Two-scale Approach Research Articles

INTERLAYER EFFECT ON DEFORMATION AND FRACTURE OF DENDRITIC STRUCTURE FORMED DURING WIRE-FEED ELECTRON-BEAM ADDITIVE MANUFACTURING OF AL-SI ALLOY

Interfaces and surfaces play an important role in tribology, mechanics and materials science, causing plastic strain localization and stress concentration of different spatial scales. The interfacial inhomogeneity is highly pronounced in 3D printed materials due to thermo-cycling and layer-by-layer building. In this paper, the inlayer and interlayer structure of a eutectic Al-Si alloy fabricated by wire-feed electron-beam additive manufacturing is investigated by optical and electron microscopy. Model structures inheriting the experimental morphology are created, and their deformation and fracture are simulated using ABACUS/Explicit, with the user-defined subroutines being developed to describe the constitutive behavior of aluminum dendrite, silicon and eutectic materials. A two-scale computational approach is implemented to study the influence of the interlayer formed in the heat-affected zone on the dendritic structure strength.

The homogenized dynamical model of a thermoelastic composite stitched with reinforcing filaments.

The dynamical problem of linear thermoelasticity for a body with incorporated thin rectilinear inclusions is studied. It is assumed that the inclusions (i.e. filaments and threads) are parallel to each other and the problem contains a small parameter [Formula: see text], which characterizes the distance between two neighbouring inclusions. Using the two-scale convergence approach, we find the limiting problem as [Formula: see text]. As a result, we get a well-posed homogenized model of an anisotropic inhomogeneous body with effective characteristics inheriting thermomechanical properties of inclusions.This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

A two-scale approach for assessing the role of defects in fatigue crack nucleation in metallic structures

Metal structures often exhibit macroscopic defects from which cracks can nucleate during cyclic loading. The current work presents a two-scale approach to enable the prediction of crack nucleation from such defects by taking into account local microstructure features. The geometrical description of the defect and associated non-homogeneous strain fields are modeled using a macroscale model which employs a continuum elastoplastic material model for cyclic deformation. The cyclic deformation of the microstructure near the defect is modeled using a mesoscale model which employs a crystal plasticity material model and uses multiple realizations to address the statistical microstructure variability. The boundary conditions of the mesoscale model are extracted from the macroscale model. By simulating the deformation of the microstructure using the strain fields near the defect and by introducing a fatigue indicator parameter for crack nucleation, along with the weakest-link based upscaling methodology, the developed approach enables the prediction of the distribution of crack nucleation life. The approach is used for analyzing different defects for crack nucleation by considering local grain orientations. The predictions are shown to not only capture phenomena such as scatter, size effects, etc. qualitatively, but also agree with a classical engineering approach and experimentally reported data sets quantitatively.

Characterizing PEM fuel cell catalyst layer properties from high resolution three-dimensional digital images, Part II: Oxygen effective diffusion and proton effective conductivity tensors

The oxygen effective diffusion and proton effective conductivity tensors of a cathode catalyst layer (CCL) are computed using a two-scale approach on CCL microstructure three-dimensional images obtained by focused ion beam-scanning electron microscopy (FIB-SEM) after reconstruction of the ionomer distribution. The results show that the obtained tensors are not isotropic. It is also found that some off-diagonal components are not negligible in the case of the proton effective conductivity tensor. The simulations confirm that Knudsen diffusion has a significant impact on oxygen diffusion. The results are comparable to those obtained in previous works on synthetic images as regards the oxygen effective diffusion through-plane component but differ as regards the proton conductivity through-plane component. Contrary to previous works using synthetic images which tend to underestimate the proton conductivity, they are globally in better agreement with experimental data. The results also show that the effective proton conductivity is heterogeneous at the scale of the computational domains typically considered in several previous works due to the variability in the ionomer distribution at this scale. The impact of liquid water in the primary pores on the proton transport is explored and found to have a significant impact.

