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Vast number of challenging problems induced by the development of the Arctic region include mechanical stability of arbitrary structures under different thermal conditions. Snow, ice, permafrost are examples of the materials with a phase change and strongly different mechanical properties of distinct phases. Over time volumes of those phases may change, depending on external conditions. The aim of the work is to develop and test an approach to solve those problems using numerical methods. Splitting by physical processes is used, two tasks Stefan and mechanical are formulated. Theoretical methods to solve them are discussed, they are demonstrated on a test ice formation – artificial ice island. [ABSTRACT FROM AUTHOR]