Numerical Modeling of Transient Creep in Polycrystalline Ice

Abstract

Transient creep, an important deformation mechanism for polycrystalline ice at quasi‐static strain rates, is characterized by rate and temperature sensitivity, by isotropic and kinematic strain hardening, as well as by fabric and deformation‐induced anisotropy. A physically based constitutive model, using internal state variables, has been developed by Shyam Sunder and Wu (1989a, b) to describe the multiaxial behavior 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 differential equations. A closed‐form Newton‐Raphson (tangent) formulation, in conjunction with the α‐method of integration, is developed to solve the constitutive equations. The fully consistent constitutive Jacobian matrix that is used to assemble the finite element tangent stiffness matrix is also established in closed form. This algorithm is implemented as a subroutine in the finite element program ABAQUS and its predictions are verified against experimental data and known solutions. The importance of transient creep is demonstrated by performing simulations of: (1) Arrested subsurface penetration; and (2) in‐plane indentation of a floating ice sheet.