Asymptotic Modeling of Nonlinear Bending and Buckling Behavior of Carbon Nanotubes

The present work investigates the nonlinear bending and buckling behavior of carbon nanotubes (CNTs) using variational asymptotic method. Considering a CNT as a slender beam structure, an asymptotically-correct nonlinear continuum beam model is presented. Through the resulting nonlinear moment-curvature relationship, the model captures the phenomenon of ovalization of the cross sections and local buckling of the CNT, which arises due to their geometrical nature. Further studies are performed in order to explore the effect of CNT wall thickness on the nonlinear bending behavior of the CNT structure. It is shown that the continuum modeling approach can capture the ovalization and further localization of the CNT deformation under bending. The study aims to provide a reduced-order modeling framework analyzing the inherent nonlinearities associated with the geometrical nature of CNTs

Continuum modeling of nonlinear buckling behavior of CNT using variational asymptotic method and nonlinear FEA

Carbon nanotubes (CNTs) exhibit a unique buckling behavior due to their slender tubular geometry and thin-walled circular cross section. This study aims to analyze effect of nonlinear cross-sectional deformation on buckling of CNTs. To accomplish this, CNTs are modeled as beam structures, and the analysis is conducted using the Variational Asymptotic Method (VAM) and a geometrically exact beam theory, as well as nonlinear finite element analysis (FEA). The study considers various loading cases, including pure axial compression and combined loading scenarios, such as bending-axial compression and torsion-axial compression. The results of the study indicate that inclusion of cross-sectional deformation-induced nonlinearity reduces the critical buckling load of CNTs. The reduction is 2–5% for pure axial compression and 10–40% for combined loading cases. The results are validated against existing literature and commercial finite element software, ABAQUS®. Additionally, parametric studies with different slenderness and radius-to-thickness ratios were carried out to further understand the impact of these parameters on buckling of CNTs. Finally, the study presents 3D deformed shapes of CNTs during buckling by combining the results of the 1D analysis and the 2D cross section analysis. The findings show that nonlinearity associated with radius-to-thickness ratio has a significant impact on the cross-sectional ovalisation of CNTs and is critical in evaluating their buckling behavior. This aspect of nonlinearity is often overlooked in continuum modeling methods of CNTs, making this study an important contribution to the field

Machine learning assisted coupled frequency analysis of skewed multi-phase magnetoelectric composite plates with temperature and moisture dependent properties

In this article, the application of an artificial neural network (ANN)-based machine learning (ML) strategy to predict the coupled frequency of geometrically skewed multiphase magnetoelectric (MME) composite plate exposed to hygrothermal environment is presented. The ANN model is trained using a dataset comprising more than one million simulations conducted using an in-house developed finite element formulation. The underlying multiphysics governing equations are derived using Hamilton’s principle and higher-order shear deformation theory (HSDT). The influence of the hygrothermal environment on the elastic stiffness of MME composites is defined by the empirical constants in the constitutive relations. Four prominent combinations of the empirical constants leading to different elastic stiffness relations have been considered in this study. Alongside, the influence of geometrical skewness on the coupled fundamental frequency is also assessed. For the training of the ANN model, the Levenberg–Marquardt optimization algorithm with 30 neurons along with a tangent sigmoid activation function is used. The trained ANN model is tested on an unseen dataset, different from the training data, and it is shown to accurately predict the natural frequency of MME plate with a maximum error of 2.3%. Further, excluding the training time and considering the computational time alone, the ANN model is found to be 6.3 times faster than the FE simulations. It is anticipated that such ML-based reduced order models can be effective in the design process, especially in complex multiphysics problems, such as the one considered in the work, involving a multitude of geometric, loading and material parameters

