An Elastic-Plastic Constitutive Law for Sea Ice

Abstract

The AIDJEX sea ice model is extended by a careful consideration of the deformation measured relative to a reference configuration which changes according to the plastic flow. This approach makes the strain more meaningful than it was previously. The kinematic relations properly allow both finite stretch and rotation. The resulting kinematic relations reflect the feeling that sea ice response is independent of any fixed reference configuration. This formulation has been achieved by writing an incremental kinematic relation using the Finger deformation tensor. A special relation is presented for the case when elastic strain is small, as with sea ice. The elastic response and yield criterion as well as the plastic flow rule remain unchanged from those presently in use. The flow rule is derived by maximizing the rate at which plastic work is done. This approach unifies the development and also helps us to study the material instabilities that occur when the material softens. The material model satisfies the principle of material frame indifference. The model has been subjected to known deformation histories and the response is satisfactory. In many cases the stress history is indistinguishable from that of the previously used elastic-or-plastic model.