Self-consistent Clustering Analysis Research Articles

Identification of component material in-situ properties of C/SiC composites based on self-consistent clustering analysis and Bayesian method

In the paper, a method for identifying the mechanical properties of the in-situ component materials in carbon fiber reinforced silicon carbide ceramic matrix composites based on the macro mechanical test data is proposed. Firstly, the computation efficiency of considering damage behavior in the meso-mechanial model is improved through the self-consistent clustering analysis. Subsequently, sensitivity analysis is introduced in the parameter identification based on the Bayesian network to reduce the number of parameters to be identified simultaneously, thereby alleviating the ill-posedness of the inverse problem. Numerical and experimental cases were conducted to validate the proposed method. The maximum error of parameter identification is 6.0 % and the prediction error for strength is only 1.7 % in the numerical case with 5 % Gaussian noise. In the experimental case, the stress–strain curve calculated using the identified results shows good agreement with the experimental data. The prediction error for strength is only 2.2 %, while the maximum deviation between the identified results and the reference value in the literature can be up to 50 %, indicating the importance of obtaining the properties of component materials in-situ.

A damage-related adaptive self-consistent clustering analysis method with localized refinement capability for the damage problem of 3D woven composites

In this work, a Damage-related Adaptive Self-Consistent Clustering Analysis (DASCA) method is developed to achieve higher solving accuracy for 3D damage problems than Self-Consistent Clustering Analysis (SCA) method, which is applied to investigate the mesoscale damage behavior of 3D woven composites (3DWC). The developed clustering adaptivity framework is based on the characteristics of the damage problem, which consists of five fundamental stages: evaluation of the adaptivity conditions, selection criterion of potential damage clusters, online adaptive clustering analysis, update of the cluster database and adaptive rewind of the analysis process. In the second stage, the clusters with the highest potential to enter the damage state are identified and marked as adaptivity target clusters. In the solving process, the distribution of clusters can achieve problem-dependent dynamic adjustments, ensuring that clusters are concentrated on the regions of interest. Though the numerical examples of 3DWC, the DASCA solutions, using fewer clusters and less computational cost, exhibit higher prediction accuracy for macroscopic mechanical performance, first damage initiation moments and damage evolution process than the SCA solutions.

A low-cost multiscale model with fiber/matrix interface for cryogenic composite storage tanks considering temperature effects based on self-consistent clustering analysis

Matrix (including interface) failure is a typical form of failure in the composite laminates for cryogenic storage tanks causing functionally useless of the structure. In this work, a low-cost multiscale model based on the Self-consistent Clustering Analysis (SCA) method is developed to predict the matrix failure process of the composite storage tanks. First, a reduced order model modeling method with fiber/matrix interfaces is proposed. Then, in conjunction with Progressive Failure Analysis (PFA), a reduced-order model is used to predict matrix failure and interface failure of the composites, mesh sensitivity analyses were carried out, and strength damage envelopes were obtained for unidirectional composites subjected to a combination of transverse stresses and in-plane shear. Compared with the prediction results of the Puck criterion, the errors in predicting damage strength for compressive-shear load and tensile-shear load do not exceed 10% and 30%, respectively. And finally, the thermal-mechanical load analysis of the composite storage tanks is carried out and the effect of homogenous temperature field and heterogenous temperature field on the load-bearing performance of the composite structure is analyzed. The method is proved to have good accuracy and to be very efficient. Its main feature is the ability to rapidly predict the stiffness and strength properties of composite structures under different environmental conditions, in agreement with experimental results, showing the potential to reduce the time and cost required for structural design.

Extended tensor decomposition model reduction methods: Training, prediction, and design under uncertainty

This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the approximation accuracy and the reducibility (compressibility) in highly nonlinear and singular cases. The proposed XTD method can be a powerful tool for solving nonlinear space–time parametric problems. The method has been successfully applied to parametric elastic–plastic problems and real time additive manufacturing residual stress predictions with uncertainty quantification. Furthermore, a combined XTD-SCA (self-consistent clustering analysis) strategy is presented for multi-scale material modeling, which enables real time multi-scale multi-parametric simulations. The efficiency of the method is demonstrated with comparison to finite element analysis. The proposed method enables a novel framework for fast manufacturing and material design with uncertainties.