Interface engineering of carbon fiber composites using CNT: A review

This paper aims to explore the potential of carbon nanotubes (CNTs) in enhancing the structural capability and multifunctionality of carbon fiber composites in aerospace applications, primarily by focusing on interfacial applications. The conventional method of dispersing CNTs in a matrix is not fully efficient in exploiting the mechanical and multifunctional performance of CNTs. Hence, the use of CNTs at the interface or as a coating on the surface of carbon fibers has been suggested as a means of achieving multifunctionality, in addition to enhanced mechanical performance. The paper presents an overview of the various processes for growing CNTs on carbon fiber surfaces and examines the effects of CNT geometry and growth parameters on the properties of grafted fibers and their composites. Furthermore, it discusses the potential improvements in thermal and electrical conductivity achievable by incorporating CNTs at the interface, as well as the benefits of using CNTs as a sizing layer for carbon fibers, including enhanced fracture toughness and resistance to delamination. Highlights: Comprehensive study of interface engineering in carbon fibers and Carbon Fibre Reinforced Plastic (CFRPs) using carbon nanotubes (CNTs). Improved transverse mechanical properties and overall thermal and electrical properties. Multifunctional applications possible with the use of CNT. Both experimental and numerical studies reviewed

Influence of fibre cross-section profile on the multi-physical properties of uni-directional composites

The present work comprehensively examines the influence of fibre-matrix interface perimeter on the multi-physical properties of uni-directional composite materials. Three-dimensional microstructures (containing fibres of triangular, elliptical, rectangular, C-shape and two-lobe cross-section shape) are analysed to evaluate effective thermal conduction, thermo-elastic and piezo-electric properties. Each of these properties is normalised with the respective property of RVE with circular fibre cross-section; These normalised properties are, objectively, compared with the normalised fibre cross-section perimeter (shape factor). For all the considered properties and fibre cross-sectional shapes, a novel observation is that the property experiences a drop (or rise) in the initial range of the shape factor but rises (or drops) monotonically afterwards. This is in contrast with the existing literature observations, where properties are understood to have only a monotonic increase/decrease with the shape factor. Further, it is observed that the magnitude of the initial drop (or rise) is sensitive to the fibre volume fraction and the fibre-matrix property contrast. In accordance with the literature, a strong correlation is observed among the variation of in-plane shear moduli, transverse thermal conduction and transverse dielectric constants

A computationally efficient approach for generating RVEs of various inclusion/fiber shapes

A computationally efficient method for generating virtual periodic representative volume element (RVE), capable of handling arbitrary inclusion shapes, is developed. A universal collision/overlap detection and repair method is proposed, where each inclusion shape is represented as a union of n-Spheres (UnS). A constrained optimization problem is formulated and solved to remove inclusion overlaps; a closed-form solution is derived for calculating the degree of inclusions overlap and its gradient vector with respect to inclusion position. RVE generation is illustrated with circular, spherical, four non-circular and four non-spherical inclusion shapes. Computational efficiency is demonstrated using an elaborate RVE generation time study. The generated RVEs are evaluated using various statistical metrics; results confirm the random distribution of inclusions. Effective properties of RVEs, representing unidirectional composites, are determined using homogenization with various fibre cross-section shapes; obtained mechanical properties have shown transverse isotropy

Development and mechanical characterization of cenosphere-reinforced CFRP and natural rubber core sandwich composite

Driven by the growing concern for environmental sustainability, there is an increasing need to explore innovative approaches for repurposing industrial waste materials. This study focuses on investigating the potential uses and challenges associated with cenosphere, a waste product derived from coal combustion in thermal power plants. Typically regarded as waste, cenosphere offers an opportunity to contribute to sustainability efforts. The objective of this research is to evaluate the influence of cenosphere, a ceramic-rich industrial waste, on the mechanical properties of woven CFRP-Rubber-CFRP (Carbon fibre-reinforced polymers) sandwich composites. The composite specimens were fabricated using the conventional hand lay-up technique, incorporating different weight percentages (5, 10, 15, and 20 wt.%) of cenosphere as a particulate filler. Tensile, flexural, and impact testing were conducted according to ASTM standards to assess the impact of the filler content on the mechanical properties. The results demonstrate that the inclusion of approximately 15% by weight of discarded cenosphere significantly enhances the tensile strength, flexural strength, interlaminar shear strength (ILSS), and impact strength of the sandwich composites, yielding improvements of approximately 1.6, 1.56, 2.06, and 1.85 times, respectively, compared to unfilled composites. Microscopic analysis of the composites reveals a well-dispersed cenosphere distribution within the matrix, contributing to the notable enhancement in overall strength characteristics

