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The purpose of this study is to develop a homogenization approach that ensures both high accuracy and time-efficient solution for elastic-plastic functionally graded composites.

The paper presents a novel two-stage hybrid homogenization approach that combines advantages of the mean field homogenization and homogenization based on the finite element method (FEM). The groundbreaking nature of the developed approach is associated with division of the hybrid homogenization procedure into two stages, which allows to very efficiently determine the solution for arbitrary volume fraction of the reinforcement. This paper concerns also on modelling of composites with randomly distributed prolate and oblate particles. For this purpose, the hybrid homogenization was implemented in the framework of the discrete orientation averaging procedure involving pseudo-grain discretization method.

Agreement between the results obtained using the proposed approach and the standard FEM-based homogenization is very good (up to the volume fraction of 0.3).

The proposed two-stage homogenization approach allows to obtain the solution for materials with arbitrary volume fraction of the reinforcement very efficiently; therefore, it is highly beneficial for the two-scale modeling of nonlinear functionally graded materials and structures.

Effectiveness of the homogenization method for various heat transfer problems of engineering composites is the main aim of the paper. This comparative study is done for layered, fiber and particle reinforced Representative Volume Elements (RVE) for composites made of widely used components. Mathematical model is based on the effective modules method introduced for periodic composites ‐ effective heat conductivity is calculated in the closed form for specific spatial distribution of the components, while effective volumetric heat capacity is obtained from a simple spatial averaging. Such a homogenization scheme makes possible to significantly simplify the numerical analysis of transient heat transfer phenomena in various types of composites. The comparison of temperature histories obtained for the real and homogenized composite models is carried out using the Finite Element Method system ANSYS. As is demonstrated for various boundary problems, a homogenization technique in terms of composites types collected in the paper give satisfactory agreement with the real structure modeling; further numerical studies on composite cells discretization should increase modeling efficiency and diminish the numerical errors.

To review and discuss recently proposed homogenization methods for laminated magnetic cores and multi‐turn windings in FE models of electromagnetic devices.

The frequency‐domain homogenization is based on the adoption of complex and frequency‐dependent material characteristics (e.g. reluctivity) in the homogenized domain. The value of the complex quantity is obtained analytically or by means of a simple 2D FE model. The time‐domain counterpart requires the introduction of additional unknowns and equation.

The homogenization methods allow to take into account the global eddy current effect in the individual laminations and wires, with a reasonable precision and computational cost.

The homogenization methods have been validated numerically, i.e. by comparison with brute‐force FE computations where the eddy current effects are directly and accurately taken into account. Experimental validation should follow.

The analogy between the homogenization of laminated cores and windings has been evidenced.

This paper aims to present a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the representative volume element (RVE) of discrete particle assembly in the frame of the second-order computational homogenization methods for granular materials.

The proposed scheme is based on the generalized Hill’s lemma of gradient Cosserat continuum and the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE of discrete particle assembly. The generalized Hill’s lemma conducts to downscale the macroscopic strain or stress measures and to impose the periodic boundary conditions on the RVE boundary so that the Hill-Mandel energy equivalence condition is ensured. Because of the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE, the periodic boundary displacement and traction constraints together with the downscaled macroscopic strains and strain gradients, micro-rotations and curvatures are imposed in the point-wise sense without the need of introducing the Lagrange multipliers for enforcing the periodic boundary displacement and traction constraints in a weak sense.

Numerical results demonstrate that the applicability and effectiveness of the proposed scheme in imposing the periodic boundary conditions on the RVE. The results of the RVE subjected to the periodic boundary conditions together with the displacement boundary conditions in the second-order computational homogenization for granular materials provide the desired estimations, which lie between the upper and the lower bounds provided by the displacement and the traction boundary conditions imposed on the RVE respectively.

Each grain in the particulate system under consideration is assumed to be rigid and circular.

The proposed scheme for imposing periodic boundary conditions on the RVE can be adopted solely for estimating the effective mechanical properties of granular materials and/or integrated into the frame of the second-order computational homogenization method with a nested finite element method-discrete element method solution procedure for granular materials. It will tend to provide, at least theoretically, more reasonable results for effective material properties and solutions of a macroscopic boundary value problem simulated by the computational homogenization method.

This paper presents a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the RVE of discrete particle assembly for granular materials without need of introducing Lagrange multipliers for enforcing periodic boundary conditions in a weak (integration) sense.

To analyze effectively magnetic shielding effects by shields with fine structure.

Simplification of the fine structure makes it possible to analyze them efficiently. The authors have introduced a homogenization method to estimate effective permeability of magnetic composite structure for the static field. The homogenization method is applied to the analysis of magnetic shields composed of steel plates and steel rods against DC power lines to test its feasibility.

The properties of the magnetic shielding are analyzed by using the homogenization method. The errors of the magnetic fields increase in case of very few layers.

