Computational Homogenization Technique Research Articles

Electromagnetohydrodynamic (EMHD) flow through porous media—Multiscale approach

Electromagnetohydrodynamic (EMHD) flow in porous media is recently gaining substantial attention from researchers. EMHD involves analyzing the combined effects of electric and magnetic fields on the behavior of fluid flow through a medium. The effective permeability of porous materials is of great interest for many environmental and industrial applications. The present study focuses on the modeling of single-phase fluid flow in porous media under combined effects of electric and magnetic fields at the pore scale by employing a two-scale computational homogenization technique. The primary objective of this study is to establish a definition of “electromagnetopermeability” that accurately characterizes the effective permeability of a porous medium under the EMHD effects. Additionally, the study investigates the impact of wall zeta potential, Debye length, and the intensity of external magnetic and electric fields, represented by the Hartmann number and the non-dimensional parameter S, respectively, on the electromagnetopermeability tensor within an idealized three-dimensional periodic porous domain. It is observed that the EM-permeability is significantly affected by the existence of the flow-assisting and flow-opposing components of the Lorentz force term in the momentum equation. The implications of this research extend to several industries, including geology, medicine, chemistry, and energy conversion.

An FFT-based homogenization scheme for cohesive zones with an application to adhesives and the core material of thin metal sandwich plates

Cohesive Zone Models with finite thickness are widely used for the fracture mechanical modeling of material layers, e.g., adhesive layers. Within this approach, the whole layer is modeled as a cohesive zone. Moreover, computational homogenization techniques are crucial for the development of advanced engineering materials, which are often heterogeneous. Compared to the commonly used Finite Element Method (FEM), solvers based on the Fast Fourier Transform (FFT) are expected to reduce the computational effort needed for the homogenization. Originated from an existing method for the computational homogenization of cohesive zones using FEM, a novel FFT-based homogenization scheme for cohesive zone models is presented. Our implementation of the FFT solver uses a displacement-based Barzilai–Borwein scheme and a non-local ductile damage model for the fracture behavior. Finally, the practical application of the method is discussed using an adhesive layer and the core material of HybrixTM metal sandwich plates as examples.

Development and analysis of functionally-graded SiAlON composites with computationally designed properties for cutting inserts

There is an increasing demand for developing new cutting tools with exceptional thermomechanical and tribological properties to meet the growing demands of the machining industry. By introducing a novel concept of functionally graded (FG) materials, the work aims to develop a new class of SiAlON-based ceramic composites for cutting tool applications. The effective properties of hybrid (TiCN/Co/hBN) functionally graded SiAlON-based composites are predicted using effective medium approximation and mean-field computational homogenization technique. Thermal conductivity, thermal expansion coefficient, elastic modulus, and fracture toughness are among the predicted properties. To get the optimal composite properties, attributes such as reinforcing volume fractions, particle sizes, layer numbers, layer material compositions, interfacial resistance, and porosity are considered. As a validation, FG SiAlON composite insert samples with tailored properties are developed using spark plasma sintering. The sintered samples are characterized to relate the microstructure with obtained properties.

ZnO microrods sandwiched between layered CNF matrix: Fabrication, stress transfer, and mechanical properties

Functional metal oxide particles are often added to the polymers to prepare flexible functional polymer composites with adequate mechanical properties. ZnO and cellulose nanofibrils (CNF) outstand among these metal oxides and the polymer matrices respectively due to their various advantages. Herein, we in situ prepare ZnO microrods in the presence of CNF, which resultes in a layered composite structure. The ZnO microrods are sandwiched between the CNF layers and strongly bind to highly charged CNF, which provides a better stress transfer during mechanical activity. Digital image correction (DIC) and finite element analysis-based computational homogenization methods are used to investigate the relationship between mechanical properties and composite structure, and the stress transfer to the ZnO microrods. Full-field strain measurements in DIC reveal that the in situ ZnO microrods preparation leads to their homogenous distribution in the CNF matrix unlike other methods, which require external means such as ultrasonication. The computational homogenization technique provides a fairly good insight into the stress transfer between constituents in microstructure as well as a good prediction of macroscopic mechanical properties, which otherwise, would be challenging to be assessed by any ordinary mechanical testing in the layered composites. Finally, we also demonstrate that these composites could be used as physiological motion sensors for human health monitoring.

