Multiscale Homogenization Approach Research Articles

Multi-scale plasticity homogenization of Sn–3Ag-0.5Cu: From β-Sn micropillars to polycrystals with intermetallics

The mechanical properties of β-Sn single crystals have been systematically investigated using a combined methodology of micropillar tests and rate-dependent crystal plasticity modelling. The slip strength and rate sensitivity of several key slip systems within β-Sn single crystals have been determined. Consistency between the numerically predicted and experimentally observed slip traces has been shown for pillars oriented to activate single and double slip. Subsequently, the temperature-dependent, intermetallic-size-governing behaviour of a polycrystal β-Sn-rich alloy SAC305 (96.5Sn–3Ag-0.5Cu wt%) is predicted through a multi-scale homogenization approach, and the predicted temperature- and rate-sensitivity reproduce independent experimental results. The integrated experimental and numerical approaches provide mechanistic understanding and fundamental material properties of microstructure-sensitive behaviour of electronic solders subject to thermomechanical loading, including thermal fatigue.

Prediction of Ultrasonic Pulse Velocity for Cement, Mortar, and Concrete through a Multiscale Homogenization Approach

Ultrasonic testing (UT) is an important method for concrete, and ultrasonic pulse velocity is commonly used to evaluate the quality of concrete materials in existing studies. The ultrasonic pulse velocity of concrete materials is affected by many factors; therefore, it is necessary to establish a quantitative prediction model for the ultrasonic pulse velocity of concrete materials. Based on the multiscale homogenization method, concrete material is divided into different scales of homogenized materials, namely cement paste, mortar, and concrete. Then, a multiscale ultrasonic pulse velocity model is established through a combination of elasticity formulation and the hydration model. At the three scales of cement paste, mortar, and concrete, the elastic parameters and ultrasonic pulse velocity were predicted with the water-to-cement ratio of 0.35, 0.5, and 0.65, respectively. The ultrasonic pulse velocity of concrete with different water-to-cement ratios and different ages were measured in the test and predicted by the model. The results show that the predicted value of ultrasonic pulse velocity is within the error range of ±1.5% of the measured ultrasonic pulse velocity, suggesting that the established prediction model of ultrasonic pulse velocity can reliably predict the velocity change in concrete materials.

Effect of agglomeration and dispersion on the elastic properties of polymer nanocomposites: A Monte Carlo finite element analysis

Abstract Owing to their superior mechanical and physical properties, carbon nanotubes (CNT) seem to hold a great promise as an ideal reinforcing material for composites of high-strength and low-density. In most of the experimental results up to date, however, only modest improvements in the strength and stiffness have been achieved by incorporating carbon nanotubes in polymers. In the present paper, the influence of single wall carbon nanotube agglomeration on the effective stiffness is analyzed by using an Eshelby’s inclusion model. Analytical expressions are derived for the effective elastic stiffness of single wall carbon nanotubereinforced composites with the effects of agglomeration. The present study not only provides the important relationship between the effective properties and the morphology of CNT-reinforced composites, but also may be useful for improving and tailoring their mechanical properties. In addition, a multiscale Monte Carlo finite element method (MCFEM) was used for determining mechanical properties of polymer nanocomposites (PNC) that consist of polymers reinforced with single-walled carbon nanotubes (SWCNT). Specifically, the method uses a multiscale homogenization approach to link the structural variability at the nano/micro scales with the local constitutive behavior. Subsequently, the method incorporates a FE scheme to determine the Young’s modulus and Poisson ratio of PNC. The use of the computed properties in macroscale modeling is validated by comparison with experimental tensile test data.

A multiscale analysis approach to predict mechanical properties in fused deposition modeling parts

Additive manufacturing has evolved from a rapid prototyping tool to a set of manufacturing processes for functional parts. One of their most outstanding features is the ability to build complex geometry parts. However, their industrial application is limited because these parts exhibit heterogeneous and porous micro/mesostructures with anisotropic behavior. These structural characteristics, mainly porosity, are strongly related to the building parameters. In this work, a computational multiscale homogenization approach was implemented to determine the mechanical properties of unidirectional and criss-cross mesostructures generated by a material extrusion process (MEP). Representative volume elements (RVE) for simplified and real-like pore geometries were created to model the mesostructures and to perform the multiscale analysis. Stiffness tensor for each RVE was obtained and graphically represented to observe the mechanical properties as a function of the orientation. A great influence of the pore geometry on mechanical properties was observed. Finally, by comparing with experimental data, the results obtained were validated.

