The role of multi-scale finite element methods in analysis and design of advanced mechanical and aerospace structures

The fast rise of nanotechnology and the corresponding discovery of novel nanomaterials and nanostructures have attracted the attention of the research, scientific, as well as business community for finding possible effective solutions in challenging problems of human everyday life. The key point of this attention is based mainly on the combination of superior mechanical, electrical, thermal and generally physical performance of nanostructures, as well as their light weight. In our days, it is well accepted that computational techniques, and specifically multi-scale finite element methods, have a leading role in the analysis and design process. Its multi physics nature makes it an ideal candidate for an efficient design tool of advanced mechanical and aerospace structures. © 2019 TJPRC Pvt. Ltd. All rights reserved

Vibration analysis of carbon fiber-graphene-reinforced hybrid polymer composites using finite element techniques

In this study, a computational procedure for the investigation of the vibration behavior of laminated composite structures, including graphene inclusions in the matrix, is developed. Concerning the size-dependent behavior of graphene, its mechanical properties are derived using nanoscopic empiric equations. Using the appropriate Halpin-Tsai models, the equivalent elastic constants of the graphene reinforced matrix are obtained. Then, the orthotropic mechanical properties of a composite lamina of carbon fibers and hybrid matrix can be evaluated. Considering a specific stacking sequence and various geometric configurations, carbon fiber-graphene-reinforced hybrid composite plates are modeled using conventional finite element techniques. Applying simply support or clamped boundary conditions, the vibrational behavior of the composite structures are finally extracted. Specifically, the modes of vibration for every configuration are derived, as well as the effect of graphene inclusions in the natural frequencies, is calculated. The higher the volume fraction of graphene in the matrix, the higher the natural frequency for every mode. Comparisons with other methods, where it is possible, are performed for the validation of the proposed method. © 2020 by the authors

Thermomechanical response of fullerene-reinforced polymers by coupling MD and FEM

The aim of the present study is to provide a computationally efficient and reliable hybrid numerical formulation capable of characterizing the thermomechanical behavior of nanocomposites, which is based on the combination of molecular dynamics (MD) and the finite element method (FEM). A polymeric material is selected as the matrix-specifically, the poly(methyl methacrylate) (PMMA) commonly known as Plexiglas due to its expanded applications. On the other hand, the fullerene C240 is adopted as a reinforcement because of its high symmetry and suitable size. The numerical approach is performed at two scales. First, an analysis is conducted at the nanoscale by utilizing an appropriate nanocomposite unit cell containing the C240 at a high mass fraction. A MD-only method is applied to accurately capture all the internal interfacial effects and accordingly its thermoelastic response. Then, a micromechanical, temperature-dependent finite element analysis takes place using a representative volume element (RVE), which incorporates the first-stage MD output, to study nanocomposites with small mass fractions, whose atomistic-only simulation would require a substantial computational effort. To demonstrate the effectiveness of the proposed scheme, numerous numerical results are presented while the investigation is performed in a temperature range that includes the PMMA glass transition temperature, Tg. © 2020 by the authors

Mechanical Response of Hybrid Laminated Polymer Nanocomposite Structures: A Multilevel Numerical Analysis

The prediction of mechanical elastic response of laminated hybrid polymer composites with basic carbon nanostructure, that is carbon nanotubes and graphene, inclusions has gained importance in many advanced industries like aerospace and automotive. For this purpose, in the current work, a hierarchical, four-stage, multilevel framework is established, starting from the nanoscale, up to the laminated hybrid composites. The proposed methodology starts with the evaluation of the mechanical properties of carbon nanostructure inclusions, at the nanoscale, using advanced 3D spring-based finite element models. The nanoinclusions are considered to be embedded randomly in the matrix material, and the Halpin-Tsai model is used in order to compute the average properties of the hybrid matrix at the lamina micromechanics level. Then, the standard Halpin-Tsai equations are employed to establish the orthotropic elastic properties of the unidirectional carbon fiber composite at the lamina macromechanics level. Finally, the lamination theory is implemented in order to establish the macroscopic force-strain and moment-curvature relations at the laminate level. The elastic mechanical properties of specific composite configurations and their performance in different mechanical tests are evaluated using finite element analysis and are found to considerably increase with the nanomaterial volume fraction increase for values up to 0.5. Further, the hybrid composite structures with graphene inclusions demonstrate better mechanical performance as compared to the identical structures with CNT inclusions. Comparisons with theoretical or other numerical techniques, where it is possible, demonstrate the accuracy of the proposed technique.

A multi-scale method for designing hybrid fiber-reinforced composite drive shafts with carbon nanotube inclusions

In this paper, the modal and linear buckling analysis of a laminated composite drive shaft reinforced by 11 multi-walled carbon nanotubes (MWCNTs) was carried out using an analytical approach, as well as the finite element method (FEM). The theoretical model is based on classical laminated theory (CLT). The fundamental frequency and the critical buckling torque were determined for different fiber orientation angles. The Halpin–Tsai model was employed to calculate the elastic modulus of composites having randomly oriented nanotubes. The effect of various carbon nanotube (CNT) volume fractions in the epoxy resin matrix on the material properties of unidirectional composite laminas was also analyzed. The fundamental frequency and the critical buckling torque obtained by the finite element analysis and the analytical method for different fiber orientation angles were in good agreement with each other. The results were verified with data available in the open literature, where possible. For the first time in the literature, the influence of CNT fillers on various composite drive shaft design parameters such as the fundamental frequency, critical speed, and critical buckling torque of a hybrid fiber-reinforced composite drive shaft is finally predicted. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Damage characteristics in laminated composite structures subjected to low-velocity impact