Effect of damage evolution on the auxetic behavior of 2D and 3D re-entrant type geometries

In this work, a mathematical formulation based on variational asymptotic method (VAM) has been proposed to determine the effect of damage on the auxetic properties of two-dimensional (2D) and three-dimensional (3D) re-entrant geometries. The influence of damage progression on the auxetic behavior was captured using a geometrically exact one-dimensional beam theory and an isotropic damage law, implemented in a nonlinear finite element framework. The effect of material degradation on the macroscale effective elastic properties such as the elastic modulus and Poisson’s ratio for the two-dimensional and three-dimensional re-entrant auxetic geometries was quantified. The mechanical behavior as predicted by the in-house Python-based implementation of the proposed VAM-based formulation is verified with the results from the commercial finite element solver Abaqus, wherein the user material subroutine was used to capture damage evolution. The numerical examples presented in this paper reveal that the macroscale auxetic behavior of the geometries was affected significantly by damage progression. The results of this research will provide insights into the design and analysis of auxetic materials for applications that warrant consideration of damage evolution

Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials

Classical approaches to enhance auxeticity quite often involve exploring or designing newer architectures. In this work, simple geometrical features at the member level are engineered to exploit non-classical nonlinearities and improve the auxetic behaviour. The structural elements of the auxetic unit cell are here represented by thin strip-like beams, or thin-walled tubular beams. The resulting nonlinear stiffness enhances the auxeticity of the lattices, especially under large deformations. To quantify the influence of the proposed structural features on the resulting Poisson's ratio, we use here variational asymptotic method (VAM) and geometrically exact beam theory. The numerical examples reveal that 2D re-entrant type micro-structures made of thin strips exhibit an improvement in terms of auxetic behaviour under compression. For the auxetic unit cell with thin circular tubes as members, Brazier's effect associated with cross-sectional ovalisation improves the auxetic behaviour under tension; the enhancement is even more significant for the 3D re-entrant geometry. Thin strip-based auxetic unit cells were additively manufactured and tested under compression to verify the numerical observations. The experimentally measured values of the negative Poisson's ratio are in close agreement with the numerical results, revealing a 66% increase due to the nonlinearity. Simulation results showcase these alternative approaches to improve the auxetic behaviour through simple geometric engineering of the lattice ribs

Computationally Efficient yet Accurate Analysis of Composite Plate

Many primarily loaded aircraft structure such as skin panels, have the form factor of plates or shells. The Variational Asymptotic Method (VAM) is used to systematically reduce the dimensionality of such structures by taking advantage of the smallness of their thickness vis-a-vis their other dimensions. VAM systematically reduces the 3D elasticity problem into a linear 1-D through-the-thickness analysis and a geometrically nonlinear 2-D plate analysis. The reduced order 2-D model, which is transformed into Reissner-like model, is used to predict 3-D displacement, 3-D stress and 3-D strain. The significant feature of VAM is that it does not use any ad-hoc assumptions on the displacement and stress fields in order to derive the reduced model. Present paper deals with analysis of a composite plate under bending and shear using VAM. The 3-D results recovered from VAM (1-D+2-D) are compared with that obtained from commercial 3-D finite element analysis. A comparative study is carried out to validate the plate results. Acceptable engineering accuracy of the present approach amidst major savings in computational resources is demonstrated with supporting data for both accuracy and efficiency