A Uniaxial Nonlinear Viscoelastic Constitutive Relation for Ice

Abstract

The present paper concerns the description of uniaxial deformation and failure of ice in uniaxial compression in terms of a nonlinear viscoelastic constitutive theory. The constitutive model incorporates explicit dependence upon micro-structural defect growth and assumes the form of a so-called modified superposition integral contaiing a linear kernel which depends only upon time. This last feature will greatly simplify the task of experimentally characterizing the various material properties which appear in the theory. The existence of correspondence principles for the model will also facilitate the solution of practical boundary value problems. Predictions based upon this model will be shown to agree qualitatively with experimental results for creep (constant stress) and strength (constant strain-rate) tests on ice. In addition, specific empirically deduced relationships between stress, strain, strain-rate and time at certain critical points in these standard tests will be shown to result directly from the constitutive theory as special cases.