Homogenization models for the rheology and microstructure evolution of sea ice
Abstract
Sea ice is a multi-phase material, with complex structure at several length scales, exhibiting elastoviscoplasticrheology. At the larger scales, sea ice is made up of o` es that are up to 1 km in lateradimensions and are separated by `leads of open water or (refrozen) thinner ice. At the smaller scales, theo es are made of polycrystalline aggregates of hexagonal ice crystals with embedd inclusions of brine. The dominant structure at this scale consists of columnar grains displaying a pronounced texture where the c-symmetry axes of the grains lie in the horizontal plane, but with random orientations in this plane. Because the HCP ice crystals exhibit highly anisotropic viscoplastic behavior, with `easy glide on basal planes and `hard slip on non-basal systems, this strong texture has significant implications for the macroscopic response. On the other hand, the intra-grain brine inclusions, which have elongated shapes with the largest dimension in the vertical direction, are also expected to have signi#cant implications for the rheological response of sea ice. The primary objective of this project is the development and application of homogenization techniques for sea ice. For this purpose, we propose a fundamental bottom-up approach, starting with the basic mechanisms at the smaller scales, namely, dislocation slip on crystallographic planes, complemented by elastic deformation to accommodate general deformations in the kinematically constrained grains, and accounting for the microstructures at the singlecrystal and polycrystal levels. Building on recently developed nonlinear homogenization techniques for purely viscoplastic response, we propose an incremental variational method (IVM) allowing their generalization to account for coupled elastic-viscoplastic e -ects. The IVM reduces the two-potential (i.e., fre energy + dissipation) homogenization problem to one for a single-potential incremental problem, albeit with non-uniform phase properties. To solve this problem, a two-step procedure is proposed: (1) a nonlinear homogenization method is introduced to deal with the nonlinearity of the dissipation potential by means of a suitably de?ned linear comparison composite (LCC) with nonuniform phases, and (2) a related linear homogenization approach is then used to deal with the heterogeneity of the eigenstrains in the phases by means of a second LCC with piecewise uniform properties. Finally, the constitutivemodels to be developed will be used to investigate the possible development of shear localization instabilities in sea ice. We hypothesize that such shear bands may provide the source for crack formation in the solid ice cover leading to the formation of leads.The development of accurate and reliable models for sea ice rheology, as well as the understanding of sea icefracture, is of crucial importance in numerous applications of interest to the Navy, including ice breaking, ice forces on ships, submarines and other marine structures, shipping forecasts and navigation in the Arctic, ice dynamics in the polar regions and global climate models. Although the focus of this project will be on sea ice, the homogenization techniques to be developed will be applicable to many other material systems, including metallic and polymer-based composite systems that are also of interest for other Navy applications, including ballistic penetration in metal-based ships and structural integrity of composite-based submarines.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 04, 2017
- Source ID
- N000141712076
Entities
People
- Pedro Ponte Castañeda
Organizations
- Office of Naval Research
- United States Navy
- University of Pennsylvania