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1. A quasi-one-dimensional ice mélange flow model based on continuum descriptions of granular materials

   https://doi.org/10.5194/egusphere-2024-297  

   Amundson, Jason M; Robel, Alexander A; Burton, Justin C; Nissanka, Kavinda (March 2024, EGU)

   Abstract. Field and remote sensing studies suggest that ice mélange influences glacier-fjord systems by exerting stresses on glacier termini and releasing large amounts of freshwater into fjords. The broader impacts of ice mélange over long time scales are unknown, in part due to a lack of suitable ice mélange flow models. Previous efforts have included modifying existing viscous ice shelf models, despite the fact that ice mélange is fundamentally a granular material, and running computationally expensive discrete element simulations. Here, we draw on laboratory studies of granular materials, which exhibit viscous flow when stresses greatly exceed the yield point, plug flow when the stresses approach the yield point, and stress transfer via force chains. By implementing the nonlocal granular fluidity rheology into a depth- and width-integrated stress balance equation, we produce a numerical model of ice mélange flow that is consistent with our understanding of well-packed granular materials and that is suitable for long time-scale simulations. For parallel-sided fjords, the model exhibits two possible steady state solutions. When there is no calving of new icebergs or melting of previously calved icebergs, the ice mélange is pushed down fjord by the advancing glacier terminus, the velocity is constant along the length of the fjord, and the thickness profile is exponential. When calving and melting are included, the ice mélange evolves to another steady state in which its location is fixed relative to the fjord walls, the thickness profile is relatively steep, and the flow is extensional. For the latter case, the model predicts that the steady-state ice mélange buttressing force depends on the surface and basal melt rates through an inverse power law relationship, decays roughly exponentially with both fjord width and gradient in fjord width, and increases with the iceberg calving flux. The increase in buttressing force with the calving flux, which depends on glacier thickness, appears to occur more rapidly than the force required to prevent the capsize of full-glacier-thickness icebergs, suggesting that glaciers with high calving fluxes may be more strongly influenced by ice mélange than those with small fluxes. 

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2. A quasi-one-dimensional ice mélange flow model based on continuum descriptions of granular materials

   https://doi.org/10.5194/tc-19-19-2025  

   Amundson, Jason M; Robel, Alexander A; Burton, Justin C; Nissanka, Kavinda (January 2025, The Cryosphere)

   Field and remote sensing studies suggest that ice mélange influences glacier–fjord systems by exerting stresses on glacier termini and releasing large amounts of freshwater into fjords. The broader impacts of ice mélange over long timescales are unknown, in part due to a lack of suitable ice mélange flow models. Previous efforts have included modifying existing viscous ice shelf models, despite the fact that ice mélange is fundamentally a granular material, and running computationally expensive discrete element simulations. Here, we draw on laboratory studies of granular materials, which exhibit viscous flow when stresses greatly exceed the yield point, plug flow when the stresses approach the yield point, and exhibit stress transfer via force chains. By implementing the nonlocal granular fluidity rheology into a depth- and width-integrated stress balance equation, we produce a numerical model of ice mélange flow that is consistent with our understanding of well-packed granular materials and that is suitable for long-timescale simulations. For parallel-sided fjords, the model exhibits two possible steady-state solutions. When there is no calving of icebergs or melting of previously calved icebergs, the ice mélange is pushed down-fjord by the advancing glacier terminus, the velocity is constant along the length of the fjord, and the thickness profile is exponential. When calving and melting are included and treated as constants, the ice mélange evolves into another steady state in which its location is fixed relative to the fjord walls, the thickness profile is relatively steep, and the flow is extensional. For the latter case, the model predicts that the steady-state ice mélange buttressing force depends on the surface and basal melt rates through an inverse power-law relationship, decays roughly exponentially with both fjord width and gradient in fjord width, and increases with the iceberg calving flux. The buttressing force appears to increase with calving flux (i.e., glacier thickness) more rapidly than the force required to prevent the capsizing of full-glacier-thickness icebergs, suggesting that glaciers with high calving fluxes may be more strongly influenced by ice mélange than those with small fluxes. 

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3. Hybrid discrete-continuum modeling of shear localization in granular media

   https://doi.org/10.1016/j.jmps.2021.104404  

   Chen, Peter Yichen; Chantharayukhonthorn, Maytee; Yue, Yonghao; Grinspun, Eitan; Kamrin, Ken (August 2021, Journal of the Mechanics and Physics of Solids)

   null (Ed.)
4. Hybrid grains: adaptive coupling of discrete and continuum simulations of granular media

   https://doi.org/10.1145/3272127.3275095  

   Yue, Yonghao; Smith, Breannan; Chen, Peter Yichen; Chantharayukhonthorn, Maytee; Kamrin, Ken; Grinspun, Eitan (January 2019, ACM Transactions on Graphics)
5. ATOMIC-TO-CONTINUUM MULTISCALE MODELING OF DEFECTS IN CRYSTALS WITH NONLOCAL ELECTROSTATIC INTERACTIONS

   https://doi.org/10.1115/1.4056111  

   Jha, Prashant; Marshall, Jason; Knap, Jaroslaw; Dayal, Kaushik (January 2023, Journal of Applied Mechanics)

   This work develops a multiscale modeling framework for defects in crystals with general geometries and boundary conditions in which ionic interactions are important, with potential application to, e.g., ionic solids and electric field interactions with materials. The overall strategy is posed in the framework of the Quasicontinuum multiscale method; specifically, the use of a finite-element inspired kinematic description enables a significant reduction in the large number of degrees of freedom to describe the atomic positions. The key advance of this work is a method for the efficient and accurate treatment of nonlocal electrostatic charge-charge interactions without restrictions on the geometry or boundary conditions. Electrostatic interactions are long-range with slow decay, and hence require consideration of all pairs of charges making a brute-force approach computationally prohibitive. The method proposed here accounts for the exact charge-charge interactions in the near-field and uses a coarse-grained approximation in the far-field. The coarse-grained approximation and the associated errors are rigorously derived based on the limit of a finite body with a small periodic lengthscale, thereby enabling the errors in the approximation to be controlled to a desired tolerance. The method is applied to a simple model of Gallium Nitride and it is shown that electrostatic interactions can be approximated with a desired level of accuracy using the proposed methodology. 

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