Showing papers on "Representative elementary volume published in 2021"

Higher order formulations for doubly-curved shell structures with a honeycomb core

Abstract: Anisotropic doubly-curved shells reinforced with a honeycomb core are innovative structures for applications in civil, biomedical, and aerospace engineering. In this context, the homogenization technique represents one of the simplest way for analyzing such complex structures. A proper formulation must be capable to give accurate results for any cell configuration and/or curved shape. In the present work an innovative model is proposed, based on an Equivalent Single Layer (ESL) approach and higher order theories, for an accurate estimation of the vibrational response of plates, panels and shells, whose results are compared with predictions from a classical Finite Element Method (FEM). The work starts with a comparative study performed on aluminum sandwich plates with hexagonal, rectangular and re-entrant cells. Then, a sensitivity analysis evaluates the dynamic response of single- and doubly-curved panels with different cell typologies. The fundamental equations are tackled numerically by resorting to the 2D Generalized Differential Quadrature (GDQ) method. The influence of the kinematic assumptions throughout the thickness on the dynamic response of shells is investigated, accounting for different Representative Volume Element (RVE) deformation effects within the homogenized model. In all the analyses, cell units are analyzed by means of different geometric angles, thin and thick cores, as well as classic and double thickness vertical walls or commercial honeycomb cores.

A review of the FE2 method for composites

Abstract: Composite materials and structures are inherently inhomogeneous and anisotropic across multiple scales. Multiscale modelling offers opportunities to understand the coupling of material behaviour and characteristics from the micro- to meso- and macro-scales, critical to the optimal design of composite structures for lightweighting and mechanical performance. FE2 is an increasingly popular class of multiscale methods because of its versatility to model heterogeneous material behaviour across multiple scales. In classical FE2 analysis, two finite elements (FE) calculations are carried out in a nested manner, one at the macroscale and the other at the microscale. Unlike conventional analysis, the macroscale FE analysis does not require homogenized constitutive properties because these are derived from the microscale FE simulations at the representative volume element (RVE) level. This has exciting significance for composite mechanics because properties characterized and defined at the microscale can be directly transferable to higher scales and validated with experiments. For example, failure criteria for composites need only be formulated at the microscale level of fibers and matrix. However, FE2 analysis is computationally expensive and the generally more complex classical nested implementation of FE2 is disadvantageous. This paper presents a review of the FE2 method to model various phenomena in the mechanics of composite materials and discusses various implementations. Recently, the Direct FE2 method, a variant of the FE2 method, has been shown to be particularly easy to implement in commercial FE codes, which also means that it has the additional advantage of ready access to inbuilt constitutive models library and other advanced features of the commercial code. We conclude with future directions for multiscale modelling of composites using FE2.

Experimental and computational analysis of structure-property relationship in carbon fiber reinforced polymer composites fabricated by selective laser sintering

Abstract: A fundamental understanding of structure-property relationship of carbon fiber reinforced polymer (CFRP) composites fabricated by selective laser sintering (SLS) is essential to provide guidance to improve the mechanical properties in this promising additive manufacturing process. In the present study, we propose a new computational framework to evaluate the mechanical behavior of SLSed CFRP based on the representative volume element (RVE) model. Firstly, a new voxel-based fiber packing algorithm is proposed with the three-dimensional fiber orientation tensor to describe the fiber distribution. The porosity generated in the manufacturing process is also considered by adding spherical voids in the matrix region. In order to remove the artificial stress concentration induced by the voxel-based algorithm, a python script is developed to regenerate the geometries of different phases with conforming mesh. Meanwhile, the constitutive models of different phases in SLSed CFRP, i.e., matrix, fiber and interface, are established according to the material characteristics. Next, the proposed computational framework of SLSed CFRP is validated by the X-ray computed tomography (XCT) measurements and tensile tests of a representative SLSed carbon fiber/polyamide 12 (CF/PA12) composite. The effects of fiber volume fraction and fiber orientation distribution on the mechanical behavior of SLSed CF/PA12 composite are further quantitatively explored and ranked with regards to their influence on stiffness and failure strength.

Numerical modelling of the elastic properties of 3D-printed specimens of thermoplastic matrix reinforced with continuous fibres

Abstract: Numerical modelling of 3D-printed Fused Filament Fabrication (FFF) specimens with thermoplastic matrices reinforced with continuous fibres is still in its infancy. The existing numerical work is mostly related to the adhesion between printed filaments and not to the mechanical properties. However, the latter are one of the most important parameters that define the structural behaviour of the material. A numerical three-step multi-scale model is introduced in the present study, concentrating on the fundamental aspect of the elastic properties. The most encountered reinforced Nylon FFF structures with continuous fibres of glass, carbon and, Kevlar, are examined. The concept of Representative Volume Element (RVE) is utilized for the combination of matrix and fibres at the micro-scale and the addition of voids at the meso-scale. Finally, at the macro-scale, tension simulations are performed for specimens with various lay-ups. The results of the numerical model are validated using analytical models and experimental data. A new analytical micro-mechanical model is developed as an alternative to the more cumbersome Mori–Tanaka model. A series of experimental testing is performed for Kevlar-reinforced Nylon specimens to accompany the limited existing data and aid the validation process. The comparison reveals a good correlation with the analytical models for the micro- and meso-scale and to the experimental data for the macro-scale, leading to a robust conclusion for its validity and efficiency.

