Abstract
In this paper, a novel finite-element based method for finite-strain mechanochemistry with moving reaction fronts, which separate the chemically transformed and the untransformed phases, is proposed. The reaction front cuts through the finite elements and moves independently of the finite-element mesh, thereby removing the necessity for remeshing. The proposed method solves the coupled mechanics-diffusion–reaction problem. In the mechanical part of the problem, the force equilibrium and the displacement continuity conditions at the reaction front are enforced weakly using a Nitsche-like method. The formulation is applicable to the case of large deformations and arbitrary constitutive behaviour, and is also consistent with the minimisation of the total potential energy.
Highlights
Chemical reactions, such as oxidation or lithiation, in solid bodies lead to large volumetric expansions of materials and thereby lead to the emergence of mechanical stresses, which, in turn, affect the rates of the chemical reactions
A computational approach for finite-strain mechanochemistry with the reaction fronts that are non-conforming to the finite-element mesh was first proposed in [27,28], where the interface motion was handled using the level-set method, while the non-conforming interface was handled by the enhanced gradient finite-element method (FEM) in the mechanical and the diffusion problems
For the purpose of this paper, the diffusion is assumed to be quasi-stationary. This assumption is motivated by the fact that in most cases, the rate of the diffusion is much higher than the rate of the chemical reaction [17,42] and the diffusion process can be assumed to take place at the thermodynamic equilibrium
Summary
Chemical reactions, such as oxidation or lithiation, in solid bodies lead to large volumetric expansions of materials and thereby lead to the emergence of mechanical stresses, which, in turn, affect the rates of the chemical reactions. An established way of modelling mechanochemistry and phase transformations using FEM without remeshing is the combination of the extended finite-element method (XFEM) to solve the mechanical problem and the level-set method to move the interface, e.g. A computational approach for finite-strain mechanochemistry with the reaction fronts that are non-conforming to the finite-element mesh was first proposed in [27,28], where the interface motion was handled using the level-set method, while the non-conforming interface was handled by the enhanced gradient FEM in the mechanical and the diffusion problems. The method is illustrated with 2D numerical examples to show its numerical robustness in application to finite-strain mechanochemical problems with moving reaction fronts
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