Thermobarokinetics of ice: constitutive formulation for the coupled effect of temperature, stress, and strain rate in ice

Abstract. Understanding and modeling the mechanical behavior of ice under varying thermal and loading conditions is essential for cryospheric science, permafrost engineering, and the design of polar infrastructure. A central challenge lies in capturing the strong coupling between stress, strain rate, and temperature, an interdependence referred to in this work as the thermobarokinetics of ice. This study presents a three-dimensional constitutive model that explicitly incorporates this coupling through a unified thermomechanical framework. Notably, the model employs shared functional dependencies for both viscosity and damage initiation, allowing key rate- and temperature-sensitive processes to be represented using a minimal set of physically interpretable parameters. Damage evolution is governed by an energy-based law that depends on strain rate and temperature. The model is calibrated and validated against triaxial compression and relaxation test data on polycrystalline ice, demonstrating its ability to capture salient features of ice mechanics such as ductile to brittle transitions, strain-rate-dependent strength, stress relaxation, and thermal softening. In addition, a novel healing mechanism inspired by viscous sintering is introduced, in which the rate of damage reversal is driven by viscous energy dissipation and modulated by pressure and temperature.