A computational two-scale approach to cancellous bone remodelling

We propose a novel two-scale (meso-macro-scale) approach to computationally capture cancellous bone remodelling allowing for efficient and effective numerical implementation. Therein, the macro-scale is governed by the well-established kinematics and kinetics of one-scale continuum bone remodelling. However, the constitutive behaviour is not postulated phenomenologically at the macro-scale, but rather follows from the meso-scale. There, for the sake of computational efficiency, the trabecular architecture is idealised as a truss network with the cross-sectional area of the trabeculae adapting to mechanical loading. Then, the meso- and the macro-scale are coupled through up- and down-scaling. Computational results on benchmark problems from bio-mechanics demonstrate that the proposed two-scale approach is effective from a modelling perspective and efficient from a computational perspective. In particular, it automatically captures anisotropy resulting from the irregular trabecular architecture at the meso-scale, and, most importantly, enables the direct investigation of different trabecular structures at the meso-scale, thereby serving as a virtual “magnifiying glass”. As an outlook, the proposed two-scale approach to cancellous bone remodelling provides an excellent launch pad for further extension, e.g., by considering more complex trabecular architectures and/or through inclusion of micro-scale bone cellular activities.

Numerical fatigue assessment of a cross-ply carbon fiber laminate using a probabilistic framework

A probabilistic framework is developed utilizing a two-scale modeling approach to efficiently consider the material variability that is typical for composite materials. The modeling integrates a macro-scale model with effective elastic properties extracted from micro-mechanical simulations. Using a weakest link modeling approach for fatigue assessment the combined effects of defects on fatigue strength in a Carbon Fiber Reinforced Polymer (CFRP) material can be investigated. A full fatigue test program is presented and is used to calibrate the probabilistic fatigue model. By including material variability in the numerical model, the calibrated probabilistic model improves the fatigue life prediction.

A Ring-Projection-Based Two-Scale Approach for Accurate Digital Image Correlation of Large Translations and Rotations

A Ring-Projection-Based Two-Scale Approach for Accurate Digital Image Correlation of Large Translations and Rotations

Modeling of 3D-printed composite filaments using X-ray computer tomography images segmented by neural networks

This study introduces a novel semi-analytical two-scale approach to model 3D-printed composite filament where both fibers and voids are present. The proposed approach utilizes micro computer tomography (micro-CT) images to visualize fibers and voids. Then, a novel segmentation process based on neural network algorithms (specifically the YOLO v7 algorithm) is employed to segment the distinct fiber and void phases. The volume fractions and the geometries of the phases are then used in the first scale (the micro-scale) of the approach and the effective elastic properties of internal regions of the filament are obtained using the Mori–Tanaka effective field method. These regions are then joined together to form the second scale (the macro-scale), for which the elastic properties are evaluated using the finite element method. The two-scale approach is applied for 3D-printed nylon reinforced with continuous carbon fibers and the predictions of the elastic properties are compared to tensile tests conducted on the single filament. A great agreement is observed for Young’s modulus along the fiber direction of the single printed filament.

Experimental and numerical investigation of heterogeneous strain fields in intralayer hybrid composites with aramid-carbon reinforcement

This research aims to analyze the elastic behavior of intralayer hybrid composites that consist of an epoxy matrix and aramid-carbon reinforcement. The contrast in stiffness between the aramid and carbon fibers leads to highly heterogeneous distributions of strains at the mesoscopic level. Therefore, our main objective is to investigate the strain fields at the mesoscopic level experimentally and numerically. We performed measurements using the digital image correlation (DIC) method, while the numerical model was built using a two-scale approach involving the finite element method (FEM). Good agreement was observed between the experimental and numerical results.

EyeRADAR-Dam: Integration of MT-InSAR with monitoring technologies in a pilot monitoring system for embankment dams

Dams are one of the larger infrastructures of human civilization in the 21st century and subjected to increasing safety monitoring in the frame of global change. The quick development of SAR interferometry and processing capabilities allow near-real time monitoring of dams and associated areas and infrastructures. A pilot project for the surveillance and management of embankment dams, EyeRADAR-Dam has been developed in an industry-academia collaboration, supported by scientific validation. The potential of EyeRADAR-Dam lies in the integration via API of monitoring data and SAR time series dating from 1992 to present. The processed SAR data is input to the platform, together with relevant monitoring data (climate, topography, geotechnics, hydrology, flows…). A two-scale approach allows monitoring the entire reservoir, with slopes and infrastructures as a whole while simultaneously monitoring in detail critical infrastructures and dam body. EyeRADAR-Dam is part of a new generation of management platforms that integrate space data in daily operations.

