Related papers: Micromorphic Computational Homogenization for Mech…
In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities.…
In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic…
We apply the method of asymptotic homogenization to metamaterials with microscopically bianisotropic inclusions to calculate a full set of constitutive parameters in the long wavelength limit. Two different implementations of…
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure.…
A coupled hygro-thermo-mechanical computational model is proposed for fibre reinforced polymers, formulated within the framework of Computational Homogenisation (CH). At each macrostructure Gauss point, constitutive matrices for thermal,…
A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is provided in the present study. Field equations for the first-order equivalent medium are derived and overall constitutive tensors are…
This paper analyzes the random fluctuations obtained by a heterogeneous multi-scale first-order finite element method applied to solve elliptic equations with a random potential. We show that the random fluctuations of such solutions are…
An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral type featuring contributions of bulk and interfacial…
This paper deals with the homogenization problem of one-dimensional pseudo-elliptic equations with a rapidly varying random potential. The main purpose is to characterize the homogenization error (random fluctuations), i.e., the difference…
We investigate volume-element sampling strategies for the stochastic homogenization of particle-reinforced composites and show, via computational experiments, that an improper treatment of particles intersecting the boundary of the…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
We present an efficient method for the computation of homogenized coefficients of divergence-form operators with random coefficients. The approach is based on a multiscale representation of the homogenized coefficients. We then implement…
One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal…
Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to…
The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…
In homogenization theory, mathematical models at the macro level are constructed based on the solution of auxiliary cell problems at the micro level within a single periodicity cell. These problems are formulated using asymptotic expansions…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…