Computational homogenization of fully coupled hydro-mechanical analysis of micro-fractured porous media

In this paper, a computational homogenization technique is developed for fluid flow through the deformable micro-fractured porous media. The coupled hydro-mechanical analysis is performed using an efficient multiscale procedure. Micro-fractures are defined within the microscopic domain, which is associated with each macro-scale quadrature point. According to the first-order homogenization approach, proper form of virtual power relations is defined by applying the Hill-Mandel principle of macro-homogeneity to achieve a consistent multiscale formulation. Moreover, the transient behavior of micro-structures is taken into account by employing transient governing equations for the micro-scale problem. In order to transfer the transient effects of micro-structures, an additional domain integral constraint is augmented to the conventional periodic boundary conditions in the micro-scale analysis. The fractures in micro-scale domain are modeled using the X-FEM technique with appropriate enrichment functions for the displacement and pressure fields. In order to study the accuracy of the proposed computational approach, several numerical examples with different boundary conditions and crack configurations, such as mechanical and hydro-mechanical analyzes are solved and the results are compared with those obtained from the direct numerical simulation. It has been shown that the proposed computational multiscale algorithm on the basis of domain integral constraint, which is augmented to periodic boundary conditions can be used efficiently to achieve accurate results in comparison with the direct numerical simulations, while the linear boundary conditions fails to produce acceptable results in some complex cases.

A hybrid numerical-experimental strategy for predicting mechanical response of components manufactured via FFF

In this paper a new methodology developed for predicting the mechanical performance of the structures additively manufactured by Fused Filament Fabrication is presented.The novelty of the approach consists in accounting for the anisotropy in the material properties induced by the printing patterns. To do so we partition the manufactured structure according to the printing patterns used in a single component. For determining the material properties of each partition, a hybrid experimental/computational characterization is proposed.The external partitions with aligned (contour) and crossed (cover) filaments are characterized through uniaxial tensile tests on General Purpose Acrylonitrile Butadiene Styrene dog-bone samples with corresponding patterns. Characterization of the inner structure (infill/lattice) is done through computational homogenization technique using Representative Volume Element.The presented methodology is validated against experimental results of square cross-section demonstrators. It is shown that the material properties depend on the geometrical relationship of the different printing patterns, exclusively. Therefore, the exhaustive experimental procedure can be avoided characterizing the printed material by a pre-defined anisotropic constitutive relationship proportional to the properties of the raw material. Moreover, the acquired geometrical relationship is validated for components made of Polylactic Acid.The given methodology may be used as design-for-manufacture tool for creating functional components.

Network science approach to predict the yield strength of metals containing soft particles and pores

Local fluctuations in particle size and spatial distributions can substantially affect the yield strength of metals containing soft particles and/or porosities. The phenomenon can be studied via computational homogenization techniques, which, however, can be highly computationally demanding when large representative volume elements are needed. A more efficient approach to model the plastic deformation that controls the yield strength of metals containing pores has recently been proposed by the author and co-workers. The key idea is to treat the material as a network rather than as a continuum. In fact, plastic deformation in porous metals occurs via the formation of shear bands connecting the pores, and it can thus be modelled as a time-evolving network where the nodes represent the pores and the links represent the shear bands. So far, the applicability of this new approach has only been tested against 2D synthetic microstructures. The present work takes it a step further by applying the approach to real spheroidal graphite iron. Based on strain data collected in-situ via digital volume correlation, it is shown that the new network approach can explain the spatial variations of the plastic deformation that arise from local variations of the particle distribution throughout a tensile specimen.

A novel FFT-based homogenization scheme for cohesive zones

Cohesive Zone Models with finite thickness are widely used for the fracture mechanical modeling of layers of material, e.g., adhesives. Within this approach, the whole layer is modeled as a Cohesive Zone. Moreover, computational homogenization techniques are crucial for the development of advanced engineering materials, which are often heterogeneous. Compared to the classical Finite Element Method (FEM), computationally more efficient solvers based on the Fast Fourier Transform (FFT) are expected to reduce the computational effort needed for the homogenization. Originated from an existing method for the computational homogenization of Cohesive Zones using FEM, a novel FFT-based homogenization scheme for Cohesive Zone Models was developed. Our implementation of the FFT solver uses the Barzilai-Borwein scheme and a non-local ductile damage model for the fracture behavior. Finally, the method is applied to the core material of HybrixTM metal sandwich plates, and the good agreement with experimental results in opening mode I is shown.