Probabilistic fatigue strength assessment of cross-ply laminates: Exploring effects of manufacturing defects through a two-scale modeling approach

The study presents a two-scale modeling approach allowing for an efficient fatigue strength evaluation on a macro scale considering a micro-mechanical defect characterization of a Carbon Fiber Reinforced Polymer (CFRP) material. The modeling approach integrates a macro model with the effective elastic properties from micro-mechanical simulations considering voids. This enables the analysis of defects’ influence on material fatigue strength using a probabilistic weakest link approach. A CFRP laminate with a cross-ply layup was investigated. Two simulation case studies demonstrate the effect of void content and size on the characteristic fatigue strength. An experimental investigation was conducted testing the laminates in tension–tension fatigue verifying the predicted numerical behavior. The numerical models identify a difference in the characteristic fatigue strength consistent with the fatigue test results. It is numerically concluded that the investigated CFRP material’s fatigue strength is affected by the presence of voids and even with only a slight difference in the global void volume fraction a scatter in fatigue strength is identified.

Assessing Fatigue Life Cycles of Material X10CrMoVNb9-1 through a Combination of Experimental and Finite Element Analysis

This paper uses a two-scale material modeling approach to investigate fatigue crack initiation and propagation of the material X10CrMoVNb9-1 (P91) under cyclic loading at room temperature. The Voronoi tessellation method was implemented to generate an artificial microstructure model at the microstructure level, and then, the finite element (FE) method was applied to identify different stress distributions. The stress distributions for multiple artificial microstructures was analyzed by using the physically based Tanaka–Mura model to estimate the number of cycles for crack initiation. Considering the prediction of macro-scale and long-term crack formation, the Paris law was utilized in this research. Experimental work on fatigue life with this material was performed, and good agreement was found with the results obtained in FE modeling. The number of cycles for fatigue crack propagation attains up to a maximum of 40% of the final fatigue lifetime with a typical value of 15% in many cases. This physically based two-scale technique significantly advances fatigue research, particularly in power plants, and paves the way for rapid and low-cost virtual material analysis and fatigue resistance analysis in the context of environmental fatigue applications.

Buckling optimization of additively manufactured cellular structures using numerical homogenization based on beam models

Interest in components with detailed structures increased with the progress in advanced manufacturing techniques. Parts with lattice elements can provide improved global buckling stability compared to solid structures of the same weight. However, thin features are prone to local buckling. We present a two-scale optimization approach that simultaneously improves the local and global stability of parametrized graded lattice structures. Elastic properties and local buckling behavior are upscaled via homogenization based on geometric exact beam theory. To reduce computational effort, we construct a worst-case model for the homogenized buckling load factor, which acts as a safeguard against local buckling. We briefly discuss advantages and limitations by means of numerical examples.

Wave Polarization Control in Anisotropic Locally Resonant Materials

Elastic wave propagation in solids can be controlled and manipulated by properly designed metamaterials. In particular, polarization conversion can be obtained by using anisotropic materials. In this paper, we propose a three-component locally resonant material with non-symmetrically coated inclusions, and we study the effect of the anisotropic equivalent mass on band gap formation and the polarization conversion of elastic waves. The equivalent frequency-dependent mass tensor is obtained through the two-scale homogenization approach. The study of the eigenvalues of the mass tensor enables to predict band gaps and polarization bands, as well as identifying a priori the effect of different geometric and material parameters, thus opening the way to metamaterial optimization.

Nuclear induction lineshape modeling via hybrid SDE and MD approach.

