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(a-c) Typical distribution of the representative micromechanical properties concerning the longitudinal Young's modulus (d) Spatial variation of a representative micromechanical property corresponding to a random realization (e) Typical distribution of the representative macromechanical properties concerning the longitudinal Young's modulus for macromechanical (in red colour) and micromechanical (in blue colour) analyses (f) Spatial variation of a representative macromechanical property corresponding to a random realization (g-h) Representative results for the probability distributions of first natural frequency and first buckling load considering micro mechanical analysis for different degree of stochasticity (Here () f  and () b  denote the stochastic natural

(a-c) Typical distribution of the representative micromechanical properties concerning the longitudinal Young's modulus (d) Spatial variation of a representative micromechanical property corresponding to a random realization (e) Typical distribution of the representative macromechanical properties concerning the longitudinal Young's modulus for macromechanical (in red colour) and micromechanical (in blue colour) analyses (f) Spatial variation of a representative macromechanical property corresponding to a random realization (g-h) Representative results for the probability distributions of first natural frequency and first buckling load considering micro mechanical analysis for different degree of stochasticity (Here () f  and () b  denote the stochastic natural

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This article presents a probabilistic framework to characterize the dynamic and stability parameters of composite laminates with spatially varying micro and macro-mechanical system properties. A novel approach of stochastic representative volume element (SRVE) is developed in the context of two dimensional plate-like structures for accounting the c...

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... 22 Naskar et al. presented different spatial random microstructures for composites using an finite element model (FEM)-based computational study to investigate the manufacturing as well as environmental uncertainties, which are later extended to nanocomposites. 23,24 Mehvari et al. analyzed the electrical performance of copper/ polyurethane composite under pressure both experimentally and computationally. 25 Tamayo-vegas et al. presented two simulation models (resistor model and FEM) to calculate the electrical conductivity and percolation threshold of CNT/ epoxy nanocomposites. ...
Article
Developing a printed elastomeric wearable sensor with good conformity and proper adhesion to skin, coupled with the capability of monitoring various physiological parameters, is very crucial for the development of point-of-care sensing devices with high precision and sensitivity. While there have been previous reports on the fabrication of elastomeric multifunctional sensors, research on the printable elastomeric multifunctional adhesive sensor is not very well explored. Herein, we report the development of a stencil printable multifunctional adhesive sensor fabricated in a solvent-free condition, which demonstrated the capability of having good contact with skin and its ability to function as a temperature and strain sensor. Functionalized liquid isoprene rubber was selected as the matrix while carboxylated multiwalled carbon nanotubes (c-CNTs) were used as the nanofiller. The selection of the above model compounds facilitated the printability and also helped the same composition to demonstrate stretchability and adhesiveness. A realistic three-dimensional microstructure (representative volume element model) was generated through a computational framework for the current c-CNT-liquid elastomer. Further computational simulations were performed to test and validate the correlation between electrical responses to that of experimental studies. Various physiological parameters like motion sensing, pulse, respiratory rate, and phonetics detection were detected by leveraging the electrically resistive nature of the sensor. This development route can be extended toward developing different innovative adhesives for point-of-care sensing applications.
... Prismatic smart beams, periodically attached to piezo sensors coupled with single and multi resonant shunt resistiveinductive circuits would be considered with the following objectives: (i) to develop the random impedance formulation for unimorph beam spectral elements coupled with shunt circuits, (ii) to investigate the physical state of flexural wave propagation under the effect of random impedance due to the variabilities of electrical components in the shunt circuit, (iii) to explore the bandgap formation effects and the optimal RL shunt circuit needed for controlling structural vibration response along with wave propagation and attenuation. It is worthy to mention here that we do not intend to consider the spatial variation of the beam-like metastructure along with its length here; rather we would adopt a random variable based approach for the stochastic quantification [58,59]. The article hereafter is organized as, section 2: Elements formulation based on SEM, followed by the stochastic approach for considering random uncertainty in the impedance parameters, section 3: results and discussions, section 4: conclusions and perspective. ...
