Related papers: An Efficient Iterative Decoupling Method for Therm…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with a mixed three-field formulation with weak stress symmetry. The fluid flow is modeled with a…
The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for "intermediate" potentials…
A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in [R. Oyarz\'ua and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity, SIAM J. Numer.…
We propose a novel phase-field model to predict elastic microphase separation in polymer gels. To this end, we extend the Cahn-Hilliard free-energy functional to incorporate an elastic strain energy and a coupling term. These contributions…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
We present a new phase field crystal model for structural transformations in multi-component alloys. The formalism builds upon the two-point correlation kernel developed in Greenwood et al. for describing structural transformations in pure…
A theoretical-computational framework is proposed for predicting the failure behavior of two anisotropic brittle materials, namely, single crystal magnesium and boron carbide. Constitutive equations are derived, in both small and large…
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
A range of phenomena in the subsurface is characterised by the interplay between coupled thermal, hydraulic and mechanical processes and deforming structures such as fractures. Modelling subsurface dynamics can provide valuable…
In this study, we propose a parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions. This model describes the energy-driven motion of a surface cluster whose distributional solution was studied by…
In this paper, we present a novel solution strategy for the Cahn-Hilliard-Biot model, a three-way coupled system that features the interplay of solid phase separation, fluid dynamics, and elastic deformations in porous media. It is a…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied…
This paper proposes a phase field model (PFM) for describing hydraulic fracture propagation in transversely isotopic media. The coupling between the fluid flow and displacement fields is established according to the classical Biot…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a…