Hierarchical Multiscale Method Research Articles

Multiscale nonlinear analysis of 3D orthogonal woven C/SiC composites based on the CT reconstruction

AbstractDue to the effects of manufacturing process, there are lots of distributed voids in the interior area of three‐dimensional (3D) woven C/SiC composites, leading to the difficulties in predictions of damage evolution and ultimate strength. In this work, the mesoscale geometry of 3D woven C/SiC composites is reconstructed based on the high‐resolution CT scanning, considering the yarn path, yarn profile, and void content. The CT‐based reconstructed model agrees well with the experimental observations. Then, the constitutive laws of mesoscale constituents and macroscale structure are established and implemented numerically by the user‐defined material subroutine UMAT. Finally, the established constitutive laws are applied for the reconstructed model, and the mesoscale and macroscale nonlinear progressive damage behavior of 3D woven C/SiC composite structures are predicted using the hierarchical multiscale method, which are also validated by the experiments. The established CT‐based multiscale computational scheme would be a potential tool for performance evaluation and design of composites.

A multiscale FEM-MD coupling method for investigation into atomistic-scale deformation mechanisms of nanocrystalline metals under continuum-scale deformation

This study aims to develop a multiscale bridging method for investigating nanocrystalline metals based on macro-scale deformation. For this purpose, we propose a hierarchical multiscale computational method that can focus on some of the elements in a finite element model for scale bridging to atomistic-scale models. This method assumes that atomistic-scale nanocrystalline models are related to the integration points in a finite element and deform based on the macro-scale deformation. Nanocrystalline aluminum was chosen for the validation of the multiscale method. The finite element method (FEM) and the molecular dynamics (MD) method were used for continuum-scale and atomistic-scale simulations, respectively. We utilized the notion of the CauchyBorn rule (CBR) for communicating deformation information from the continuum scale to the atomistic scale. We studied three different cases with two nanocrystalline models and two loading cases to compare differences resulting from crystal structures and loading. Based on the crystal structure change during relaxation, nonequilibrium grain boundaries (NEGBs) were shown to play a role as deformation mechanisms in the plastic regime and induce the onset and migration of crystal defects, including deformation twins, as reported in the experiment. Furthermore, the crystal orientation dependence of the onset of crystal defects was confirmed by the comparison of the results from the two different nanocrystalline models. The qualitative agreement of the results with experimental observations is also confirmed. The proposed ‘FEM-MD’ method can bridge a large-scale gap, for example, from a nano-scale to a continuum-scale such that an MD model can be coupled to a millimeter or centimeter scale compared to other embedding methods. The present method is ideal for investigating the dislocation behavior of nanocrystalline materials, which contain multi-grained nanostructure at finite temperature, undergoing various loading scenarios at the macro-scale.

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.

Convolutional Neural Network for Enhancement of Localization in Granular Representative Unit Cells

A convolutional neural network was used to enhance the localization of strain and stress for a generalized method of cells model of a metallic microstructure. Enhanced shear strains, measured in terms of the linear regression coefficients as a function of ground truth strains, were improved from inaccurate and uncorrelated (, ) to accurate and well correlated (, ) relative to ground truth (, ). Kernel sizes of 2 or 3 were effective in the convolutional neural network (padding = “same”). graphical processing unit (GPU)-parallelized enhancement costs were low after training (range 0.41–3.45%) compared to the baseline generalized method of cells, and are significantly faster than finite element. The accuracy of enhanced localized shear strains and stress is expected to yield benefits for damage progression models, especially in the context of hierarchical multiscale methods where the generalized method of cells is applied at the intermediate scale.

Hierarchical multi-scale models for mechanical response prediction of highly filled elastic–plastic and viscoplastic particulate composites

Though a vast amount of literature can be found on modelling particulate reinforced composites and suspensions, the treatment of such materials at very high volume fractions Vf (>90%), typical of high performance energetic materials, remains a challenge. The latter is due to the very wide particle size distribution needed to reach such a high value of Vf. In order to meet this challenge, multiscale models that can treat the presence of particles at various scales are needed. This study presents a novel hierarchical multiscale method for predicting the effective properties of elasto-viscoplastic polymeric composites at high Vf. Firstly, simulated microstructures with randomly packed spherical inclusions in a polymeric matrix were generated. Homogenised properties predicted using the finite element (FE) method were then iteratively passed in a hierarchical multi-scale manner as modified matrix properties until the desired filler Vf was achieved. The validated hierarchical model was then applied to a real composite with microstructures reconstructed from image scan data, incorporating cohesive elements to predict debonding of the filler particles and subsequent catastrophic failure. The predicted behaviour was compared to data from uniaxial tensile tests. Our method is applicable to the prediction of mechanical behaviour of any highly filled composite with a non-linear matrix, arbitrary particle filler shape and a large particle size distribution, surpassing limitations of traditional analytical models and other published computational models.