Elastic Constants Prediction of 3D Fiber-Reinforced Composites Using Multiscale Homogenization

This paper presents a multi-scale-homogenization based on a two-step methodology (micro-meso and meso-macro homogenization) to predict the elastic constants of 3D fiber-reinforced composites (FRC). At each level, the elastic constants were predicted through both analytical and numerical methods to ascertain the accuracy of predicted elastic constants. The predicted elastic constants were compared with experimental data. Both methods predicted the in-plane elastic constants “ E x ” and “ E y ” with good accuracy; however, the analytical method under predicts the shear modulus “ G x y ”. The elastic constants predicted through a multiscale homogenization approach can be used to predict the behavior of 3D-FRC under different loading conditions at the macro-level.

A novel second-order reduced homogenization approach for nonlinear thermo-mechanical problems of axisymmetric structures with periodic micro-configurations

A novel second-order reduced homogenization (SORH) approach is introduced for analyzing dynamic thermo-mechanical coupling problems in axisymmetric inelastic structures with periodic micro-configuration. The axisymmetric heterogeneous structures are periodically distributed in radial and axial directions and homogeneous distribution in circumferential directions. Firstly, the nonlinear coupled thermo-mechanical model is proposed, and the high-order nonlinear local problems, effective material parameters and the nonlinear homogenization equations are derived successively by the multiscale asymptotic expansion. Further, in order to reduce the large computational amount evaluated by the classical multiscale homogenization approach, the reduced-order nonlinear multiscale models and the corresponding finite-element algorithms are established in detail. The key features of the proposed approach are that an efficient reduced-model form based on transformation field analysis (TFA) to analyze nonlinear local cell problems is proposed and a nonlinear thermo-mechanical problem which considers the mutual coupling for the temperature and displacement fields is computed. In particular, a new SORH algorithm is proposed for investigating the axisymmetric inelastic structures. Finally, three typical numerical experiments are carried out, and the effectiveness and correctness of our presented algorithms in simulating and predicting the macroscopic behavior of the heterogeneous structures are confirmed.

A Multiscale Homogenization Approach for Architectured Knitted Textiles

Abstract As a type of architectured material, knitted textiles exhibit global mechanical behavior which is affected by their microstructure defined at the scale at which yarns are arranged topologically given the type of textile manufactured. To relate local geometrical, interfacial, material, kinematic and kinetic properties to global mechanical behavior, a first-order, two-scale homogenization scheme was developed and applied in this investigation. In this approach, the equivalent stress at the far field and the consistent material stiffness are explicitly derived from the microstructure. In addition, the macrofield is linked to the microstructural properties by a user subroutine which can compute stresses and stiffness in a looped finite element (FE) code. This multiscale homogenization scheme is computationally efficient and capable of predicting the mechanical behavior at the macroscopic level while accounting directly for the deformation-induced evolution of the underlying microstructure.

Compliant riblets: Problem formulation and effective macrostructural properties

Small-scale, deformable riblets, embedded within the viscous sublayer of a turbulent boundary layer and capable to adapt to the overlying motion, are studied. The wall micro-grooves are made of a linearly elastic material and can undergo small deformations; their collective behavior is assumed to occur over a large, elastic wavelength. The presence of two length scales allows for the use of a multiscale homogenization approach yielding microscopic problems for convolution kernels and parameters, which must then be employed in macroscopic boundary conditions to be enforced at a virtual wall through the riblets. The results found suggest that, in analogy to the case of rigid riblets, compliant, blade-like wall corrugations are more effective than triangular riblets in reducing skin friction drag, provided the spanwise periodicity of the indentations is sufficiently small for the creeping flow approximation to be tenable.

A bridge between dual porosity and multiscale models of heterogeneous deformable porous media

SummaryIn this paper, a multiscale homogenization approach is developed for fully coupled saturated porous media to represent the idealized sugar cube model, which is generally employed in fractured porous media on the basis of dual porosity models. In this manner, an extended version of the Hill‐Mandel theory that incorporates the microdynamic effects into the multiscale analysis is presented, and the concept of the deformable dual porosity model is demonstrated. Numerical simulations are performed employing the multiscale analysis and dual porosity model, and the results are compared with the direct numerical simulation through 2 numerical examples. Finally, a combined multiscale‐dual porosity technique is introduced by employing a bridge between these 2 techniques as an alternative approach that reduces the computational cost of numerical simulation in modeling of heterogeneous deformable porous media.

