Hierarchical Multiscale Analysis Research Articles

Hierarchical multi-scale analysis of the effect of varying fiber bundle geometric properties on the mechanical properties of 3D braided composites

A hierarchical multi-scale numerical model is developed to predict the effect of cross-sectional geometric properties on the mechanical response of three-dimensional (3D) braided composites. In this model, the effective properties are transferred from the fiber bundle scale to the mesoscale, and the finite element and analytical methods are used to predict the macroscopic mechanical properties. Damage evolution was evaluated, based on a continuous damage mechanics approach. A user-defined material subroutine (UMAT), in a nonlinear finite element analysis, has been developed to implement the proposed model and further determine the response and subsequent damage evolution in 3D braided composites subjected to quasi-static tension. The elastic properties of the composites are predicted using a hybrid multi-scale model. The agreement between the numerical simulations and the experimental results is good. It has been shown that the cross-sectional geometry of the fiber bundle properties has a significant influence on the tensile behavior of the composite, which is captured by the proposed multi-scale damage model. This research offers a theoretical analysis for selecting the optimized fiber bundle geometry for using in FE predictions of 3D braided composites.

Hierarchical multiscale analysis for 3D woven composite leaf spring landing gear

In this work, a hierarchical multiscale analysis method was used for 3D woven composite leaf spring landing gear. The structural finite element models at micro, meso and macro scales were established and discussed, respectively. The influence of weave patterns on the tensile properties of 3D woven composites were carried out by experiment and numerical simulation. Finally, the multiscale model was established to predict the mechanical properties of 3D woven composite leaf spring landing gear. The results showed that the maximum prediction error was 9.01% at the microscopic scale, 4.55% at the mesoscopic scale, and 5.61% at the macroscopic scale, thus verifying the effectiveness of the used hierarchical multiscale analysis strategy. The presence of stuffer yarn within the material and the yarn arrangement density were the key factors affecting the structural load-bearing capacity in the design of 3D woven composite leaf spring landing gear.

Urban neighbourhood classification and multi-scale heterogeneity analysis of Greater London

We study the compositional and configurational heterogeneity of Greater London at the city- and neighbourhood-scale using Geographic Information System (GIS) data. Urban morphometric indicators are calculated including plan-area indices and fractal dimensions of land cover, frontal area index of buildings, evenness, and contagion. To distinguish between city-scale heterogeneity and neighbourhood-scale heterogeneity, the study area of 720 km2 is divided into 1 [Formula: see text] 1 km2 neighbourhoods. City-scale heterogeneity is represented by categorisation of the neighbourhoods using a k-means clustering algorithm based on the morphometric indicators. This results in six neighbourhood types ranging from “greenspace” to “central business district”. Neighbourhood-scale heterogeneity is quantified using a hierarchical multi-scale analysis for each neighbourhood type. The analysis reveals the dominant length scales for land-cover and neighbourhood types and the resolutions with the most information gain. We analyse multi-scale anisotropy and show that small-scale features are homogeneous, and that anisotropy is present at larger length scales.

3D large strain hierarchical multiscale analysis of soft fiber-reinforced tissues: application to a degraded arterial wall

PurposeThe purpose is to analyze the mechanical behavior of the arterial wall in the degraded region of the arterial wall and to determine the stress distribution, as an important factor for predicting the potential failure mechanisms in the wall. In fact, while the collagen fiber degradation process itself is not modeled, zones with reduced collagen fiber content (corresponding to the degradation process) are assumed. To do so, a local weakness in the media layer is considered by defining representative volume elements (RVEs) with different fiber collagen contents in the degraded area to investigate the mechanical response of the arterial wall.Design/methodology/approachA three-dimensional (3D) large strain hierarchical multiscale technique, based on the homogenization and genetic algorithm (GA), is utilized to numerically model collagen fiber degradation in a typical artery. Determination of material constants for the ground matrix and collagen fibers in the microscale level is performed by the GA. In order to investigate the mechanical degradation, two types of RVEs with different collagen contents in fibers are considered. Each RVE is divided into two parts of noncollagenous matrix and collagen fiber, and the part of collagen fiber is further divided into matrix and collagen fibrils.FindingsThe von Mises stress distributions on the inner and outer surfaces of the artery and the influence of collagen fiber degradation on thinning of the arterial wall in the degraded area are thoroughly studied. Comparing the maximum stress values on outer and inner surfaces in the degraded region shows that the inner surface is under higher stress states, which makes it more prone to failure. Furthermore, due to the weakness of the artery in the degraded area, it is concluded that the collagen fiber degradation considerably reduces the wall thickness in the degraded area, leading to an observable local inflation across the degraded artery.Originality/valueConsidering that little attention has been paid to multiscale numerical modeling of collagen fiber degradation, in this paper a 3D large strain hierarchical multiscale technique based on homogenization and GA methods is presented. Therefore, while the collagen fiber degradation process itself is not modeled in this study, zones with reduced collagen fiber content (corresponding to the degradation process) are assumed.