The simplification of the magnetic shields with fine structure by using the homogenization method makes it possible to analyze efficiently magnetic shielding effects, although the accuracy becomes worse in case of very few layers.

The present paper aims to explore a computational homogenisation procedure to investigate the full geometric representation of yield surfaces for isotropic porous ductile media. The effects of cell morphology and imposed boundary conditions are assessed. The sensitivity of the yield surfaces to the Lode angle is also investigated in detail.

The microscale of the material is modelled by the concept of Representative Volume Element (RVE) or unit cell, which is numerically simulated through three-dimensional finite element analyses. Numerous loading conditions are considered to create complete yield surfaces encompassing high, intermediate and low triaxialities. The influence of cell morphology on the yield surfaces is assessed considering a spherical cell with spherical void and a cubic RVE with spherical void, both under uniform strain boundary condition. The use of spherical cell is interesting as preferential directions in the effective behaviour are avoided. The periodic boundary condition, which favours strain localization, is imposed on the cubic RVE to compare the results. Small strains are assumed and the cell matrix is considered as a perfect elasto-plastic material following the von Mises yield criterion.

Different morphologies for the cell imply in different yield conditions for the same load situations. The yield surfaces in correspondence to periodic boundary condition show significant differences compared to those obtained by imposing uniform strain boundary condition. The stress Lode angle has a strong influence on the geometry of the yield surfaces considering low and intermediate triaxialities.

The exhaustive computational study of the effects of cell morphologies and imposed boundary conditions fills a gap in the full representation of the flow surfaces. The homogenisation-based strategy allows us to further investigate the influence of the Lode angle on the yield surfaces.

This paper aims to propose a homogenization method considering magnetic anisotropy for a magnetic field analysis of a turbine generator. To verify the validity of the proposed method, the effects of magnetic anisotropy and a space factor on a no-load saturation curve and no-load iron loss of the turbine generator are discussed.

The proposed method was derived from the combination of the homogenization of microscopic fields in a laminated iron core with the modelling of two-dimensional magnetic properties based on free energy. To verify the validity, the proposed method was applied to a finite-element analysis of a simple ring core model. Finally, a no-load saturation curve and iron loss of the turbine generator was investigated by using the proposed method.

The computational accuracy of the homogenization method considering magnetic anisotropy is almost the same as that of the detailed modelling of the laminated structure in the magnetic field analysis of the laminated iron core. Furthermore, it is clarified that magnetic anisotropy does not have a large influence on the no-load saturation curve of the turbine generator because of the large air gap. On the other hand, the space factor affects the shape of the no-load saturation curve.

This paper verifies the validity of the homogenization method considering magnetic anisotropy method and elucidates the effects of magnetic anisotropy and a space factor on no-load characteristics of the turbine generator.

In this paper, a new homogenization technique for the determination of dynamic and kinematic quantities of representative elementary volumes (REVs) in granular assemblies is presented. Based on the definition of volume averages, expressions for macroscopic stress, couple stress, strain and curvature tensors are derived for an arbitrary REV. Discrete element model simulations of two different test set‐ups including cohesionless and cohesive granular assemblies are used as a validation of the proposed homogenization technique. A non‐symmetric macroscopic stress tensor, as well as couple stresses are obtained following the proposed procedure, even if a single particle is described as a standard continuum on the microscopic scale.

Using finite element (FE) method corrects the microstress field resulting from the theory of homogenization in the region of composite in vicinity of the boundary. Obtains the corrected microstress field via an unsmearing procedure based on the known global solution and local peturbation. Analyses two examples: near a free boundary and next to a constrained border. FE models are constructed using both commercial FE code and the authors’ program for homogenization with some interfacing procedures. Shows qualitative results of computations and estimates influence on the microstress description of the local perturbation near the boundary.

Purpose — The purpose of this paper is to assess the accuracy of homogenization or the smeared stiffness approach in analyzing quadrigrid plates under transverse loads is assessed by comparing two distinct finite element solutions. The grid is assumed to be made of homogeneous isotropic material. However, the numerical solution procedure adopted here is applicable to grids made of unidirectional composite ribs. Design/methodology/approach — The finite element structural analysis is conducted by using plate elements based on the first‐order shear deformable theory (FSDT) and grillage analysis using first‐order shear deformable beam elements. The grillage analysis results, which are taken as the exact results, are compared with the approximate results obtained using FSDT plate elements, where the stiffness matrices obtained by the smeared stiffness approach are incorporated in the plate finite element formulation. Several sample problems are solved and the influences of rib spacing, rib thickness‐to‐width ratio, plate dimensions, and loading are examined. Findings — The results presented here show that homogenization yields reliable results when certain conditions are satisfied. Originality/value — The paper demonstrates that it is necessity to conduct thorough and systematic research studies revealing the accuracy of these models, as the applicability limits of homogenization are not clearly known.