A novel anisotropic analytical model for effective thermal conductivity tensor of dry lime-hemp concrete with preferred spatial distributions

This article develops a novel mathematical model using multi-scale homogenization approach to model the effective thermal conductivity tensors of a hemp shiv particle and lime hemp concrete (LHC). This bio-based material is an environmentally-friendly material that is used more and more in building construction. The thermal conductivity of lime hemp concrete which is generally either cast or sprayed, cannot be expressed as a scalar due to its anisotropic microstructure. The paper develops a novel model to predicting effective thermal conductivity tensor of lime-hemp concrete that takes into account the anisotropy and the size of hemp shiv, the preferred spatial distributions due to fabrication process and the imperfect particle-binding interfaces. Two probability density functions are used for modeling the particle size distributions of hemp shiv and the preferred alignment distribution of hemp particles. A good agreement is obtained between the model and experimental data provided in the literature. The presented analytical solutions offer a suitable tool for a fast optimization of the thermal conductivity of hemp concrete. Such promising future is very useful for the building design, in particular in three-dimensional (3D) simulation models.

Analysis for deformation behavior of multilayer ceramic capacitor based on multiscale homogenization approach

Given the rapid improvements in the miniaturization, functionality, and efficiency of electronic products in recent years, the dielectric layers and electrodes of multilayer ceramic capacitors have become thinner, with the number of stacked layers also increasing. As a result, the deformation defects induced during manufacturing of the capacitors have increased. In this study, the deformation behavior of a multilayer ceramic capacitor composed of ceramic dielectric layers and Ni electrode layers during the compression process was analyzed numerically using the FEM. To analyze the deformation behavior of the capacitor, which consisted of several hundred laminated ceramic and Ni layers, in the plane direction, the material properties were represented by equivalent material properties based on the multiscale homogenization approach. Then, the deformation of the capacitor in the plane direction owing to the residual stress arising during the compression process was analyzed based on the calculated equivalent material properties. Finally, the possibility of a product defect with the size of the ceramic dielectric and electrode layers during the cutting process was predicted.

Multiscale Rubber Friction Analysis on Rough and Flexible Surfaces

AbstractIn this work, a multiscale homogenization approach is introduced to provide friction features between rubber and rough contact partners. Different length scales of the rough surface are considered by using a decomposition of the height difference correlation (HDCF) or the power spectral density function (PSDF) in several sinusoidal waves to accumulate the micro‐ and mesoscopic friction into a macroscopic friction coefficient. By using the finite element method (FEM), the sensitivity of the influencing factors for instance slip velocity and contact pressure may be investigated for rigid and flexible surfaces in the two‐ and the three‐dimensional case. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A multi-scale homogenization approach for the effective thermal conductivity of dry lime–hemp concrete

Lime–hemp concrete is an environmentally friendly material that is used more and more in building construction. This study develops a multi-scale homogenization approach to model the effective thermal conductivity of this bio-based material. The developed model dedicated to non-compacted and compacted hemp concrete takes into account the shape and the orientations of pores of hemp particles as well as imperfect particle-binding interfaces. Unknown properties of the solid phase of hemp particles and binding, and that of the particle-binding interface are calibrated by inverse analysis using available experimental data. The model is then used to carry out a sensitivity analysis to study the effect of the porosities of hemp particles and binding, the volume fraction of hemp particles, density and temperature on the overall thermal conductivity of hemp concrete. Analytical solution proposed can be used for a fast estimation and optimization of the thermal conductivity of hemp concrete, which is very useful for the building design.

Analytical Homogenization for Dynamic Analysis of Composite Membranes with Circular Inclusions in Hexagonal Lattice Structures

Free vibrations of a composite membrane with a hexagonal lattice circular inclusion are investigated. We aim at a study of the lower frequency spectrum, i.e. it is assumed that the minimum space period of the eigenform is essentially larger than the characteristic dimension of the cell periodicity of the analyzed structure. This implies a possibility of approximating the composite structure by the homogenized one with effective characteristics. The latter is yielded by the multi-scale homogenization approach. Introduction of slow and fast variables yields both counterpart quasistatic local problem regarding the periodically repeated cell and global (homogenized) dynamic problem for homogeneous material with effective properties. The most complicated part of this approach concerns in finding a solution to the local problem. It has been analytically found in the presented paper for relatively large inclusion sizes using lubrication approach. The performed numerical validation of the obtained results shows high accuracy of the implemented approach.

