Related papers: Multiscale Finite Element Modeling of Nonlinear Ma…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying…
In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
In this paper, we propose a multicontinuum homogenization approach for nonlinear problems involving dynamically evolving multiscale media. The main idea of the proposed approach is that one of the fine-scale variables defines continua. It…
In this paper, we propose a novel multiscale model reduction strategy tailored to address the Poisson equation within heterogeneous perforated domains. The numerical simulation of this intricate problem is impeded by its multiscale…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…
Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the…
The last decade has witnessed the emergence of magneto-active polymers (MAPs) as one of the most advanced multi-functional soft composites. Depending on the magnetisation mechanisms and responsive behaviour, MAPs are mainly classified into…
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…
The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…
We present three-dimensional solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
This research investigates dynamic response of tunable periodic structures and homogenization methods in magnetoelastic composites (MECs). The research on tunable periodic structures is focused on the design, modeling and understanding of…
We carry out the homogenization of time-harmonic Maxwell's equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. In this setting,…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…