An adaptive granular representative volume element model with an evolutionary periodic boundary for hierarchical multiscale analysis

AbstractThe hierarchical multiscale analysis normally utilizes a microscopic representative volume element (RVE) model to capture path/history‐dependent macroscopic responses instead of using phenomenological constitutive models. However, for problems involving large deformation, the current RVE model used in geomechanics may lose representative properties due to the progressive distortion of the RVE box, unless a proper reinitialization is applied. This work develops an adaptive RVE model in conjunction with an evolutionary periodic boundary (EPB) algorithm for hierarchical multiscale analysis of granular materials undergoing large deformation based on a recent RVE model proposed for coupling molecular dynamics and the material point method. The proposed adaptive RVE model avoids the reinitialization of the RVE box that even undergoes extremely large shear deformation; meanwhile, it accounts for the deformation history of the RVE model and treats the interaction between boundary particles and other image particles in a more efficient way. Numerical examples with extremely large deformation are used to illustrate the adaptive granular RVE model enhanced by the proposed EPB algorithm. Furthermore, some key features of this new methodology are further discussed for clarification.

Creep lifetime prediction of virgin and service-exposed Super304H austenitic stainless steel boiler tubes based on hierarchical multiscale analysis and creep cavitation model

ABSTRACTCreep deformation of Super304H austenitic stainless steel boiler tubes in thermal power plants is evaluated using crystal elasto-viscoplastic finite element analysis (CEV-FEA). The material properties of Super304H at elevated temperatures are obtained from experiments and computations at different scales as follows: anisotropic elastic constants of Super304H at elevated temperatures (500–700°C) are obtained from molecular dynamics simulations; microstructures of virgin and service-exposed Super304H boiler tubes are observed using scanning electron microscopy; and macroscopic stress–strain and creep strain curves at 650°C are measured from tensile and miniature creep tests, respectively. Stress concentration evolution at a triple junction of grains featuring various combinations of crystallographic orientations in polycrystalline Super304H is evaluated using CEV-FEA during creep deformation. The remaining creep lifetime of polycrystalline Super304H austenitic stainless steel boiler tubes is estimated from the creep cavitation model, where the stress concentration at the triple junction is used as a representative stress driving creep cavitation.

Hierarchical multiscale analysis of polyimide films by molecular dynamics simulation: Investigation of thermo-mechanical properties

The molecular dynamics simulations are adopted to investigate the thermo-mechanical properties of pyromellitic dianhydride(PMDA)/2-(4-aminophenyl)-1H-benzimidazole-5-amine(BIA), PMDA/p-phenylene diamine(PDA), PMDA/4,4′-oxidianiline(ODA), 3,3′,4,4′-biphenyldianhydride(BPDA)/BIA, BPDA/PDA, and BPDA/ODA polyimide films in hierarchical multiscale level. The results indicate that the properties follow the order of BIA > PDA > ODA. At a small scale, the hydrogen bonding in the BPDA/BIA polyimide strengthens the chain interactions and results in a coiling-shaped chain conformation, endowing the polyimide with superior properties. But the ODA increases the helical-shaped segments conformation, therefore possessing large elongation under small tension. At the scale of the entire polymeric chain, the chain mobility was discussed by the ratio of <Ree2> to <s2> and MSD. And higher chain mobility corresponds to lower tensile modulus. At a large scale, the torsion angle distribution changes apparently before and after stretching, which increases the d-spacing and elongates the entire molecular chain simultaneously, serving as the main cause of polyimide tensile deformation.

