Numerical examination of the state of deformation in large terrestrial objects
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The reader could find in this paper an introduction to a numerical examination of the state of deformation of large bodies such as planets. This numerical study is done under the continuum mechanics theory and solved following the Finite Elements Method using the code-free FEniCS. This study is elaborated under two different hypothesis. The first one considers the Earth as a large object and therefore the solution is found under the hypothesis of finite displacements. With this consideration, the body is studied in the current placement in which are used the Almansi’s strains notation. Moreover, even though the solution to be found depends on the displacement, the model used to solve it can be a new variable called beta (β) that make the convergence of the solution easier. The second hypothesis used to solve the problem is viscoelasticity. Therefore, the solution now depends on time apart form the position. Nonetheless, before starting the 3-dimensional case of the Earth, some other examples are done in order to get used to work under viscoelasticity. Consequently, the study in 1D and in 3D of a viscoelastic beam can also be found in the present paper. As a matter of time and excessive difficulty, the study of the 3D Earth under viscoelastic hypothesis is done under infinitesimal strains. Both studies and previous cases are a satisfying approximation to examine the deformation state both in beams and massive bodies such as planets.