A quasi-steady form of the Hibler VP model with replacement closure is shown to be unstable during all opening deformations and some closing deformations. To obtain these results, we derived equations governing linear perturbations to the model solutions and solved the homogeneous linear equations by introducing normal modes. Modes that can grow without external forcing represent instabilities. Some modes double in about a year. They likely give predictable solutions over reasonable periods. Other modes double every few seconds, so their results are unpredictable for meaningful simulation periods. The analysis should help all modelers modify their constitutive laws so that future ice dynamics models are stable.
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