The temperature dependence of the nuclear free induction decay in the presence of a magnetic-field gradient was found to exhibit motional narrowing in gases upon heating, a behavior that is opposite to that observed in liquids. This has led to the revision of the theoretical framework to include a more detailed description of particle trajectories since decoherence mechanisms depend on histories. In the case of free diffusion and single components, the new model yields the correct temperature trends. The inclusion of boundaries in the current formalism is not straightforward. We present a hybrid SDE-MD (stochastic differential equation - molecular dynamics) approach whereby MD is used to compute an effective viscosity and the latter is fed to the SDE to predict the line shape. The theory is in agreement with the experiments. This two-scale approach, which bridges the gap between short (molecular collisions) and long (nuclear induction) timescales, paves the way for the modeling of complex environments with boundaries, mixtures of chemical species, and intermolecular potentials.

Monitoring selective logging intensities in central Africa with sentinel-1: A canopy disturbance experiment

Forest degradation is a major threat to tropical forests, and effective monitoring using remotely sensed data is subject to significant challenges. In particular, consistent methods for detecting subtle changes in the forest canopy structure caused by selective logging are lacking. Here, using a unique dataset collected in southeastern Cameroon, covering over 22,000 ha of monthly harvesting areas, >6000 locations of harvested trees, and an independent canopy gap dataset developed from an uninhabited aerial vehicle flight (UAV; RGB camera) of approximately 1500 ha, a new method was designed to monitor canopy disturbance and logging intensity in Central Africa. Using Sentinel-1 synthetic aperture radar (SAR) data, the method was conceptualised using a two-step, two-scale approach, which better matched logging practices. First, (non-)harvesting activity areas were identified using textural indices at a spatial resolution of 300 m (step 1), and within these harvesting activity areas, canopy gaps were detected at a resolution of 10 m (step 2). Both steps were based on monthly differences in the Sentinel-1 SAR time series computed using the average of the 12 months preceding and the average of the three months following the month of interest. This method identified harvesting activity areas (step 1 at 300 m resolution) of over 12,004 km2 with high accuracy (omission and commission errors for both classes ≤0.05) and, within them, detected canopy gaps (step 2 at 10 m resolution) with a global accuracy of 0.89. Although some canopy gaps were subject to omission and commission errors (0.39 and 0.05, respectively), this method yielded better results than other available approaches. Compared to the UAV canopy gaps, this method detected most of the small gaps (≤ 500 m2), which represent 80% of all disturbed areas, whereas other available approaches missed at least 70% of these and consequently missed most of the disturbance events occurring in a selectively logged forest. Furthermore, the predictions were correlated with logging intensity, i.e., the number of trees and volume cut per hectare, which are two important criteria for assessing the sustainability of logging activities. This two-step two-scale method for short-term, monthly monitoring of logging disturbances and intensity has strong practical implications for forest administration and certification bodies in Central Africa.

Correlation Studies of Different Decoupled Two-Scale Simulations for Lattice Structures

By deliberately designing microscopic internal mechanisms, architected materials can achieve a variety of material properties without changing constituent materials. Integration of the architected materials into a structure as substructures has a good potential to enhance structural performance and realize wide design freedom. This paper explores the capabilities of multiscale approaches for lattice structures, which is a major mechanism in architected materials. The objectives of this paper are (1) to demonstrate the capabilities of the framework to evaluate stiffness characteristics of lattice structures with two different two-scale analysis approaches and (2) to assess the accuracies and validity ranges of both approaches for appropriate evaluations of lattice structures. The two-scale analysis framework consists of the computational homogenizations for the generalized stiffness (ABD) and 3D stiffness (C) matrices. Equivalent stiffness characteristics of the unit cell are obtained by computational homogenizations to effectively capture the macroscopic responses of lattice structures. This study provides a comprehensive correlation study between the prediction accuracies of the two-scale analysis approaches in terms of tensile, bending, and torsional stiffness characteristics for practical modeling and development of lattice structures. The study will contribute a guideline for effective designs of high-performance structures with architected materials.