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Randomness in the media breaks its periodicity affecting the vibration and wave propagation performance. Such disorder caused by the variability may lead to interesting physical phenomena such as trapping and scattering waves, wave reflection, and energy localisation. While the randomness may be attributed to manufacturing irregularities and quantifying its effect is crucial for ensuring adequate performance of a range of smart systems, these effects can also be exploited for manipulating the wave properties. Here we investigate a smart metastructure in the form of a beam integrated with piezoelectric transducers coupled to a resonant shunt circuit. The piezoelectric shunt in a periodical arrangement can induce locally resonant bandgaps that can be employed in wave and vibration manipulation (and control). This paper quantifies the uncertainty associated with electrical circuit components that affect the circuit impedance. Such uncertainty essentially propagates to the beam smart metamaterial, influencing its wave and vibration control feature. Numerical results of the unimorph meta-beam with single and multi-frequency shunt configuration show that the bandgap behaviour is sensitive to the random disorder associated with circuit impedance parameters, which can, in turn, be exploited for enhanced functionalities based on optimal RL shunt circuits for controlling structural vibration response along with wave propagation and attenuation.
... In the recent years, machine learning (ML) has emerged as a promising tool for the predictive modeling of polymer composites with significant computational efficiency [25][26][27][28][29][30][31][60][61][62][63][64]. Out of different ML algorithms, Artificial Neural Network (ANN) is a well-known predictive technique used successfully by various researchers to model the mechanical behaviour of polymer composites [32][33][34][35][36]. ANN is a universal function approximator that has the capability of handling large covariate spaces with significant level of accuracy [37]. ...
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This paper presents an experimental investigation supported by data-driven approaches concerning the influence of critical stochastic effects on the dynamic fracture toughness of glass-filled epoxy composites using a computationally efficient framework of uncertainty quantification. Three different shapes of glass particles are considered including rod, spherical and flaky shapes with coupled stochastic variations in aspect ratio, dynamic elastic modulus and volume fraction. An artificial neural network based surrogate assisted Monte Carlo simulation is carried out here in conjunction with advanced experimental techniques like digital image correlation and scanning electron microscopy to quantify the uncertainty and sensitivity associated with the dynamic fracture toughness of composites in terms of stress intensity factor under dynamic impact. The study reveals that the pre-crack initiation time regime shows the most prominent effect of uncertainty. Additionally, rod shape and the aspect ratio are the most sensitive filler type and input parameter respectively for characterizing dynamic fracture toughness. Here the quantitative results based on large-scale data-driven approaches convincingly demonstrate using a computational mapping between the stochastic input and output parameter spaces that the effect of uncertainty gets pronounced significantly while propagating from the compound source level to the impact responses. Such outcomes based on experimental data essentially bring us to the realization that quantification of uncertainty is of utmost importance for developing a reliable and practically relevant inclusive analysis and design framework for the dynamic fracture of particulate composites. With limited literature available on the determination of fracture toughness considering inertial effects, the present work demonstrates a novel and insightful experimental approach for uncertainty quantification and sensitivity analysis of dynamic fracture toughness of particulate polymer composites based on surrogate modeling.
... Random spatial discretization methods have been applied to study uncertainties in composite materials in the past. For example, Naskar et al. [126,127] proposed stochastic or fuzzy representative volume elements to include uncertainties in the microscale level, which were then propagated to the macroscopic level for dynamic and stability analyses. ...
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In this paper, a finite element-based framework is presented to model the probabilistic progressive failure of fiber-reinforced composite laminates with high fidelity and efficiency. The framework is based on the semidiscrete modeling approach that can be seen as a good compromise between continuum and discrete methods. The enhanced semidiscrete damage model (ESD2M) tool set comprises a smart meshing strategy with failure mode separation, a new version of the enhanced Schapery theory with a novel generalized mixed-mode law, and a novel probabilistic modeling strategy. These three joined components make the model efficient in capturing failure modes such as matrix cracks, fiber tensile failure, and delamination, as well as their interactions with high fidelity, while taking material nonuniformities into account. The model capabilities are demonstrated using single-edge notched tensile cross-ply laminates as an example. The ESD2M was not only capable of capturing the complex damage progression but also provided insights and explanations for some of the failure events observed in the laboratory. The presented framework efficiently integrates failure mode predictions with probabilistic modeling and enables Monte Carlo simulations to predict the ultimate failure strength with good accuracy, as well as its scatter.
... In this context, it is essential to conduct uncertainty quantification, sensitivity analysis, and stochastic modeling to demonstrate the effect of input parameters on output results to reduce the possibility of unexpected system behavior [42][43][44][45][46]. Such analyses are particularly crucial for composite structures which involve a high dimensional input parameter space and there exists a considerable degree of manufacturing complexity [47][48][49][50][51]. Vu-Bac et al. [52] performed a sensitivity analysis (SA) based on the stochastic framework for clay/epoxy nanocomposite to demonstrate the most influencing input parameters on Young's modulus of nanocomposites. ...