Identification of Growing Points of Cotton Main Stem Based on Convolutional Neural Network

Identification of growing points of cotton main stem is the key to realize intelligent and precise machine topping and chemical topping. The identification of growing points by applying the traditional target detection model is subject to a series of shortcomings such as low accuracy, slow identification speed, large number of model parameters, huge storage cost and high calculation workload. On the basis of the advantages and disadvantages of YOLOv3, this paper proposed a modified YOLOv3 lightweight model for identifying the growing points of cotton main stem, which realized the multiplexing integration of low-level semantic features and high-level semantics features by adding dense connection modules and modifying the nonlinear transformation within the dense modules. This model significantly reduced the number of model parameters by utilizing deep separable convolution and improved the learning ability of multi-scale features by applying the hierarchical multi-scale method. Our model achieved an accuracy rate of 90.93% based on a self-prepared dataset, which is higher than the accuracy of the original YOLOv3 model by 1.64%, while the number of training parameters was significantly reduced by 48.90%. Compared with other target detection models under different illumination conditions and actual complex environments, the modified YOLOv3 model proposed in this paper showed better robustness, higher accuracy and higher speed in identifying the growing points of cotton main stem.

Stochastic multiscale modeling of heat conductivity of Polymeric clay nanocomposites

We propose a stochastic multi-scale method to quantify the most significant input parameters influencing the heat conductivity of polymeric nano-composites (PNCs) with clay reinforcement. Therefore, a surrogate based global sensitivity analysis is coupled with a hierarchical multi-scale method employing computational homogenization. The effect of the conductivity of the fibers and the matrix, the Kapitza resistance, volume fraction and aspect ratio on the ’macroscopic’ conductivity of the composite is systematically studied. We show that all selected surrogate models yield consistently the conclusions that the most influential input parameters are the aspect ratio followed by the volume fraction. The Kapitza Resistance has no significant effect on the thermal conductivity of the PNCs. The most accurate surrogate model in terms of the R2 value is the moving least square (MLS).

A machine-learning-enhanced hierarchical multiscale method for bridging from molecular dynamics to continua

In the community of computational materials science, one of the challenges in hierarchical multiscale modeling is information-passing from one scale to another, especially from the molecular model to the continuum model. A machine-learning-enhanced approach, proposed in this paper, provides an alternative solution. In the developed hierarchical multiscale method, molecular dynamics simulations in the molecular model are conducted first to generate a dataset, which represents physical phenomena at the nanoscale. The dataset is then used to train a material failure/defect classification model and stress regression models. Finally, the well-trained models are implemented in the continuum model to study the mechanical behaviors of materials at the macroscale. Multiscale modeling and simulation of a molecule chain and an aluminum crystalline solid are presented as the applications of the proposed method. In addition to support vector machines, extreme learning machines with single-layer neural networks are employed due to their computational efficiency.

Atomistic simulation of diffusion bonding of dissimilar materials undergoing ultrasonic welding

Ultrasonic welding (UW) process offers the ability to create highly efficient solid-state joints for lightweight metal alloys with low power consumption. During the process, a distinct diffusion layer is observed at the joint interface that undergoes severe plastic deformation at elevated temperature. A hierarchical multiscale method is proposed in this study to predict the diffusion behavior of the UW process of dissimilar materials. The method combines molecular dynamics and classical diffusion theory to calculate the thickness of the diffusion layer at the welded interface. A molecular dynamics model is developed for the first time that considers the effect of transverse ultrasonic vibration to simulate the evolution of the diffusion layer. The effect of ultrasonic vibration at the atomic level is assumed to provide thermal energy at the joint interface and the mechanical movement of atoms. The influence of sinusoidal velocity change during ultrasonic vibration is incorporated by numerically time integrating the diffusivity at different ultrasonic velocity. The simulation result shows that the solid-state diffusivity depends on temperature, pressure, and transverse ultrasonic velocity. Higher temperature, pressure, and ultrasonic velocity result in higher diffusivity leading to larger diffusion layer thickness. This article provides a comprehensive review of the diffusion bonding behavior and its dependence on process variables. It also presents a numerical approach combining molecular dynamics and hierarchical multiscale calculation to predict the diffusion layer thickness for the UW process of dissimilar materials.

Peridynamics with Corrected Boundary Conditions and Its Implementation in Multiscale Modeling of Rolling Contact Fatigue

There is a boundary effect due to incomplete horizons of boundary or near-boundary points in peridynamics. In this paper, we propose to attach “fictitious walls” to boundary surfaces so that the boundary effect can be reduced or eliminated. Differing from the concept of “fictitious material layers”, which is only attached to displacement boundary surfaces, “fictitious walls” are attached to both displacement and force boundary surfaces. Three types of fictitious walls are considered in this paper: undeformed, deformed, and periodic. It is recommended to attach “undeformed fictitious walls” to displacement boundaries and “deformed fictitious walls” to force boundaries. “Periodic fictitious walls” are suggested for use in peristatics only. In addition, peridynamics with corrected boundary conditions is then implemented in a hierarchical multiscale method to study rolling contact fatigue. In this hierarchical multiscale framework, the coefficient of friction is passed from molecular dynamics simulations to peridynamics, which models crack initiation and propagation in rolling contact simulations.

