INDUCED ANISOTROPY IN LARGE ICE SHIELDS - THEORY AND ITS HOMOGENIZATION

For polycrystalline ice, an isothermal flow law is derived from micros copic considerations concerning constitutive equations and kinematic a ssumptions. On the basis of an elasto-plastic decomposition of the def ormation gradient on the grain level and by assuming a continuous dist ribution of different orientated grains in the vicinity of each materi al point the classical macroscopic field quantities are obtained by ca lculating the weighted mean values of the associated microscopic quant ities. The weighting function is represented by a so called Orientatio n Distribution Function (ODF). For the general two dimensional (plane and rotationally symmetric) flow regime analytical representations of the ODF are derived under the assumption of a uniform stress distribut ion over all polycrystals (Sachs-Condition) and a plane or rotationall y symmetric orientation distribution. Additionally, the influence of t he macroscopic constitutive relations on the microscopic level is rest ricted to isotropic parts only. Simple examples are used to demonstrat e the ability of the ODF to perform the evolving texture. The microsco pic constitutive relation for the dissipation potential is assumed to be an objective function of the stress deviator and is expressed as a polynomial law up to the power n(max) = 4, as proposed by Lliboutry (1 993). A second order structure tensor which depends on the ODF is intr oduced to consider induced anisotropy. The resulting macro fluidities (inverse viscosities) are then calculated from the analytical represen tation of the ODF for the case of uniaxial loading underlying linear n (max) = 1 and nonlinear n(max) = 3 material behaviour.