Numerical simulation of dynamic failure behavior for cylindrical carbon fiber reinforced polymer

This paper presents a prediction for the dynamic matrix-dominated failure behavior of a carbon fiber reinforced polymer (CFRP) under impact loading, by using hierarchical multi-scale analysis. In this study, the analysis results were compared to experimental results to verify the validity of the multi-scale model. In the experiment, the split Hopkinson pressure bar (SHPB) test was conducted by using two types of cylindrical CFRP specimens. The commercial finite element analysis (FEA) software Abaqus was used for the analysis. We conducted micro-scale and macro-scale analysis, which corresponded to the experiments. In the micro-scale analysis, a two-dimensional periodic unit-cell (PUC) model, which consisted of 20 fibers, resin, and zero-thickness interface is used. The micromechanical model could simulate the matrix failure and debonding of the fiber/matrix interface by the Christensen failure criterion and cohesive zone modeling, respectively. Additionally, the strain rate dependency failure of matrix was considered. The PUC analysis was conducted under a multi-axial stress state, to obtain the failure envelope. Subsequently, a macro-analysis by FE was conducted with parameters obtained from the micromechanics analysis. The simulation was found to be in good agreement with experimental results. Finally, we investigated the relationship between interfacial strength and the failure load of CFRP.

Disaster early warning and damage assessment analysis using social media data and geo-location information

Societies are confronted with destructive natural disasters of increasing frequency. Social networks are playing an increasingly important role as early warning systems, aiding with rapid disaster assessment and post-disaster recovery. There is a need for both the public and disaster-relief agencies to better understand how social media can be utilized to assess and respond to natural disasters. However, existing research on the role of social media in society's response to natural disasters is neither holistic nor systematic. In this study, we conduct a hierarchical multiscale analysis based on multiple data resources, combining social media data, economic losses, and geo-information. We verify the role played by social media before, during, and after a natural disaster. We investigate whether the combination of social media and geo-location information can contribute to a more efficient early warning system and help with disaster assessment. This paper draws attention to the fact that during a disaster, citizens turn to social media and the majority of tweets contain information about the hurricane and/or its impact with negative sentiment. We demonstrate that the severity of damage in one area is positively correlated with the intensity of disaster-related activity. Meanwhile, the coastal areas and areas with close proximity to Hurricane center tend to suffer from higher losses during a disaster. Our findings explore the role played by social media from individuals in affected populations and how they respond to unfolding natural disasters. Results hold significance with regard to providing timely assistance for both official institutions and netizens.

Multiscale modeling of carbon nanotube reinforced concrete

The present paper proposes a hierarchical multiscale approach in order to evaluate the nonlinear constitutive behavior of concrete reinforced with carbon nanotubes (CNTs). To this purpose, representative volume elements, consistent to the microstructural topology of the material, are constructed and analyzed using finite elements. As the dimensions of the CNTs and those of a typical mesoscale concrete RVE differ by orders of magnitude, a hierarchical multiscale analysis strategy is implemented to pass information through scales with different RVEs assigned at each scale of separation. Both elastic and inelastic analyses are performed on all scales for various CNT weight fractions, defining a different nonlinear constitutive stress–strain behavior at each scale of separation. It is shown that the proposed computational approach can be used alternatively to corresponding costly experiments in order to accurately evaluate the nonlinear constitutive behavior of such complex materials.

3D hierarchical multiscale analysis of heterogeneous SMA based materials

A 3D hierarchical multiscale computational homogenization framework with periodic Representative Volume Element (RVE) is proposed in the present study for analysis of shape memory alloy (SMA) fiber reinforced composite and porous SMA specimen. The shape memory alloy, which exhibits forward and reverse transformations, is wired through a matrix, while a dense SMA matrix encircles voids as inclusions in the porous model. The asymptotic mathematical homogenization approach is used to express the microscopic and macroscopic governing equations. An iterative solution is used at each point in order to derive the tangential constitutive response of the corresponding periodic RVE. Several numerical problems are solved and the results are compared with those obtained from a fully meshed direct numerical model. Detailed discussions are presented regarding the distribution of field variables, in particular the martensitic volume fraction and the stress state inside RVEs located at critical points of the macro models, subjected to cyclic stress loads in the form of tension, flexure and torsion. Moreover, a micromechanical analysis is conducted to investigate the effect of the shape of ellipsoid porosities on the overall response of porous SMA.

Behind the rapid expansion of urban impervious surfaces in China: Major influencing factors revealed by a hierarchical multiscale analysis

Urban impervious surfaces (UIS) are well known to have negative impacts on the environment. Studies that consider multiple UIS-influencing factors at multiple administrative levels and spatial scales are still lacking. The main goal of this study was to determine the major socioeconomic factors that shaped the spatiotemporal patterns of UIS in China from the county to provincial levels over the most recent decades. Specifically, remote sensing and statistical data from 1992 to 2009 were used to examine the relationship of UIS to a suite of socioeconomic factors across hierarchical administrative levels from small (county), medium (prefectural) to large (provincial) levels. Our results show that the key influencing factors of UIS varied substantially across hierarchical administrative levels: economic factors dominated the provincial level, demographic factors were most significant at the county level, and a mixed group of economic, demographic and traffic factors were important at the prefectural level. This suggests that, for determining major influencing factors for UIS, a hierarchical or multiscale approach is preferred to any single-scale analysis. Our findings from such a hierarchical perspective provide useful information for formulating mitigation strategies for excessive UIS expansions and for designing more sustainable cities. It is recommended that policies to control rampant expansion of UIS in China need to combine macro-scale economic regulations with micro-scale demographic planning measures.

