state dependent mea sures of elastic and inelastic material features. For any negative constant order this operator coincides with the well-known operator of fractional i ntegration. The suggested operator is especially effective in cases with st rong dependence of the behavior of the material on its present state-i.e., with pronounced nonlinearity. Its efficiency is demonstrated for cases of v iscoelastic and elastoplastic spherical indentation into such materials (al uminum, vinyl) and into an elastic material (steel) used as a reference. Pe culiarities in the behavior of the order function are observed in these app lications, demonstrating the "physicality" of this function which character izes the material state. Mathematical generalization of the fractional-orde r integration-differentiation in the sense of variability of the operator o rder, as well as definitions and techniques, are discussed.