Efficient multiscale investigation of mechanical behavior in Nb3Sn superconducting accelerator magnet based on self-consistent clustering analysis

The High Luminosity Large Hadron Collider (HL-LHC) is one of the large-scale projects currently being developed at the European Organization for Nuclear Research (CERN). Many Nb3Sn superconducting magnets are employed in this project, which exhibit complicated multiscale characteristics. The mechanical behaviors of magnets, which are directly related to the safety and stability of the overall structure, are affected by the electromagnetic–mechanical-thermal loading in actual service conditions. However, detailed modeling of magnets requires significant computing resources. A reduced-order method named self-consistent clustering analysis (SCA) has been proposed recently to reduce the cost. We have combined the SCA and finite element method (FEM) as an efficient multiscale framework, which is utilized to analyze the mechanical behaviors of accelerator magnets. Firstly, the computation results by presented framework are compared with direct numerical simulation (DNS) and existed experimental data to validate the accuracy and efficiency. Then, the FEM-SCA2 framework is utilized to study the mechanical behaviors of MQXFS accelerator magnet model under assembly, cool-down and excitation steps. The influences of material parameters, friction coefficient and stiffness degradation are also discussed. This paper provides an efficient multiscale analysis framework for investigating mechanical behavior in Nb3Sn accelerator magnet, which could be employed to study other magnets.

An extended full field self-consistent cluster analysis framework for woven composite

In this work, the self-consistent clustering analysis (SCA) framework is extended to include homogenization and full field analysis of 3D anisotropic woven composite Representative Unit Cell (RUC). The developed extended framework has two new features, namely, (i), to reconstruct the local field variables, a strain refinement stage is presented by solving full field Lippmann–Schwinger equations within 3D anisotropic woven composite RUC following the online predictive stage in SCA, and (ii), discrete Green’s operator based on finite difference is adopted to improve the accuracy of refined point-wise physical field variables. To demonstrate the accuracy and efficiency of the proposed method, benchmark problems are analyzed, and results are compared to directly numerical simulation (DNS). For the reproducibility of presented results, the developed code can be freely downloaded from https://github.com/Tong-RuiLiu/Extended-SCA-and-FFT-based-strain-refinement-method-.

Transformation field analysis as a background of clustering discretization methods in micromechanics of composites

A linear composite material (CM) consisting of a homogeneous matrix with either the periodic or random set of heterogeneities is considered. One of the first reduced-order models (ROMs), Transformation Field Analysis (TFA) by Dvorak for the pair strain-eigenstrain (or stress-eigenstress) is modified in terms of the “mixed” pair strain-eigenstress (or stress-eigenstrain) for implementation to clustering-based ROMs initiated by the self-consistent clustering analysis (SCA) by WK Liu. A set of consistency conditions are obtained for both the effective properties and modified eigenfield concentration factors. It is found that modified TFA represents a unified background of all three central clustering-based ROMs: the SCA, virtual clustering analysis (VCA), and finite element analysis–clustering analysis (FCA). One presents the scheme of estimation of inhomogeneous strain concentration factors in some prescribed clusters analyzed by the SCA (nonlinear problem). For statistically homogeneous CMs, a localized version of the modified TFA is proposed for clustering of the matrix (coating) in the vicinity of inclusions. VCA used for the analysis of a finite size inclusion can be modified for the implementation of a combination of both the modified TFA and functional gradient theory.

An introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysis

An introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysis

Understanding the helicoidal damage behavior of bio-inspired laminates by conducting multiscale concurrent simulation and experimental analysis

Bio-inspired helicoidal structures exhibit excellent fracture toughness. A multiscale concurrent simulation of the damage propagation process is critical for understanding the fracture behavior of such structures with pre-existing cracks. However, such an analysis is extremely challenging owing to computational complexity. In this study, the in-plane critical stress intensity factor and energy release rate of six different helicoidal carbon-fiber-reinforced plastic structures are measured experimentally by conducting a single-edge-notch bending test. The damage distribution of the different structures is examined by performing computed tomography scanning. Several multiscale concurrent analyses are conducted by using the self-consistent clustering analysis method to study the specific damage propagation process and evaluate the fracture toughness contribution of different layers. The results indicate that the pitch angle significantly impacts the fracture toughness, whereas the stacking mode changes the crack propagation orientation. When the pitch angle is appropriately adjusted, the fiber damage length is enhanced, resulting in a significant increase in the fracture toughness. The interaction between fiber damage, matrix damage, and hybrid damage during the failure process is interpreted using the dissipated energy ratios of the fiber damage layer, transition layer, and matrix damage layer.

