Transient creep, an important deformation mechanism for polycrystallin
e ice at quasi-static strain rates, is characterized by rate and tempe
rature sensitivity, by isotropic and kinematic strain hardening, as we
ll as by fabric and deformation-induced anisotropy. A physically based
constitutive model, using internal state variables, has been develope
d by Shyam Sunder and Wu (1989a, b) to describe the multiaxial behavio
r of ice undergoing transient creep. To solve boundary value problems
using this constitutive theory requires the numerical time integration
of a coupled set of stiff and highly nonlinear first-order differenti
al equations. A closed-form Newton-Raphson (tangent) formulation, in c
onjunction with the alpha-method of integration, is developed to solve
the constitutive equations. The fully consistent constitutive Jacobia
n matrix that is used to assemble the finite element tangent stiffness
matrix is also established in closed form. This algorithm is implemen
ted as a subroutine in the finite element program ABAQUS and its predi
ctions are verified against experimental data and known solutions. The
importance of transient creep is demonstrated by performing simulatio
ns of: (1) Arrested subsurface penetration; and (2) in-plane indentati
on of a floating ice sheet.