Search results for "Homogenization"
showing 10 items of 74 documents
Virtual element method for computational homogenization of composite and heterogeneous materials
2020
Abstract In this study, a two-dimensional multi-region framework, based on the use of the Virtual Element Method (VEM), is developed for computational materials homogenization and applied to different classes of widely employed heterogeneous materials. The VEM has recently emerged as a powerful generalisation of the Finite Element Method capable of dealing with very general polygonal mesh elements, including non-convex or highly distorted elements. Such features are appealing for the treatment of problems whose analysis domains present complex or statistical morphological features, which would generally require careful and time-consuming mesh/data preparation and regularization. In this wor…
The FE-Meshless multiscale approach applied to masonry structures
2015
Heterogeneous structures have an overall response that is strongly dependent on the inelastic events developing at the local level. In these structures, the most relevant kinematical and mechanical phenomena take place at a scale which is small if compared to the dimensions of the entire structure. In literature, a mesoscopic and a macroscopic scales of interest are distinguished, directly linked to as many theoretical approaches. The mesoscopic approach [1] considers materials and their interfaces individually, but many difficulties arise in the mesh creation and a fine discretization of the structure is needed, which leads to prohibitive computational costs. The macroscopic approach consi…
A posteriori error majorants of the modeling errors for elliptic homogenization problems
2013
In this paper, we derive new two-sided a posteriori estimates of the modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non-oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity.
Effective elastic properties of biocomposites using 3D computational homogenization and X-ray microcomputed tomography
2021
A 3D computational homogenization method based on X-ray microcomputed tomography (μCT) was proposed and implemented to investigate how the fiber weight fraction, orthotropy and orientation distribution affect the effective elastic properties of regenerated cellulose fiber-polylactic acid (PLA) biocomposites. Three-dimensional microstructures reconstructed by means of the X-ray μCT were used as the representative volume elements (RVEs) and incorporated into the finite element solver within the computational homogenization framework. The present method used Euclidean bipartite matching technique so as to eliminate the generation of artificial periodic boundaries and use the in-situ solution d…
Effective coefficients of thermoconductivity on some symmetric periodically perforated plane structures
1996
In this article we discuss an auxiliary problem which arises in the homogenization theory for the Laplacian on the plane with periodic array of square holes and homogeneous Neumann boundary conditions on those. Independently, this problem describes the process of thermoconductivity. We find the explicit formulas for effective coefficients of thermoconductivity (homogenized modula). We make also the asymptotic analysis of these formulas in the cases of big and small holes.
Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
2016
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CH of masonry materials via meshless meso-modeling
2014
In the present study a multi-scale computational strategy for the analysis of masonry structures is presented. The structural macroscopic behaviour is obtained making use of the Computational Homogenization (CH) technique based on the solution of the boundary value problem (BVP) of a detailed Unit Cell (UC) chosen at the meso-scale and representative of the heterogeneous material. The smallest UC is composed by a brick and half of its surrounding joints, the former assumed to behave elastically while the latter considered with an elastoplastic softening response. The governing equations at the macroscopic level are formulated in the framework of finite element method while the Meshless Meth…
A Model for Homogenization of Solid Alloying Admixtures in an Induction Crucible Furnace
2014
The paper presents a methodology for identification of homogenization time of alloying inclusions in an induction crucible furnace. The methodology is based on the Large Eddy Simulation (LES) Euler-Lagrange calculation of inclusions and a regression model for size of the inclusions and their density. The presented regression model avoids the repeated LES calculations and, therefore, is suitable for an optimization task.
A hybrid virtual–boundary element formulation for heterogeneous materials
2021
Abstract In this work, a hybrid formulation based on the conjoined use of the recently developed Virtual Element Method (VEM) and the Boundary Element Method (BEM) is proposed for the effective computational analysis of multi-region domains, representative of heterogeneous materials. VEM has been recently developed as a generalisation of the Finite Element Method (FEM) and it allows the straightforward employment of elements of general polygonal shape, maintaining a high level of accuracy. For its inherent features, it allows the use of meshes of general topology, including non-convex elements. On the other hand, BEM is an effective technique for the numerical solution of sets of boundary i…
From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography
2016
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the de…