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In the present study, the progressive failure on MWCNT reinforced 5-Harness satin fabric composite materials is analysed using finite element (FE) analysis for Hashin and Puck failure criteria and degradation models. The progressive failure analysis of laminated composites is carried out on open-hole tensile (OHT) and short beam shear test (SBST) specimens for different volume percentages of MWCNT as reinforcements. The inter-ply delamination in CNT reinforced laminated composites is demonstrated through cohesive zone modeling. The load–displacement responses obtained from FE analyses are with a reasonable agreement when compared with available experimental data in the literature. Further, the effect of MWCNTs are demonstrated on fiber fracture and inter-fiber crack in longitudinal and transverse directions, and on matrix failure using sub-modeling of mesoscopic representative volume cell. The damage propagation was retarded due to the addition of CNT as reinforcement up to a volume percentage of 2.0%. FE simulations for sub-modeling confirmed that the presence of MWCNTs in woven composites decreased the percentages of damaged regions especially fiber, matrix, and shear damages to yarns. The flexural strength degradation of SBST samples was observed mainly due to delaminations between layers. Sensitivity analysis and uncertainty quantification have been performed for the influencing input parameters used in FE simulations on the critical output parameters, especially for peak load and stiffness of the OHT laminated composite specimens.
... Carrere et al. [16] proposed a method to consider the influence of uncertain data in structural calculations, to achieve this goal, they proposed a surface Method (RSM), which approximates the response as a function of uncertain data. Naskar et al. [17] developed a novel approach of stochastic volume element (SVE) to consider the spatially varying randomly inhomogeneous form of uncertainty in the context of two dimensional plate-like structures, and they presented a bottom-up micromechanical probabilistic analysis framework to quantify the effect of source-uncertainty in the dynamics and stability behavior of composite plates. The SVE can be employed to analyze, quantify, and calibrate the relationships between uncertainty sources and property outputs more accurately compared with RVE. ...
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The characterization and evaluation of uncertainties caused by the automated manufacturing procedure are essential for the early structural design and application of 3D woven composites. To account for the inherent uncertainties, numerical simulations must be integrated with statistical uncertainty quantification and propagation methods. However, in some cases, it is very challenging and computationally time consuming. In this paper, a multiscale uncertainty quantification method combining finite element analysis, wide & deep neural network and sensitivity analysis is proposed to probabilistically evaluate the tensile response of 3D angle-interlock woven composites. The required dataset for training and validating the model is created by a two-step numerical simulation. With the present model, a framework of the importance of each uncertainty in determining the macroscopic properties’ variance can be established with fewer computational resources. The results indicate that the effect of uncertainties on the material tensile response is significant and the sensitivity information can serve as a guide for reducing uncertainties at the macroscale.
... The uncertainties in hybrid composite structures can be divided into constituent level (micro scale), ply level (meso scale) and component level (macro scale). The multi-scale uncertainties are quantified using many probabilistic and non-probabilistic methodologies, such as determinate probability density function, interval number, fuzzy number, convex model, evidence theory, etc. [28,29] The uncertainties of performance functions (natural frequency, buckling load, compliance, failure probability, etc.) are quantified through multi-scale uncertainty propagation analysis based on a series of approximate models, such as Karhunen-Loève expansion method [30], polynomial chaos expansion method [31], neural network [32], Kriging model [33]. Due to the model complexity and multiple uncertainties, the uncertainty optimization design of hybrid composite structures is still a hot research issue, and many methodologies are proposed in recent years. ...
Article
A multi-objective uncertainty optimization design methodology of hybrid composite structures considering multiple-scale uncertainties is presented in this paper. The hybrid composite structures comprise of multiple materials with different types and volume ratios of matrix and fibers. The objective is to maximize the first-order natural frequency and frequency gap with the cost constraint, the micro-scale material parameters of matrix and fibers are considered as uncertain but bounded variables, and the optimization variables are stacking sequence and material patches (material selection in every patch of composite structures). Firstly, the uncertainty propagation analysis is implemented based on representative volume element method, and the macro material uncertainties are quantified based on neural network model. Furthermore, the multiple objective robust optimization design function is constructed based on the uncertainty analysis results of first-order natural frequency, frequency gap, and the total cost. An adaptive nondominated sorting genetic algorithm II (NSGA-II) method is proposed to optimize the stacking sequence and material patches simultaneously. The engineering examples of 9-layer laminated plate and conical cylindrical shell show that the proposed methodology can make full use of hybrid composite structures to improve the vibration characteristics while maintaining the low material cost.
