Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change

This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur...

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Bibliographic Details
Published in:Computation 2023-04, Vol.11 (4), p.71
Main Authors: Ammosov, Dmitry, Vasilyeva, Maria
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Differential equations
Elastic properties
Finite element analysis
Finite element method
heterogeneous medium
Mathematical models
Mechanical properties
Mechanics
Methods
Modulus of elasticity
Multiscale analysis
online generalized multiscale finite element method
Partial differential equations
permafrost
phase change
Phase transformations (Statistical physics)
Phase transitions
Porous materials
Simulation
Soil porosity
Soils
thermo-mechanics
Two dimensional models
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Summary:This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur due to porosity growth caused by ice and water density differences. A finite-element approximation of this model on a fine grid is presented. The linearization from the previous time step is used to handle the nonlinearity of the problem. For reducing the size of the discrete problem, offline and online multiscale approaches based on the Generalized Multiscale Finite Element Method (GMsFEM) are proposed. A two-dimensional model problem simulating the heaving process of heterogeneous soil with a stiff inclusion was considered for testing the mathematical model and the multiscale approaches. Numerical solutions depict the process of soil heaving caused by changes in porosity due to the phase transition. The movement of the phase transition interface was observed. The change of medium properties, including the elastic modulus, was traced and corresponds to the phase transition interface. The proposed multiscale approaches significantly reduce the size of the discrete problem while maintaining reasonable accuracy. However, the online multiscale approach achieves better accuracy than the offline approach with fewer degrees of freedom.
ISSN:2079-3197
2079-3197
DOI:10.3390/computation11040071