Purpose: The present study deals with the numerical modeling of the low-velocity impact damage of laminated composites which have increasingly important applications in aerospace primary structures. Such damage, generated by various sources during ground handling, substantially reduces the mechanical residual performance and the safe-service life. The purpose of this paper is to present and validate a computationally efficient approach in order to explore the effect of critical parameters on the impact damage characteristics. Design/methodology/approach: Numerical modeling is considered as one of the most efficient tool as compared to the expensive and time-consuming experimental testing. In this paper, a finite element model based on explicit dynamics formulations is adopted. Hashin criterion is applied to predict the intralaminar damage initiation and evolution. The numerical analysis is performed using the ABAQUS® programme. Findings: The employed modeling approach is validated using corresponding numerical data found in the literature and the presented results show a reasonable correlation to the available literature data. It is demonstrated that the current model can be used to capture the force-time response as well as damage parameter maps showing the intralaminar damage evolution for different impact cases with respect to the physical boundary conditions and a range of impact energies. Originality/value: Low-velocity impact damage of laminated composites is still not well understood due to the complexity and non-linearity of the damage zone. The presented model is used to predict the force-time response which is considered as one of the most important parameters influencing the structural integrity. Furthermore, it is used for capturing the damage shape evolution, exhibiting a high degree of capability as a damage assessment computational tool. © 2019, Emerald Publishing Limited

Mechanical properties of hexagonal boron nitride monolayers: Finite element and analytical predictions

The mechanical response of two-dimensional nanostructures may be significantly affected by their size. In this work, a molecular structural mechanics model is developed and is implemented in order to predict the nanomechanical behavior and calculate the corresponding elastic properties of hexagonal boron nitride sheets and describe their size-dependence. The finite element approach utilizes appropriate spring-like elements for the modeling of interactions between atoms within the hexagonal boron nitride structure, the stiffness constants of which are obtained by the molecular mechanics theory. Adopting conventional finite element techniques, the global stiffness matrix of the structure of a desired sheet size can be assembled. Applying appropriate boundary conditions, the governing equilibrium static equation can be solved and the elastic mechanical properties as Young’s modulus, shear modulus, and Poisson’s ratio of the structure can be calculated. Fitting the results of the mechanical properties calculated by the finite element analysis, analytical–empirical equations are proposed for their direct prediction for an hexagonal boron nitride sheet having the size parameters of the structure as independent variables. © IMechE 2020

Combining FEM and MD to simulate C60/PA-12 nanocomposites

Purpose: The purpose of this paper is the computation of the elastic mechanical behaviour of the fullerene C60 reinforced polyamide-12 (PA-12) via a two-stage numerical technique which combines the molecular dynamics (MD) method and the finite element method (FEM). Design/methodology/approach: At the first stage, the proposed numerical scheme utilizes MD to characterize the pure PA-12 as well as a very small cubic unit cell containing a C60 molecule, centrally positioned and surrounded by PA-12 molecular chains. At the second stage, a classical continuum mechanics (CM) analysis based on the FEM is adopted to approximate the elastic mechanical performance of the nanocomposite with significantly lower C60 mass concentrations. According to the computed elastic properties arisen by the MD simulations, an equivalent solid element with the same size as the unit cell is developed. Then, a CM micromechanical representative volume element (RVE) of the C60 reinforced PA-12 is modelled via FEM. The matrix phase of the RVE is discretized by using solid finite elements which represent the PA-12 mechanical behaviour predicted by MD, while the C60 neighbouring location is meshed with the equivalent solid element. Findings: Several multiscale simulations are performed to study the effect of the nanofiller mass fraction on the mechanical properties of the C60 reinforced PA-12 composite. Comparisons with other corresponding experimental results are attempted, where possible, to test the performance of the proposed method. Originality/value: The proposed numerical scheme allows accurate representation of atomistic interfacial effects between C60 and PA-12 and simultaneously offers a significantly lower computational cost compared with the MD-only method. © 2019, Emerald Publishing Limited

Mechanical response of hybrid laminated polymer nanocomposite structures: a multilevel numerical analysis

The prediction of mechanical elastic response of laminated hybrid polymer composites with basic carbon nanostructure, that is carbon nanotubes and graphene, inclusions has gained importance in many advanced industries like aerospace and automotive. For this purpose, in the current work, a hierarchical, four-stage, multilevel framework is established, starting from the nanoscale, up to the laminated hybrid composites. The proposed methodology starts with the evaluation of the mechanical properties of carbon nanostructure inclusions, at the nanoscale, using advanced 3D spring-based finite element models. The nanoinclusions are considered to be embedded randomly in the matrix material, and the Halpin-Tsai model is used in order to compute the average properties of the hybrid matrix at the lamina micromechanics level. Then, the standard Halpin-Tsai equations are employed to establish the orthotropic elastic properties of the unidirectional carbon fiber composite at the lamina macromechanics level. Finally, the lamination theory is implemented in order to establish the macroscopic force-strain and moment-curvature relations at the laminate level. The elastic mechanical properties of specific composite configurations and their performance in different mechanical tests are evaluated using finite element analysis and are found to considerably increase with the nanomaterial volume fraction increase for values up to 0.5. Further, the hybrid composite structures with graphene inclusions demonstrate better mechanical performance as compared to the identical structures with CNT inclusions. Comparisons with theoretical or other numerical techniques, where it is possible, demonstrate the accuracy of the proposed technique