Ice Mechanics. Part 1. Viscoelastic Solid Relations for the Deformation of Ice. Part 2. Single Integral Representations for Non-Linear Viscoelastic Solids

摘要

The finite linear viscoelastic solid and single integral representation with non-linear dependence on history are investigated in uni-axial stress. Both integral kernels in the stress formulation are determined by single-step constant strain tests, and both kernels in the strain formulation are determined by single-step constant stress tests. Single integral stress and strain formulations are not equivalent. The stress histories required to maintain constant strain-rate for both models are determined from the Volterra integral equations given by the strain formulations once their kernels are determined by constant stress tests. A frame indifferent differential operator law relating stress, stress-rate, strain, and strain-rate is constructed to describe the qualitative features of both constant load and constant displacement rate response in uni-axial stress experiments. No lower order differential relation can describe both responses, but the two responses are not sufficient to determine the response coefficients of the relation. The jump relation is determined for a stress discontinuity applied in a general configuration. A simple initially isotropic model is proposed to investigate the effects of loading history and the anisotropy induced in a configuration following a loading-unloading cycle.