Modeling thermal conductivity of hemp insulation material: A multi-scale homogenization approach

The growing awareness of environment protection and climate change have increased the attention on the development of new environmentally-friendly materials. This study will concentrate on the thermal performance of hemp shives which are used as insulation material. A multi-scale homogenization approach accounting for the shape and orientation of pores and particles is developed to model the effective thermal conductivity and anisotropy of this bio-based material. An inverse analysis using the experimental thermal conductivity data of dry shives in bulk allows determining the thermal conductivity of the solid phase of hemp shiv, which is difficult to measure. The latter is then used in the multi-scale model to estimate the overall thermal conductivity of a single hemp shiv particle and hemp insulation material as functions of the temperature and moisture content. The effect of hemp shiv particle's size on the effective thermal conductivity and its anisotropy will be also discussed.

Statistical multiscale homogenization approach for analyzing polymer nanocomposites that include model inherent uncertainties of molecular dynamics simulations

A statistical multiscale homogenization strategy of polymer nanocomposites is proposed to account for the inherent uncertainties of molecular dynamics (MD) simulations. The proposed statistical multiscale homogenization scheme includes a discrete MD simulation system, a continuum theory of micromechanics of Eshelby's solution and two-scale homogenization, and Monte-Carlo simulations. The means and standard deviations of the elastic properties of the nanocomposites are quantified and discussed through statistical analyses that show the interphase effect. The elastic properties of the matrix, interphase, and composites are assumed to follow a lognormal distribution. An iterative inverse algorithm for obtaining the probability density distribution of the interphase is proposed and validated.

Large strain, two-scale computational approach using C1 continuity finite element employing a second gradient theory

A two-scale computational algorithm employing second-order computational homogenization under assumption of large strain is presented. A micro–macro transition has been proposed, where the C1 continuity displacement based finite element is used for discretization at the macrolevel, while the representative volume element at the microlevel is discretized by C0 continuity finite elements. The performed finite element verifications show an advantage in comparison to available finite element formulations. In order to improve numerical efficiency of the proposed computational procedures, the algorithms are embedded into the finite element program Abaqus. The performance of the presented multiscale homogenization approach is demonstrated in numerical examples, where the elastoplastic deformation responses are considered and compared with the small strain analysis.

A second-order two-scale homogenization procedure using $$C^{1}$$ C 1 macrolevel discretization

The present study deals with a second-order two-scale computational homogenization procedure for modeling deformation responses of heterogeneous materials at small strains. The macro to micro transition and the application of generalized periodic boundary conditions on the representative volume element (RVE) at the microlevel are investigated. The structure at macroscale level is discretized by the $$C^{1}$$ C 1 two dimensional triangular finite elements, while the $$C^{0}$$ C 0 quadrilateral finite element is used for the discretization of the RVE. The finite element formulations and the new proposed multiscale scheme have been implemented into the finite element software ABAQUS using user subroutines derived. Due to the $$C^{1}-C^{0}$$ C 1 - C 0 continuity transition, an additional integral condition on microlevel fluctuation field has to be imposed, as expected. The integration has been performed using various numerical integration techniques and the results obtained are compared in a few examples. It is concluded that only trapezoidal rule gives a physically based deformed shape of the RVE. Finally, the efficiency and accuracy of the proposed multiscale homogenization approach are demonstrated by the modeling of a shear layer problem, usually used as a benchmark in multiscale analyses.

Boundary Conditions in a Multiscale Homogenization Procedure

This paper is concerned with a second-order multiscale computational homogenization scheme for heterogeneous materials at small strains. A special attention is directed to the macro-micro transition and the application of the generalized periodic boundary conditions on the representative volume element at the microlevel. For discretization at the macrolevel the C1 plane strain triangular finite element based on the strain gradient theory is derived, while the standard C0 quadrilateral finite element is used on the RVE. The implementation of a microfluctuation integral condition has been performed using several numerical integration techniques. Finally, a numerical example of a pure bending problem is given to illustrate the efficiency and accuracy of the proposed multiscale homogenization approach.

Evolution of the Elastic Properties of an Oilwell Cement Paste at Very Early Age under Downhole Conditions: Characterization and Modelling

A multi-scale homogenization approach coupled with a hydration model is adopted to predict the bulk and shear moduli evolution of an oilwell cement paste at a very early age (up to one day). Calorimetric experiments were performed to be compared with the results of the kinetics model and also to study the pressure and temperature effects on the hydration kinetics. The homogenization model results are in agreement with the elastic moduli measurements obtained from propagation of ultrasonic waves.