On strain-rate independent damping in continuum mechanics

Abstract

Strain-rate independent damping is a theory of energy dissipation in solids. It is based on the assumption that an increase or decrease in the strain-energy density correlates with a multiplication of 1+η or 1-η respectively, of the material stiffness matrix, with 0≤ η <<1 with η either a constant or a function of the strain-energy density.This type of damping has a loss (Watt m-3) of η times the absolute value of the rate of change of the strain-energy density. For uni-axial strain and a suitable function of the strain-energy density, the energy dissipation (Joule m-3) due to an infinitesimal change of the strain is strain-rate independent and proportional to the absolute value of the strain raised to a power ranging from 1 to 2. This is an idealization of tests results, based on forced harmonic strain cycles, with an energy dissipation (Joule m-3 cycle-1) found to be nearly frequency independent and almost proportional to the strain amplitude raised to a power ranging from 2 to 3.The PDEs derived for strain-rate independent damping can be solved for 1, 2 or 3 dimensions via direct integration, provided that the software supports PDE coefficients that are functions of the solution and its space and time derivatives. A 3D problem with 22,000 DOF's and 10,000 time steps was solved successfully and convincingly.