A Coupled Multiscale Approach to Modeling Aortic Valve Mechanics in Health and Disease

Mechano-biological processes in the aortic valve span multiple length scales ranging from the molecular and cell to tissue and organ levels. The valvular interstitial cells residing within the valve cusps sense and actively respond to leaflet tissue deformations caused by the valve opening and closing during the cardiac cycle. Abnormalities in these biomechanical processes are believed to impact the matrix-maintenance function of the valvular interstitial cells, thereby initiating valvular disease processes such as calcific aortic stenosis. Understanding the mechanical behavior of valvular interstitial cells in maintaining tissue homeostasis in response to leaflet tissue deformation is therefore key to understanding the function of the aortic valve in health and disease. In this study, we applied a multiscale computational homogenization technique (also known as “FE2”) to aortic valve leaflet tissue to study the three-dimensional mechanical behavior of the valvular interstitial cells in response to organ-scale mechanical loading. We further considered calcific aortic stenosis with the aim of understanding the likely relationship between the valvular interstitial cell deformations and calcification. We find that the presence of calcified nodules leads to an increased strain profile that drives further growth of calcification.

Enhanced computational homogenization techniques for modelling size effects in polymer composites

Several experimental investigations corroborate nanosized inclusions as being much more efficient reinforcements for strengthening polymers as compared to their microsized counterparts. The inadequacy of the standard first-order computational homogenization scheme, by virtue of lack of the requisite length scale to model such size effects, necessitates enhancements to the standard scheme. In this work, a thorough assessment of one such extension based on the idea of interface energetics is conducted. Systematic numerical experimentation and analysis demonstrate the limitation of the aforementioned approach in modeling mechanical behavior of composite materials where the filler material is much stiffer than the matrix. An alternative approach based on the idea of continuously graded interphases is introduced. Comprehensive evaluation of this technique by means of representative numerical examples reveals it to be the appropriate one for modeling nano-composite materials with different filler-matrix stiffness combinations.

A fast numerical method of introducing the strengthening effect of residual stress and strain to tensile behavior of metal matrix composites

Thermal residual stress and strain (TRSS) in particle reinforced metal matrix composites (PRMMCs) are believed to cause strengthening effects, according to previous studies. Here, the representative volume element (RVE) based computational homogenization technique was used to study the tensile deformation of PRMMCs with different particle aspect ratios (AR). The influence of TRSS was assessed quantitatively via comparing simulations with or without the cooling process. It was found that the strengthening effect of TRSS was affected by the particle AR. With the average strengthening effect of TRSS, a fast method of introducing the strengthening effect of TRSS to the tensile behavior of PRMMCs was developed. The new method has reduced the computational cost by a factor 2. The effect of TRSS on continuous fiber-reinforced metal matrix composite was found to have a softening-effect during the entire tensile deformation process because of the pre-yield effect caused by the cooling process.

Modeling and computational homogenization of chloride diffusion in three-phase meso-scale concrete

A computational homogenization technique for modeling diffusion in concrete is introduced with emphasis on the influence of the aggregate content and variability. The highly heterogeneous material is investigated on different scales by combining Variationally Consistent Homogenization on numerical microstructures with analytical techniques accounting for lower, unresolved, length scales. The concrete structure consists of the cement paste, the embedded aggregates, and the Interfacial Transition Zone (ITZ) in between the two. Diffusion takes place in the cement phase, as well as in the ITZ. Since the thickness of the ITZ is, typically, much smaller than the diameter of the aggregates, the effect of the ITZ can be modelled as a surface transport around the aggregates. The occurrence of different aggregate sizes is described via the Particle Size Distribution for given sieve curves, as described in design codes. The Particle Size Distribution curve is split into two parts. The effect of smaller aggregates is homogenized analytically using a mixture rule. This results in an effective matrix material consisting of cement paste and the smaller aggregates. Synthetic structures are then generated numerically to account for the larger aggregates. At first, a dense sphere packing is created based on the Particle Size Distribution. This information is used to generate a weighted Voronoi diagram, which is modified by a shrinking process. This procedure allows us to create periodic Representative Volume Elements for numerical investigations.The overall diffusivity of the concrete mixture is evaluated upon using Variationally Consistent Homogenization, in the context of Finite Element analysis, for the generated RVEs and compared with analytical homogenization results and experimental data. It is found that, depending on the Particle Size Distribution, the ITZ has a large effect on the effective properties.