Analysis of Naval Ship Evacuation Using Stochastic Simulation Models and Experimental Data Sets

In the present paper, a hierarchical multi-scale method is developed for the nonlinear analysis of composite materials undergoing heterogeneity and damage. Starting from the homogenization theory, the energy equivalence bet... | Find, read and cite all the research you need on Tech Science Press

Finite element simulation of the micromachining of nanosized-silicon-carbide-particle reinforced composite materials based on the cohesive zone model

A finite element method based on the cohesive zone model was used to study the micromachining process of nanosized silicon-carbide-particle (SiCp) reinforced aluminum matrix composites. As a hierarchical multiscale simulation method, the parameters for the cohesive zone model were obtained from the stress-displacement curves of the molecular dynamics simulation. The model considers the random properties of the silicon-carbide-particle distribution and the interface of bonding between the silicon carbide particles and the matrix. The machining mechanics was analyzed according to the chip morphology, stress distribution, cutting temperature, and cutting force. The simulation results revealed that the random distribution of nanosized SiCp causes non-uniform interaction between the tool and the reinforcement particles. This deformation mechanics leads to inhomogeneous stress distribution and irregular cutting force variation.

Effects of welding speed on the multiscale residual stresses in friction stir welded metal matrix composites

The effects of welding speed on the macroscopic and microscopic residual stresses (RSes) in friction stir welded 17 vol.% SiCp/2009Al-T4 composite plates were studied via neutron diffraction and an improved decoupled hierarchical multiscale modeling methods. Measurements showed that the macroscopic and total RSes had the largest variations in the longitudinal direction (LD). Increasing the welding speed led to higher values of measured LD macroscopic and total RSes in the matrix. The welding speed also significantly influenced the distributions and magnitudes of the microscopic RSes. The RSes were predicted via an improved hierarchical multiscale model, which includes a constant coefficient of friction based thermal model. The RSes in the composite plates before friction stir welding (FSW) were computed and then set as the initial states of the FSW process during modeling. This improved decoupled multiscale model provided improved predictions of the temperature and RSes compared with our previous model.

Prediction of mechanical properties of knitted fabrics under tensile and shear loading: Mesoscale analysis using representative unit cells and its validation

Abstract This article presents a numerical framework to predict the mechanical behavior of knitted fabrics from their discrete structure at the fabric yarn level, i.e., the mesostructure, utilizing the hierarchical multiscale method. Due to the regular distribution of yarn loops in a knitted structure, the homogenization theory for periodic materials can be employed. Thus, instead of considering the whole fabric sample under loading, a significantly less computationally demanding analysis can be done on a repeated unit cell (RUC). This RUC is created based on simple structural parameters of knitted yarn loops and its fabric yarns are assumed to behave transversely isotropic. Nonlinear finite element analyses are performed to determine the stress fields in the RUC under tensile and shear loading. During this analysis, contact friction among yarns is considered as well as the periodic boundary conditions are employed. The macroscopic stresses then can be derived from the stress fields in the RUC by means of the numerical homogenization scheme. The physical fidelity of the proposed framework is shown by the good agreement between the predicted mechanical properties of knitted fabrics and corresponding experimental data.

Stochastic analysis of interphase effects on elastic modulus and yield strength of nylon 6/clay nanocomposites

The multifunctional properties of polymer clay nanocomposites (PCNs) can be related to the interaction of clays, polymer and interphase region. Several experimental, analytical and numerical studies have been conducted to characterize the mechanical behavior of PCNs. The elastic behavior of PCNs is well documented in the literature but their other material properties like yield strength are rather vague. On the other hand, the variation of material parameters and the stochastic nature of interphase region hinder the use of deterministic methods. In this study, a stochastic analysis along with a hierarchical multiscale method is used to analyze the effect of interphase properties on the macroscopic properties of PCNs. Since the interphase layer is expected to be weaker than the polymer matrix, a weakening coefficient is defined to describe the interphase properties based on the matrix properties. This weakening coefficient and the interphase thickness are considered as the stochastic inputs. The elastic modulus and yield strength of nylon 6/clay nanocomposites are calculated using the stochastic multiscale framework. The uncertainty propagation and sobol sensitivity analysis are performed to study the effect of random inputs on the elastic modulus and yield strength of PCNs. Despite the wide range of input variations, the accuracy of the proposed stochastic multiscale framework for the prediction of the PCNs properties is estimated by validating our results against the available experimental data in the literature.