Two-Scale Computational Analysis of Deformation and Fracture in an Al-Si Composite Material Fabricated by Electron Beam Wire-Feed Additive Manufacturing

Numerical simulation of deformation and fracture of an AlSi12% alloy additively fabricated by layer-by-layer electron beam melting of a wire is carried out. The microstructure of the alloy is studied by scanning and transmission electron microscopy at different resolutions. The experimental study at a length scale of several dozens of microns reveals a dendritic structure, which can be treated as a composite material consisting of aluminum arms separated by a eutectic network. The volume fraction of dendrites varies with the distance from the base plate in the build direction. The eutectics can also be thought of as a composite with an aluminum matrix reinforced by silicon particles at a scale of a few microns. Particles of different shapes are nearly equally spaced in the matrix. The eutectic and dendritic structures are taken into account explicitly in the calculations. The dynamic boundary-value problems are solved by ABAQUS/Explicit. The isotropic elastic-plastic and elastic models are used to simulate the response of aluminum and silicon. The fracture model includes a maximum distortion energy criterion formulated for the particle and matrix materials in terms of the equivalent stress and plastic strain. A two-scale approach is proposed to investigate deformation and fracture of the AlSi12% alloy. On the eutectic scale, the thermomechanical behavior of the Al matrix-silicon particle two-phase composite is simulated to obtain the homogenized properties of the eutectic composite material, which is then used at a higher scale to investigate the deformation and fracture of a two-phase dendritic structure. Residual stresses formed during cooling of the additively manufactured material were found to decrease the strength of the composite, while the strength increases with the volume fraction of dendrites.

Multiscale Asymptotic Computations for the Elastic Quadratic Eigenvalue Problem in Periodically Composite Structure

A multiscale analysis and computational method based on the Second-Order Two-Scale (SOTS) approach are proposed for the elastic quadratic eigenvalue problems in the periodic composite domain. Two typical quadratic eigenvalue problems with different damping effects are considered, and by the asymptotic expansions of both the eigenfunctions and eigenvalues, the first- and second-order cell functions, the microscale features of this heterogeneous materials are defined successively. Then, the homogenized quadratic eigenvalue problems are derived and the second-order expansions of the eigenfunctions are formed. The eigenvalues are also broadened to the second-order terms by introducing proper auxiliary elastic functions defined in the composite structure, and the nonlinear expressions of the correctors of the eigenvalues are derived. The finite element procedures are established, linearized methods are discussed for solving the quadratic eigenvalue problems and the second-order asymptotic computations are performed. Effectiveness of the asymptotic model is demonstrated by both the qualitative and quantitative comparisons between the computed SOTS approximations and the reference solutions, and the converging behavior of the eigenfunctions are numerically verified. It is also indicated that the second-order correctors are of importance to reconstruct the detailed information of the original eigenfunctions within the micro cells.

Permeability anisotropy impact on wormhole propagation in openhole and limited-entry completions: A 3D numerical study

The permeability in carbonate reservoirs is not the same in all directions (i.e., anisotropic), a property seldom considered in acid stimulation. The study hypothesizes that permeability anisotropy impacts acid treatment efficiency significantly. The investigation included the openhole and limited-entry completions in a vertical and horizontal wellbores configuration. A model based on the two-scale continuum approach was constructed in three-dimensional space (3D), resembling the big block experiment with the wellbore at the center. Permeability anisotropy significantly impacts acid efficiency in terms of the pore volume to breakthrough (PVBT) and optimum injection rate. For instance, simulations of acid placement in an openhole horizontal well with 10 anisotropy ratio resulted in PVBT of 0.15 compared to 0.35 in a vertical well. Limited entry completions result in more extended wormholes where the permeability anisotropy positively impacted wormhole length as compared to isotropic permeability. Nevertheless, the permeability anisotropy negatively impacted wormhole coverage along the wellbore in most scenarios. The simulations showed that a spear-like wormhole propagates from a limited entry horizontal wellbore in anisotropic formation, which previous studies assumed to be spherical or ellipsoidal. This implies that the skin factors models should be revised based on the new findings. This is the first study to assess the permeability antitropy impact on the stimulation of openhole and perforated wells in a 3D space.