Abstract 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.

中文翻译：

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冰对外加应力的粘性和三次蠕变响应的本构定律

摘要 考虑到冰对外加应力的初始（二次蠕变）粘性响应，随后的三次蠕变由晶体旋转参数驱动的正交各向异性织物演化关系描述。也就是说，冰被描述为依赖于演化变形的非简单各向异性流体。提出了对先前公式的扩展和修改，其中应力的一般正交各向异性流动定律包括应变率张量的二次函数项，与先前分析的关系相比，其中仅考虑应变率张量项中的线性。扩展定律中的冰响应函数是这样构建的，即满足三次蠕变每个阶段瞬时方向粘度之间的有效性等式和不等式，并且与不同外加应力的理想化单轴和简单剪切三次蠕变曲线族的相关性是可能的。它显示了所提出的正交各向异性模型中的一系列自由参数，可以通过构建的响应函数近似假设的单轴和剪切蠕变曲线的准确程度。