Multiscale modeling and simulation of rolling contact fatigue

A hierarchical multiscale method is proposed in this paper to study the rolling contact fatigue with the consideration of lubricant effects. This multiscale model consists of a molecular model of lubricant and a continuum model of rolling contact components. At the nanoscale, molecular dynamics is employed to model the lubricant and to calculate the friction coefficient at the rolling contact surface. At the macroscale, the finite element method is used to conduct stress analysis of the rolling contact component so that the fatigue life can be predicted. The calculated friction coefficient is passed from the molecular model to the continuum model in the proposed multiscale model. The effect of fluctuating load on the rolling contact fatigue life is also studied in this paper. The objective of this paper is to develop a new multiscale framework which connects the nanoscale and the mascroscale. It shall be noted that a commonly used fatigue life model is employed in the continuum model.

A 3D Hermite-based multiscale local active contour method with elliptical shape constraints for segmentation of cardiac MR and CT volumes.

Analysis of cardiac images is a fundamental task to diagnose heart problems. Left ventricle (LV) is one of the most important heart structures used for cardiac evaluation. In this work, we propose a novel 3D hierarchical multiscale segmentation method based on a local active contour (AC) model and the Hermite transform (HT) for LV analysis in cardiac magnetic resonance (MR) and computed tomography (CT) volumes in short axis view. Features such as directional edges, texture, and intensities are analyzed using the multiscale HT space. A local AC model is configured using the HT coefficients and geometrical constraints. The endocardial and epicardial boundaries are used for evaluation. Segmentation of the endocardium is controlled using elliptical shape constraints. The final endocardial shape is used to define the geometrical constraints for segmentation of the epicardium. We follow the assumption that epicardial and endocardial shapes are similar in volumes with short axis view. An initialization scheme based on a fuzzy C-means algorithm and mathematical morphology was designed. The algorithm performance was evaluated using cardiac MR and CT volumes in short axis view demonstrating the feasibility of the proposed method.

Hierarchical multiscale modeling of Polyvinyl Alcohol/Montmorillonite nanocomposites

Abstract The mechanical responses of low volume fraction Polyvinyl Alcohol (PVA)/Montmorillonite (MMT) nanocomposites were modeled using a hierarchical multiscale modeling method. Nanoscale Molecular Dynamics (MD) and mesoscale Finite Element Analysis (FEA) were used to bridge information regarding deformation mechanics within Polymer/Clay Nanocomposites (PCNs). MD computations of PVA/MMT interfaces were employed to calibrate a Traction-Separation (T-S) relation, which was then upscaled into a cohesive zone model (CZM) to model interfaces between PVA and MMT in a mesomechanical finite element framework. Virtual Composite Structure Generation (VCSG) was used to generate a quasi-realistic Representative Volume Element (RVE), and explicit FEA was performed on the RVE to demonstrate delamination in the PCNs. The FEA featured an elasto-viscoelastic-viscoplastic Internal State Variable (ISV) model for the polymer host (PVA) and a CZM for the interfaces between MMT and PVA. The hierarchical length scale bridging methodology employed here for a polymer based composite has applications for many other material systems.

Multiscale modelling of multiple-cracking tensile fracture behaviour of engineered cementitious composites

In this paper a hierarchical multiscale modelling method is proposed to analyse the strain-hardening and multiple-cracking tensile fracture behaviour of engineered cementitious composites. A simplified multi-linear crack bridging relationship is proposed at a lower mesoscale based on analytical crack bridging analysis for a single crack. A representative volume element model is developed at an upper mesoscale accounting for random fluctuations of internal material properties and sequentially occurred cracking, and it is analysed using the extended finite element method. The multiscale modelling method is validated, and the effect of fibre distribution uniformity on the tensile behaviour of ECC is investigated.

Multiscale modeling of macroscopic and microscopic residual stresses in metal matrix composites using 3D realistic digital microstructure models

This work presents a hierarchical multiscale method for predicting accurately and efficiently the macroscopic and microscopic residual stresses (RSes) in MMCs based on large-size realistic digital microstructure models. Effects of various conditions on the multiscale modeling are systematically studied. Results indicate that the hierarchical multiscale model shows both a good self-consistency and a good accuracy. Compared with the kinematic uniform boundary conditions, the static uniform boundary conditions lead to more accurate prediction of the thermal misfit RS. The size of the volume element has significant effects on the predicted values of the thermal misfit RS. The hierarchical multiscale model gains significant advantages over the hybrid-semiconcurrent one with respect to both computational efficiency and computer memory cost. The local fluctuation profiles and total variations of the total RS are dominated by those of the thermal misfit RS at the microscale and by those of the macroscopic RS at the macroscale, respectively.