A constitutive law for the viscous and tertiary creep responses of ice to applied stress

Given the initial (secondary creep) viscous response of ice to applied stress, the subsequent tertiary creep is described by an orthotropic fabric evolution relation motivated by crystal rotation arguments. That is, the ice is described as a non-simple anisotropic fluid with dependence on the evolving deformation. Extension and modification of previous formulations are proposed, in which a general orthotropic flow law for stress includes terms which are quadratic functions of the strain-rate tensor, compared to previously analysed relations in which only linear in the strain-rate tensor terms were considered. Ice response functions in the extended law are constructed in such a way that the validity equalities and inequalities between the instantaneous directional viscosities at each stage of the tertiary creep are satisfied, and correlations with families of idealised uni-axial and simple shear tertiary creep curves for different applied stresses are possible. It is shown for a range of free parameters in the proposed orthotropic model how accurately the assumed uni-axial and shear creep curves can be approximated by the constructed response functions.