Classification of Signature-Based Phenotypes of Aging-Related Genes to Identify Prognostic and Immune Characteristics in HCC.

Hepatocellular carcinoma (HCC), which has become one of the most significant malignancies causing cancer-related mortality, presents genetic and phenotypic heterogeneity that makes predicting prognosis challenging. Aging-related genes have been increasingly reported as significant risk factors for many kinds of malignancies, including HCC. In this study, we comprehensively dissected the features of transcriptional aging-relevant genes in HCC from multiple perspectives. We applied public databases and self-consistent clustering analysis to classify patients into C1, C2, and C3 clusters. The C1 cluster had the shortest overall survival time and advanced pathological features. Least absolute shrinkage and selection operator (LASSO) regression analysis was adopted to build the prognostic prediction model based on six aging-related genes (HMMR, S100A9, SPP1, CYP2C9, CFHR3, and RAMP3). These genes were differently expressed in HepG2 cell lines compared with LO2 cell lines measured by the mRNA expression level. The high-risk score group had significantly more immune checkpoint genes, higher tumor immune dysfunction and exclusion score, and stronger chemotherapy response. The results indicated that the age-related genes have a close correlation with HCC prognosis and immune characteristics. Overall, the model based on six aging-associated genes demonstrated great prognostic prediction ability.

Concurrent multiscale virtual testing for 2D woven composite structures: A pathway towards composites design and structure optimization

Virtual testing is a powerful tool to characterize the mechanical behavior of materials owing to its excellent predictive ability. However, virtual testing for composite structures remains challenging due to their natural multiscale heterogeneities and expensive computational costs across scales. This paper proposes a FE-SCA concurrent multiscale framework to solve this challenge, where FE and SCA represent the finite element method and the self-consistent clustering analysis, respectively. The mechanical behavior of three woven structures, including open-hole plate, Isoipescu shear, and biaxial tensile specimens, are predicted using the proposed method. The results show that the established FE-SCA concurrent multiscale framework can virtually characterize the damage initiation and evolution for both macroscale woven structures and mesoscale woven representative volume elements. Moreover, it shows significantly higher efficiency compared with the traditional FE 2 framework. Due to the high efficiency and predictive ability, the FE-SCA concurrent multiscale virtual testing has the potential to be a pathway toward composites design and structure optimization.

Concurrent n-scale modeling for non-orthogonal woven composite

Concurrent analysis of composite materials can provide the interaction among scales for better composite design, analysis, and performance prediction. A data-driven concurrent n-scale modeling approach (\(\text {FExSCA}^\text {n-1}\)) is adopted in this paper for woven composites utilizing a mechanistic reduced order model (ROM) called Self-consistent Clustering Analysis (SCA). We demonstrated this concurrent multiscale modeling theory with a \(\text {FExSCA}^2\) approach to study the 3-scale woven carbon fiber reinforced polymer (CFRP) laminate structure. \(\text {FExSCA}^2\) significantly reduced expensive 3D nested composite representative volume element (RVE) computation for woven and unidirectional (UD) composite structures by developing a material database. The modeling procedure is established by integrating the material database into a woven CFRP structural numerical model, formulating a concurrent 3-scale modeling framework. This framework provides an accurate prediction for the structural performance (e.g., nonlinear structural behavior under tensile load), as well as the woven and UD physics field evolution. The concurrent modeling results are validated against physical tests that link structural performance to the basic material microstructures. The proposed methodology provides a comprehensive predictive modeling procedure applicable to general composite materials aiming to reduce laborious experiments needed.