Multi-scale constitutive modeling of Ceramic Matrix Composites by Continuum Damage Mechanics

The microscale damage mechanisms in brittle ceramics are investigated in detail and a Continuum Damage Mechanics (CDM) model is developed in this work to study two common failure modes in Ceramic Matrix Composites (CMC), i.e. matrix/interphase fracture and fiber sliding. In order to empower the developed framework for performing crashworthiness studies, the effect of the dynamic energy density content on the microscale fracture modes of CMCs is also considered. The CDM model is developed within a physically consistent framework that includes basic fracture mechanics of CMCs. Also the CDM model is developed in such a way that most of the material parameters are directly obtainable form the experimental data rather than cumbersome and time consuming numerical curve fitting techniques. In order to construct a computationally effective multiscale analysis platform for CMCs, this work aims to provide an asymptotic solution for a microscale representative volume element (RVE) which represents the fiber, interphase and matrix interactions. The developed asymptotic solution can capture the non-linear response of CMCs through CDM model; and it considerably reduces the computational cost of hierarchical multiscale analysis in comparison to the numerical methods, e.g. numerical models that simulate the real microstructure. The CDM model and the RVE asymptotic solution are utilized to study the microscale damage mechanisms in CMC systems. It is shown that the developed scheme performs quite well in capturing available experiments in the literature and provides a comprehensive description of microscale damage mechanisms in CMCs. The developed framework can be utilized in the future developments of the hierarchical multiscale analysis of CMC systems.

Multiscale Classification of Remote Sensing Images

A huge effort has been applied in image classification to create high-quality thematic maps and to establish precise inventories about land cover use. The peculiarities of remote sensing images (RSIs) combined with the traditional image classification challenges made RSI classification a hard task. Our aim is to propose a kind of boost-classifier adapted to multiscale segmentation. We use the paradigm of boosting, whose principle is to combine weak classifiers to build an efficient global one. Each weak classifier is trained for one level of the segmentation and one region descriptor. We have proposed and tested weak classifiers based on linear support vector machines (SVM) and region distances provided by descriptors. The experiments were performed on a large image of coffee plantations. We have shown in this paper that our approach based on boosting can detect the scale and set of features best suited to a particular training set. We have also shown that hierarchical multiscale analysis is able to reduce training time and to produce a stronger classifier. We compare the proposed methods with a baseline based on SVM with radial basis function kernel. The results show that the proposed methods outperform the baseline.

Concurrent and Hierarchical Multiscale Analysis for Layer-Thickness Effects of Nanoscale Coatings on Interfacial Stress and Fracture Behavior

To investigate the effects of coating layer thickness on stress and the debonding behavior near the interface of coating layer and substrate, multiscale analysis is a must since molecular dynamics (MD) simulations can only be performed on models with thicknesses of about tens of nanometers on common computers, but the real thicknesses of such layers are around 300–1200 nm. In this work, generalized particle dynamics (GP) modeling for Al coated on Fe is first developed by using an atomistic domain near the layer interface and having high-scale particles far from that region to reduce degrees of freedom. Results show that the thicker coatings experience lower local average shearing stresses for a given shear strain. However, it is found that when the layer thickness reaches a large value, further increase of the layer thickness will not greatly benefit the reduction of the stress, thereby not increasing the allowable load. This trend is consistent with the simulation for Al2O3 coated on Fe by a hierarchical multiscale analysis which is formulated by proposing a nanoscale-based key variable, Gdb, called debonding energy density. This variable, defined by the debonding energy per unit area, is used to characterize material bonding strength in realizing that failure originates from the atomistic and nanoscale. The difference and connection of this low-scale fracture variable, Gdb, with crack energy release rate, GIC, in traditional fracture mechanics is illustrated and how Gdb can be easily determined through atomistic simulation is exemplified. To make the new variable effective in engineering applications, Gdb is used as input to a macroscopic scale finite element model. The obtained layer-thickness effect directly confirms the existence of a critical thickness, predicted by the GP method. This work is an effort in developing material failure theory from lower scales where material fracture originates but with applications in continuum scale via both hierarchical and concurrent multiscale analyses.