Numerical modeling of ice behavior under high velocity impacts

In this work a constitutive relation for ice at high strain rates and an algorithm for its numerical integra tion are developed. This model is based on the Drucker Prager plasticity criteria, which allows a different behavior in tension and in compression. In addition a failure criteria, based on pressure cut offs, is imple mented to describe the ice damage. In order to validate the constitutive model, numerical simulations were compared with experimental results, in which ice cylinders were impacted against a steel plate, allowing the measurement of the contact load. Three different numerical solvers are used in order to ana lyze its performance to appropriately modeling the ice behavior.This research was done with the financial support of the Span ish Ministry of Education under Project reference DPI2010 15123 and of the Region of Madrid and University Carlos III of Madrid under Project reference CCG10 UC3M/DPI 4694.Publicad

Solidification and separation in saline water

Motivated by the formation of brine channels, this paper is devoted to a continuum model for salt separation and phase transition in saline water. The mass density and the concentrations of salt and ice are the pertinent variables describing saline water. Hence the balance of mass is considered for the single constituents (salt, water, ice). To keep the model as simple as possible, the balance of momentum and energy are considered for the mixture as a whole. However, due to the internal structure of the mixture, an extra-energy flux is allowed to occur in addition to the heat flux. Also, the mixture is allowed to be viscous. The constitutive equations involve the dependence on the temperature, the mass density of the mixture, the salt concentration and the ice concentration, in addition to the stretching tensor, and the gradient of temperature and concentrations. The balance of mass for the single constituents eventually result in the evolution equations for the concentrations. A whole set of constitutive equations compatible with thermodynamics are established. A free energy function is given which allows for capturing the main feature which occurs during the freezing of the salted water. That is, the salt entrapment in small regions (brine channels) where the cryoscopic effect forbid complete ice formation

Dynamics of coupled ice-ocean system in the marginal ice zone: Study of the mesoscale processes and of constitutive equations for sea ice

This study is aimed at the modelling of mesoscale processed such as up/downwelling and ice edge eddies in the marginal ice zones. A 2-dimensional coupled ice-ocean model is used for the study. The ice model is coupled to the reduced gravity ocean model (f-plane) through interfacial stresses. The constitutive equations of the sea ice are formulated on the basis of the Reiner-Rivlin theory. The internal ice stresses are important only at high ice concentrations (90-100%), otherwise the ice motion is essentially free drift, where the air-ice stress is balanced by the ice-water stress. The model was tested by studying the upwelling dynamics. Winds parallel to the ice edge with the ice on the right produce upwilling because the air-ice momentum flux is much greater that air-ocean momentum flux, and thus the Ekman transport is bigger under the ice than in the open water. The upwelling simulation was extended to include temporally varying forcing, which was chosen to vary sinusoidally with a 4 day period. This forcing resembles successive cyclone passings. In the model with a thin oceanic upper layer, ice bands were formed

Problems Associated with Making Mechanical Measurements on Water–Ice at Quasistatic and Dynamic Strain Rates

Abstract: Space penetrators are a potential method of inserting instrumentation onto ice-covered bodies in the solar system. Part of a study to see whether this is feasible involves numerically simulating impact of the penetrator into ice at impact velocities of a few 100 m/s. In order to do this accurately, it is necessary to have a constitutive model for water ice that is valid at the strain rates and temperatures relevant to impact in the Outer Solar System. This paper reports certain issues and difficulties that arose during a study to obtain this data

NUMERICAL SIMULATION OF ICE MILLING LOADS ON PROPELLER BLADE WITH COHESIVE ELEMENT METHOD

In ice-infested waters, propellers of a polar ship are likely to be exposed to ice loads in different scenarios. Propeller milling with ice is one of the most dangerous cases for ice-propeller interaction. In this study, we try to simulate dynamic milling process of ice-propeller and reproduce resulting physical phenomena. Cohesive element method is used to model ice in the simulation. To simulate material properties of ice, an elastoplastic softening constitutive law is developed. Both crushing and fracture failures are included in the ice-propeller milling process. The ice loads in 6 Dofs acting on blades of a propeller are calculated in time domain. The average and standard deviations of simulated dominant ice loads are compared with those from model test. A good agreement is achieved. By varying propeller rotation speed, advance velocity and cutting depth on ice block, the sensitivity study has been carried out. The results show that dominant ice loads are affected much by the three parameters. It is shown that decreasing rotation speed, or increasing advance velocity and cutting depth may lead to higher ice loads. Care should be taken to avoid over-loading on propeller when operating in ice for polar ship

A continuum-mechanical model for the flow of anisotropic polar ice

In order to study the mechanical behaviour of polar ice masses, the method of continuum mechanics is used. The newly developed CAFFE model (Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor) is described, which comprises an anisotropic flow law as well as a fabric evolution equation. The flow law is an extension of the isotropic Glen's flow law, in which anisotropy enters via an enhancement factor that depends on the deformability of the polycrystal. The fabric evolution equation results from an orientational mass balance and includes constitutive relations for grain rotation and recrystallization. The CAFFE model fulfills all the fundamental principles of classical continuum mechanics, is sufficiently simple to allow numerical implementations in ice-flow models and contains only a limited number of free parameters. The applicability of the CAFFE model is demonstrated by a case study for the site of the EPICA (European Project for Ice Coring in Antarctica) ice core in Dronning Maud Land, East Antarctica.Comment: 12 pages, 11 figures, 1 tabl

a new fully three dimensional numerical model for ice dynamics

AbstractThe problem of describing ice dynamics has been faced by many researchers; in this paper a fully three-dimensional model for ice dynamics is presented and tested. Using an approach followed by other researchers, ice is considered a non-linear incompressible viscous fluid so that a fluid-dynamic approach can be used. The model is based on the full three-dimensional Stokes equations for the description of pressure and velocity fields, on the Saint-Venant equation for the description of the free-surface time evolution and on a constitutive law derived from Glen's law for the description of ice viscosity. The model computes the complete pressure field by considering both the hydrostatic and hydrodynamic pressure components; it is time-evolutive and uses high-order numerical approximation for equations and boundary conditions. Moreover it can deal with both constant and variable viscosity. Three theoretical tests and two applications to Priestley Glacier, Antarctica, are presented in order to evaluate the performance of the model and to investigate important phenomena of ice dynamics such as the influence of viscosity on pressure and velocity fields, basal sliding and flow over perturbed bedrocks. All these applications demonstrate the importance of treating the complete pressure and stress fields