Multi-Scale Analysis of Fretting Fatigue in Heterogeneous Materials Using Computational Homogenization

This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis (FEA). The heterogeneous material for the specimens consists of a single hole model (25% void/cell, 16% void/cell and 10% void/cell) and a four-hole model (25% void/cell). Using a representative volume element (RVE), we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue. Next, the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part (single hole cell) in the contact area. The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation (DNS) method. Finally, by comparing the computational time and % deviations, we draw conclusions about the reliability and effectiveness of the proposed method.

A nonlocal computational homogenization of softening quasi‐brittle materials

SummaryIn this paper, a computational counterpart of the experimental investigation is presented based on a nonlocal computational homogenization technique for extracting damage model parameters in quasi‐brittle materials with softening behavior. The technique is illustrated by introducing the macroscopic nonlocal strain to eliminate the mesh sensitivity in the macroscale level as well as the size dependence of the representative volume element (RVE) in the first‐order continuous homogenization. The macroscopic nonlocal strains are computed at each direction, and both the local and nonlocal strains are transferred to the microscale level. Two RVEs with similar geometries and material properties are introduced for each macroscopic Gauss point, in which the microscopic damage variables and the macroscale consistent tangent modulus and its derivatives are obtained by imposing the macroscopic nonlocal strain on the first RVE, and the macroscopic stress is computed by employing the microscopic damage variables and imposing the macroscopic local strain over the second RVE. Finally, numerical examples are solved to illustrate the performance of the proposed nonlocal computational homogenization technique for softening quasi‐brittle materials.

An integrated approach for the conformal discretization of complex inclusion-based microstructures

Computational homogenization techniques nowadays are extensively used to gain a better understanding of the links between complex microstructural features in materials and their corresponding (evolving) macroscopic properties. This requires robust tools to discretize complex microstructural geometries and enable simulations. To achieve this, the present contribution presents an integrated approach for the conformal discretization of complex inclusion-based RVE geometries defined implicitly based on experimental techniques or through computational RVE generation methodologies. The conforming mesh generator extends the Persson–Strang truss analogy in order to deal with complex periodic heterogeneous RVEs. Such an approach, based on signed distance fields, carries the advantage that the level set information maintained in previously presented RVE generation methodologies (Sonon et al. in Comput Methods Appl Mech Eng 223:103–122, 2012. https://doi.org/10.1016/j.cma.2012.02.018 ) can seamlessly be used in the discretization procedure. This provides a natural link between the RVE geometry generation and the mesh generator to obtain high quality optimized FEM meshes exploitable in regular codes and softwares.

Multiscale modeling of the effect of sub-ply voids on the failure of composite materials

A multiscale fracture model is developed to study the influence of defects appearing at a microscale in a fiber-reinforced composite laminate. The model establishes a link between the geometrical characteristics of sub-ply imperfections that may be created during manufacturing and the overall fracture strength and fracture energy of the composite. In particular, a recently-developed multiscale theory is expanded to account for microvoids inside the matrix and gaps between closely-spaced fibers that prevent filling. These defects are explicitly incorporated in finite element simulations to study their influence on the onset and propagation of cracks at the sub-ply level. To connect these microcracks to the effective fracture behavior at a ply-level, a computational homogenization technique is applied to extract the energetically-equivalent macroscopic fracture properties. Through a parametric analysis of configurations, the influence of the void content (porosity), void type and void shape on the effective fracture strength and the effective fracture energy of a composite are quantified. Results show that the porosity is the main parameter influencing fracture properties while the shape of the defects and their type (matrix or interfiber) only play a secondary role. Furthermore, the influence of voids on the fracture properties appears to be strongly dependent on the loading conditions. In particular, for the range of porosity analyzed (up to 8%), the influence of voids in mode I on the transverse fracture strength is not significant but the transverse fracture energy decreases approximately linearly down to about 50% of its original value. In contrast, in mode II, the transverse fracture strength is significantly affected with increasing porosity. Furthermore, the transverse fracture energy depends nonlinearly on the porosity and the reduction is relatively more pronounced than for mode I.