... These analyses are often run in tandem, and assist modellers to simplify their assumptions: for instance, one should pay greater attention in estimating a parameter if it is more influential and drives the output, while other parameters could be excluded in further models if they are irrelevant and their variations produce negligible effects on the outputs. Many techniques to manage uncertainty modelling have been developed, including evidence theory, fuzzy theory, and Bayesian theory [12]. In general, methods and statistical tools to study the influence of the input parameters ( 1 , … , ) on the outputs ( 1 , … , ) can follow local or global approach. ...
Article
Composite materials properties are affected by uncertainties that cannot be overlooked for accurate modelling predictions. In the present study, a novel implementation of statistical screening methods for sensitivity analysis on composites is proposed. The effect of uncertainties on the behaviour of the model is assessed rapidly and reliably. Despite their efficiency when models with several input factors are employed, screening approaches are rarely used in engineering. Two sampling strategies are explored, and the results for several case studies are shown and compared with statistical estimators from regression-based methods. It is shown that screening techniques manage to provide subsets of influential parameters for a variety of applications, including analytical and finite element models, with low computational cost.
... Abolhasani et al., (2017) first prepared graphene reinforced PVDF nanocomposite and experimentally investigated its crystallinity, polymorphism, morphology, and electrical outputs. Since 2017, the pioneering works on the emerging area of FG graphene-based composites and their structures such as beams, plates, arches, and shells are being carried out by several researchers (Naskar, 2018a;Naskar et al., 2019Naskar et al., , 2018b. For instance, Feng et al. (2017) studied the nonlinear bending behavior of a novel class of multilayered FG graphene platelets (GPLs)-based composite nanobeams with non-uniform distribution of GPLs along thickness direction. ...
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Owing to inhomogeneous strain and high surface-to-volume ratio in nanostructures, it is imperative to account for the flexoelectricity as well as surface effect while analyzing the size-dependent electromechanical responses of nano-scale piezoelectric materials. In this article, a semi-analytical ‘single-term extended Kantorovich method (EKM)’ and ‘Ritz method’ based powerful framework is developed for investigating the static and dynamic electromechanical responses of graphene reinforced piezoelectric functionally graded (FG) nanocomposite plates, respectively. The residual surface stresses, elastic and piezoelectric surface modulus, and direct flexoelectric effects are taken into account while developing the unified governing equations and boundary conditions. The modified Halpin Tsai model and rules of mixture are implemented to predict the effective bulk properties. Our results reveal that the static deflection and resonance frequency of the proposed FG nanoplates are significantly influenced due to the consideration of flexoelectricity and surface effects. While such outcomes emphasize the fact that such effects cannot be ignored, these also open up the notion of on-demand property modulation and active control. The effects are more apparent for nanoplates of lesser thickness, but they diminish as plate thickness increases, leading to the realization and quantification of a size-dependent behavior. Based on the developed unified formulation, a comprehensive numerical investigation is further carried out to characterize the electromechanical responses of nanoplates considering different critical parameters such as plate thicknesses, aspect ratios, flexoelectric coefficients, piezoelectric multiples, distribution, and weight fraction of graphene platelets along with different boundary conditions. With the recent advances in nano-scale manufacturing, the current work will provide the necessary physical insights in modeling size-dependent multifunctional systems for active control of mechanical properties and harvesting electromechanical energy.
... The elastic moduli of lattices depend on dierent geometric and material parameters, which have varying sensitivity on them. It is essential to quantify the relative sensitivities of dierent inuencing parameters [48] to develop a comprehensive understanding on the eect of residual stress in comparison to the geometric and intrinsic material parameters. This could help in better quality control during manufacturing as well as more insights for designing the lattice microstructures. ...
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Characterization of the effective elastic properties of lattice-type materials is essential for adopting such artificial microstructures in various multi-functional mechanical systems across varying length-scales with the requirement of adequate structural performances. Even though the recent advancements in manufacturing have enabled large-scale production of the complex lattice microstructures, it simultaneously brings along different aspects of manufacturing irregularity into the system. One of the most prevailing such effects is the presence of intrinsic residual stresses, which can significantly influence the effective elastic properties. Here we have proposed closed-form analytical expressions for the effective elastic moduli of lattice materials considering the influence of residual stresses. Besides characterization of the effect of manufacturing irregularities, the presence of such prestress could be viewed from a different perspective. From the materials innovation viewpoint, this essentially expands the design space for property modulation significantly. The proposed analytical framework is directly useful for both property characterization and materials development aspects. The numerical results reveal that the presence of residual stresses, along with the compound effect of other influencing factors, could influence the effective elastic moduli of lattices significantly, leading to the realization of its importance and prospective exploitation of the expanded design space for inclusive materials innovation.