Modal damping in vibrating objects via dissipation from dispersed frictional microcracks

Abstract

Many materials under multiaxial periodic loading exhibit rate-independent internal dissipation per cycle. Constitutive modelling for such dissipation under spatially variable triaxial stresses is needed for calculating modal damping of solid bodies using computational packages. Towards a micromechanically motivated model for such dissipation, this paper begins with a frictional microcrack in a linearly elastic solid under far-field time-periodic tractions. The material is assumed to contain many such non-interacting microcracks. Single-crack simulations, in two and three dimensions, are conducted using ABAQUS. The net cyclic single-crack dissipation under arbitrary triaxial stresses is found to match, up to one fitted constant, a formula based on a pseudostatic spring-block model. That formula is used to average the energy dissipation from many randomly oriented microcracks using Monte Carlo averaging. A multivariate polynomial is fitted to the Monte Carlo results. The polynomial is used in finite-element simulation of a solid object, wherein modal analysis is followed by computation of the net cyclic energy dissipation via elementwise integration. The net dissipation yields an equivalent modal damping. In summary, starting from a known formula for a single crack, this paper develops and implements a method for computationally modelling the modal damping of arbitrarily shaped solid bodies.