Multi-scale concurrent analysis for bio-inspired helicoidal CFRP laminates and experimental investigation

The bio-inspired helicoidal structure has been proved to exhibit excellent load-bearing capacity and damage resistance performance. However, there are few relevant researches to analyze its failure process from micro-scale. In this study, three types of carbon fiber reinforced plastics (CFRP) laminate structures were prepared—cross-ply, quasi-isotropic, and helicoidal. The mechanical performance of the laminates was tested using an indentation test. The experiment results verified the excellent mechanical performance of the helicoidal structure. In order to analyze its intrinsic enhancement mechanism, a multi-scale damage model for self-consistent clustering analysis method was proposed, and the damage evolution process of the laminates was simulated at both macro and micro scales. The results indicated that owing to the small rotation angle between adjacent layers in the helicoidal structure, the stress distribution along the thickness direction was more uniform. Moreover, the laminate was more likely to be divided into several sub-laminates by primary delamination. The fibers of each sub-laminate would be cracked in sequence from top to bottom, accompanied by the subprime delamination, resulting in the failure of the laminate. Besides, a twisted crack path could be generated, making the helicoidal structure exhibit excellent load-bearing capacity and damage resistance.

A concurrent three-scale scheme FE-SCA[formula omitted] for the nonlinear mechanical behavior of braided composites

An efficient and accurate multiscale modeling for the mechanical behavior of braided composites with complex microstructure is an outstanding challenge in the mechanics of composite materials. In this work, a concurrent three-scale scheme FE-SCA2 is proposed for predicting the macroscopic nonlinear behavior of braided composites associated with the microscopic plastic and damage of the constituents, where FE and SCA are short for finite element method and self-consistent clustering analysis, respectively. In this concurrent scheme, the macroscale behavior of the braided composites is handled by FE analysis, and the microscale and mesoscale behavior of the constituents are handled by SCA simultaneously with the data-driven clustering discretization. To demonstrate the accuracy and efficiency of the proposed scheme, we first predict the asymmetric anisotropic yield and failure surfaces for braided composites and then analyze the nonlinear behavior of a braided composite plate under bending. The computational results are compared with FE method results and experimental data from the literature, with good agreement in cases where such data is available. It is shown that the microscale, mesoscale, and macroscale nonlinear behavior of braided composites can be captured simultaneously using the proposed FE-SCA2, which would be difficult to be characterized by experimental methods. The proposed multiscale method could be applied for composite structures with various properties of micro-structures and constituents to expedite the design and structural optimization.

Adaptivity for clustering-based reduced-order modeling of localized history-dependent phenomena

This article introduces adaptivity in Clustering-based Reduced Order Models (ACROMs). The strategy is demonstrated for a particular CROM called Self-Consistent Clustering Analysis (SCA), extending it into the Adaptive Self-Consistent Clustering Analysis (ASCA) method. This is shown to improve predictions of Representative Volume Elements (RVEs) of materials exhibiting history-dependent localization phenomena such as plasticity, damage and fracture. The overall approach is composed of three main building blocks: target clusters selection criterion, adaptive cluster analysis, and computation of cluster interaction tensors. In addition, an adaptive clustering solution rewinding procedure and a dynamic adaptivity split factor strategy are suggested to further enhance the adaptive process. The ASCA method is shown to perform better than its static counterpart when capturing the multi-scale elasto-plastic behavior of a particle–matrix composite and predicting the associated fracture and toughness. The proposed adaptivity strategy can be followed in other CROMs to extend them into ACROMs, opening new avenues to explore adaptivity in this context.

Efficient two-scale analysis with thermal residual stresses and strains based on self-consistent clustering analysis

The thermal residual stresses and strains are crucial in the industrial manufacturing process of the metal alloys and other composites. In representative volume element (RVE) of these complex composite structures, how to accurately and efficiently simulate the responses considering thermal residual stresses and strains is also vital, which could be served as a foundation to multiscale analysis. Recently an effective reduced-order method named self-consistent clustering analysis (SCA) has been proposed to solve microscopic responses in RVE. This paper modifies the original SCA method for thermoelastic and thermal elastoplastic problems, and the microscopic responses of the RVE are compared with the results of analytical and Fast Fourier Transform (FFT) methods to validate its accuracy and feasibility. Then, this study demonstrates the influences of different clustering strategies in offline stage, develops the clustering number optimization and discusses the two-scale analysis using the modified SCA method with/without thermal residual stresses and strains in microscale. In two-scale analysis, the macroscopic and microscopic responses are studied to explore the effects of thermal residual stresses and strains. The two-scale analysis framework with modified SCA method proposed in this work is proved to be efficient in simulating composites considering thermal residual strains and stresses.

Macroscale Property Prediction for Additively Manufactured IN625 from Microstructure through Advanced Homogenization.

