Break and build: the ice-splitting model will make it cheaper to build ships for the Arctic

Russian scientists have developed a realistic computer model that reliably describes the interactions of ice with the icebreaker hull. Water in this state as a material is difficult to calculate, since it simultaneously combines plasticity and brittleness. All existing formulas took into account one of these aspects. For the first time, the developers managed to combine them together. The new program will significantly reduce the costs and time for field tests of new icebreakers, which are carried out in swimming pools or the open sea, the designers are confident. For more information, see the Izvestia article.

The interaction of ice and icebreaker

MIPT scientists have developed Russia's first physico-mathematical model that realistically predicts how ice breaks upon contact with a ship's hull. This will make it possible to reduce expensive field tests during the construction of icebreakers, calculate accident risks in advance and design more advanced vessels for the Arctic.

— Ice is a complex material. Under load, it behaves like elastic glass, then like plasticine, and then suddenly crumbles. That is, it does not just break, but first deforms and accumulates stress. We have developed an approach that allows us to take these effects into account with high accuracy," said Igor Petrov, Scientific Director of the Department of Computational Physics at MIPT.

Photo: British Antarctic Survey

Now, to simulate this process, scientists are conducting complex computer calculations based on discrete element methods. However, existing models cannot fully account for the complexity of ice's behavior — its ability to behave like a fragile body, splitting into fragments, and at the same time as a plastic material, slowly deforming under pressure.

This inaccuracy forces engineers to put excessive strength into projects and conduct expensive field tests. Thus, ice trials of a vessel in Arctic conditions can cost tens of millions of dollars due to high fuel, logistics and insurance costs, as well as risks to the crew and the environment, the authors of the project specified.

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MIPT has proposed a solution by developing a computer model that takes into account the key stages of the vessel's interaction with ice in elastic, plastic and brittle states. The mathematical Prandtl–Reiss model based on a system of equations relating deformations and stresses was used to describe the complex behavior of ice under load. The solution to these equations was found using the discontinuous Galerkin method.

— The calculated area is divided into small volumes in the form of tetrahedra (polyhedra of four triangular faces. — Ed.). Usually, such a grid behaves as a single unit, but this method allows each grid cell to behave independently. When a crack occurs in the material during process modeling, the program in the algorithm simply changes the rules of interaction between the cells, turning their common boundary into a free surface," explained Igor Petrov.

Simulation of a ship moving through an ice field

Photo: MIPT

The model has already been validated for two types of tasks: high-energy impact interaction and slow ice penetration by a massive object. For calculations, real physical parameters of ice from experimental data were used and the fracture characteristics at different rates of interaction were compared.

The results showed how either main cracks or plastic deflection zones form at different speeds, which is fully consistent with field observations.

In the future, scientists plan to expand the possibilities of the mechanical and mathematical model of ice, for example, to take into account the influence of salinity and temperature on its strength characteristics.

How can we speed up the creation of new vessels

As Yuri Chashkov, the inventor and developer of the Pomor icebreaker of the new design, told Izvestia, ice is a very difficult material to model, since it has different properties in each of the three dimensions. In addition, it is in water, which must also be taken into account in the formula. According to him, an icebreaker destroys an ice floe by pressing on it from above due to its own weight, while the force required for this depends on bending and a number of other parameters that must be included in the model. In addition, the bow lines of ships can also be different.

— Now in the center where icebreakers are designed, special pools of 100 by 10 m are being built, in which ice is frozen and tests are carried out with a model vessel. Also, during the construction of the ship, it is necessary to test it in real conditions. For example, in the Kara Sea. However, all this requires time and financial resources, so the ability to do it virtually could make the job easier," the specialist said.

Photo: RIA Novosti/Pavel Lvov

According to him, tests on the stand of the Pomor model have already been carried out. These data can be used to verify the proposed model, to what extent its calculations correspond to the experimental results.

Computer simulation is widely used worldwide as an alternative to real-world testing in the creation of complex technological products, whether aircraft, icebreakers or other marine equipment. Although it cannot completely replace field tests, it allows most of them to be transferred to a virtual format, which is extremely important, important and necessary, said Prokhor Tebin, a shipbuilding expert and director of the Center for Military Economic Research at the Institute of World Military Economics and Strategy at the National Research University Higher School of Economics.