Efficient Techniques for Solution of Complex Computational Tasks in Building Physics

Various simplification or optimization techniques are sought that reduce demands of computational modeling on time or computing power while keeping a sufficient level of accuracy. In this paper, determination of hygrothermal performance of a brick block is presented using two homogenization techniques based on different principles. While the computational homogenization technique uses a multiscale method realized on the master/slave computer system, the materials homogenization comes out from the effective media theory (EMT), and after the determination of effective material properties, the whole isotropic problem can be transformed to one dimension. Contrary to most applications of EMT, free parameters of mixing formulas are not determined based on an experimental measurement of a single material property but on a complex hygrothermal performance of the element where the distribution of moisture and temperature over a reference year is taken into account. The calculated results from both techniques are compared with results obtained by high-performance computing without any computational simplifications. For materials homogenization, the best results are achieved when k = 0.9 in Lichtenecker’s mixing rule is assumed, which corresponds to a nearly parallel arrangement of the block. The root mean square error (RMSE) of relative humidity (RH) and temperature distribution is only 0.992% and 0.566°C, respectively. This is even better than the results of computational homogenization (RMSE: 1.502% of RH and 0.629°C). Besides obtaining sufficiently precise results, a significant time-saving is achieved, accounting for more than 99%, while being solved on a single-processor computer.

The scaled boundary finite element method for computational homogenization of heterogeneous media

SummaryMaterials exhibit macroscopic properties that are dependent on the underlying components at lower scales. Computational homogenization using the finite element method (FEM) is often used to determine the effective mechanical properties based on the microstructure. However, the use of FEM might suffer from several difficulties such as mesh generation, application of periodic boundary conditions or computations in presence of material interfaces, and further discontinuities. In this paper, we present an alternative approach for computational homogenization of heterogeneous structures based on the scaled boundary finite element method (SBFEM). Based on quadtrees, we are applying a simple meshing strategy to create polygonal elements for arbitrary complex microstructures by using a relatively small number of elements. We show on selected numerical examples that the proposed computational homogenization technique represents a suitable alternative to classical FEM approaches capable of avoiding some of the mentioned difficulties while accurately and effectively calculating the macroscopic mechanical properties. An example of a two‐scale semiconcurrent coupling between FEM and SBFEM is presented, illustrating the complementarity of both approaches.

A two‐scale FE‐FFT approach to nonlinear magneto‐elasticity

SummaryFourier‐based approaches are a well‐established class of methods for the theoretical and computational characterization of microheterogeneous materials. Driven by the advent of computational homogenization techniques, Fourier schemes gained additional momentum over the past decade. In recent contributions, the interpretation of Green operators central to Fourier solvers as projections opened up a new perspective. Based on such a viewpoint, the present work addresses a multiscale framework for magneto‐mechanically coupled materials at finite strains. The key ingredient for the solution of magneto‐mechanic boundary value problems at the microscale is the construction of suitable operators in Fourier space that project vector fields onto either curl‐free or divergence‐free subspaces. The resulting linear system of equations is solved by a conjugate gradient method. In addition to that, we describe the computation of the consistent macroscopic tangent operator based on the same linear operators as the microscopic equilibrium with appropriately defined right‐hand sides. We employ the framework for the simulation of representative two‐scale boundary value problems and compare the results with pure finite element schemes.

Simulation and Experimental Validation of Spacer Fabrics Based on their Structure and Yarn’s Properties

Warp-knitted spacer fabrics are considered, which are plates or shells composed of two knitted plane layers connected by vertical beams. Our aim is to compute the effective stiffness and permeability of such spacer fabrics on the basis of their structure and properties of yarns and the monofil. In order to reduce the computational effort and simplify the computational model, homogenization and dimension reduction techniques are applied. They replace the fabric by an equivalent two-dimensional plate or shell with effective elastic properties. To compute the effective permeability, the fluid simulation is done on the fully resolved micro-structure. The paper demonstrates the algorithm on application examples. We compute the elastic properties of a spacer fabric and its effective permeability for different outer-plane compression stages. Numerical examples were performed by applying the multi-scale simulation tools, developed at Fraunhofer ITWM and by comparing with the corresponding experimental results, based on measurements performed at the TU Dresden. The developed algorithms and simulation tools enable a full virtualisation of the material design adapted to exposure scenarios in various technical application cases, i.e. infiltration processes with polymers in the field of fiber reinforced composites, which enables new discoveries for the designing and manufacturing process of 3D warp-knitted spacer fabrics.