Design of additively manufactured metallic parts requires computational models that can predict the mechanical response of parts considering the microstructural, manufacturing, and operating conditions. This article documents our response to Air Force Research Laboratory (AFRL) Additive Manufacturing Modeling Challenge 3, which asks the participants to predict the mechanical response of tensile coupons of IN625 as function of microstructure and manufacturing conditions. A representative volume element (RVE) approach was coupled with a crystal plasticity material model solved within the Fast Fourier Transformation (FFT) framework for mechanics to address the challenge. During the competition, material model calibration proved to be a challenge, prompting the introduction in this manuscript of an advanced material model identification method using proper generalized decomposition (PGD). Finally, a mechanistic reduced order method called Self-consistent Clustering Analysis (SCA) is shown as a possible alternative to the FFT method for solving these problems. Apart from presenting the response analysis, some physical interpretation and assumptions associated with the modeling are discussed.

From microscale to mesoscale: The non-linear behavior prediction of 3D braided composites based on the SCA2 concurrent multiscale simulation

Compared with traditional phenomenological models, concurrent multiscale simulation is a powerful tool to capture the mechanical behavior of composites from different scales simultaneously. However, it is still a challenge to conduct a concurrent multiscale simulation for composites due to the huge computational costs. The aim of this paper is to solve the challenge by introducing an effective reduced order model (ROM), called the data-driven self-consistent clustering analysis (SCA). The SCA method solves the RVE problem into two stages. In the offline stage, the high-fidelity RVE of composites is compressed into a cluster-based RVE and the interaction tensor between two clusters is calculated. In the online stage, a cluster-based discrete incremental Lippmann-Schwinger equation is solved to get the local strain and stress responses. Based on SCA, a concurrent multiscale framework SCA2 from microscale to mesoscale is proposed to capture the non-linear behavior of 3D braided composites. Firstly, the SCA-based results for yarn RVE and braided RVE are compared with the finite element (FE) results to verify the accuracy of the algorithm. Then, the SCA2 framework is applied to simulate the uniaxial tension and compression of 3D braided composites, which is also validated with the experiments and shows great accuracy and high efficiency. The proposed SCA2 framework will be extended into a three-scale concurrent simulation for the macroscopic structure analysis.

A concurrent multiscale framework based on self-consistent clustering analysis for cylinder structure under uniaxial loading condition

Accurate and efficient multiscale simulation of multifilament composite remains challenges due to expensive computation cost of solving the nonlinear representative volume element (RVE) responses in microscale. An effective reduced-order method called self-consistent clustering analysis (SCA) has been proposed recently to solve the dilemma. This paper extends the application of traditional multilevel finite element (FE2) to cylinder structure with domain division, where the inner domain is computed by finite element method (FEM) with SCA instead of direct FE2 method and outer domain is calculated by conventional FEM. The presented framework is named as concurrent modified FEM-SCA. To validate the accuracy and efficiency of presented method, the computation results of SCA, Fast Fourier Transform (FFT) and FEM are compared in microscale at first. Then, under the presented framework, the cylinder structures with diverse RVEs in uniaxial loading are studied, and the results are compared with full-scale direct numerical simulation (DNS) by FEM. Besides, the effects of different element positions, inclusion variations and loading phases on the RVE responses are also studied.

Stochastic nonlinear analysis of unidirectional fiber composites using image-based microstructural uncertainty quantification

We present a data-driven nonlinear uncertainty quantification and propagation framework to study the microstructure-induced stochastic performance of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites. The proposed approach integrates (1) microscopic image characterization, (2) stochastic microstructure reconstruction, and (3) efficient multiscale finite element simulations enabled by self-consistent clustering (SCA) analysis. To model the complex microstructural variability, the proposed UQ methods take the non-Gaussian uncertainty sources into account through a distribution-free sampling approach leveraging nonparametric and asymptotic statistical tools. A hierarchical conditional sampling strategy enables the simultaneous sampling of multiple sources of uncertainties. Our approach provides insights into the impact of microstructural variabilities, which are shown to have an increasing impact on the nonlinear responses of UD CFRP parts under progressive compression loading and ultimately on the failure rate over time. We discover that before CFRP parts start to fail, a characteristic time period emerges with distinctive uncertainty distributions specific to the microstructure variability and the probability of failure. Identifying the failure time period is crucial to the reliability prediction, which is an essential component of CFRP design.