Multi-scale finite element analysis of effective elastic property of sisal fiber-reinforced polystyrene composites

Abstract: In recent years, natural fiber composites have attracted attention as a potential structural material. This study evaluates the effective elastic properties of sisal fiber-reinforced polystyrene co...

Percolation mechanism and effective conductivity of mechanically deformed 3-dimensional composite networks: Computational modeling and experimental verification

Abstract: In this work, the structural evolution of conductive polymer composites (CPCs) in response to mechanical deformation (uniaxial and biaxial compressive and tensile strains) is theoretically modeled and experimentally verified. The structural responses in mechanically deformed CPCs were simulated by incorporating the corresponding topological changes in representative volume element (RVE) and embedded filler networks. The percolating filler networks were then modeled as an equivalent electrical circuit consisting of tunneling and intrinsic resistances to examine the effect of deformation on the percolation threshold and the effective electrical conductivity. The results revealed that the filler alignment caused by strain changed both the vertical and lateral percolation thresholds, albeit with different trends. With an increase of uniaxial tensile (or equivalently, biaxial compressive) strain, applied on the vertical direction, the vertical percolation threshold initially reached a minimum value before rising, while the lateral percolation threshold monotonically increased. On the other hand, following incremental uniaxial compression (or equivalently, biaxial tension), the lateral percolation threshold reached a minimum value before increasing, while the vertical percolation threshold monotonically increased. The same relationship was observed in CPCs containing 1D fillers with different aspect ratios. The validity of the theoretical models was verified by comparing the predicted electrical conductivity values with the experimentally observed data obtained from polypropylene - multiwalled carbon nanotube nanocomposites.

Plastic Behavior of Ferrite–Pearlite, Ferrite–Bainite and Ferrite–Martensite Steels: Experiments and Micromechanical Modelling

Abstract: In this work, low carbon low alloy steel specimens were subjected to suitable heat treatment schedules to develop ferrite–pearlite (FP), ferrite–bainite (FB) and ferrite–martensite (FM) microstructures with nearly equal volume fraction of hard second phase or phase mixture. The role of pearlite, bainite and martensite on mechanical properties and flow behaviour were investigated through experiments and finite element simulations considering representative volume elements (RVE) based on real microstructures. For micromechanical simulation, dislocation based model was implemented to formulate the flow behaviour of individual phases. The optimum RVE size was identified for accurate estimation of stress–strain characteristics of all three duplex microstructures. Both experimental and simulation results established that FM structure exhibited superior strength and FP structure demonstrated better elongation while FB structure yielded moderate strength and ductility. The von Mises stress and plastic strain distribution of the individual phase was predicted at different stages of deformation and subsequent statistical analyses indicated that hard phases experienced maximum stress whereas, maximum straining occurred in soft ferrite phase for all three structures. Micromechanical simulation further revealed that strain accumulation occurred at the F–P and F–B interfaces while the same was observed within the martensite particles apart from the F–M interfaces for FM. These observations were further substantiated through the identification of void and crack initiation sites via subsurface examinations of failed tensile specimens.

Numerical evaluation of the representative volume element for random composites

Abstract: The Representative Volume Element (RVE) plays a central role in the homogenization of random heterogeneous microstructures, especially for composite and porous materials, with a view to predicting their effective properties. A quantitative evaluation of its size is proposed in this work in linear elasticity and linear thermal conductivity of random heterogeneous materials. A RVE can be associated with different physical and statistical properties of microstructures. The methodology is applied to specific two–phase microstructure–based random sets. Statistical parameters are introduced to study the variation in the RVE size versus volume fractions of components and the contrast in their properties. The key notion of the integral range is introduced to determine these variations. For a given desired precision, we can provide a minimal volume size for the computation of effective mechanical and thermal properties. Numerical simulations are performed to demonstrate that a volume exists which is statistically representative of random microstructures. This finding is an important component for homogenization–based multiscale modeling of materials.

Parameter analysis of damaged region for laminates with matrix defects

Abstract: Considering the influence of bridge fibers, a representative volume element (RVE) with damaged regions of vanishing thickness is developed to study for estimation of laminates with transverse matri...

Investigation of the effect of raster angle, build orientation, and infill density on the elastic response of 3D printed parts using finite element microstructural modeling and homogenization techniques

Abstract: Although the literature is abundant with the experimental methods to characterize mechanical behavior of parts made by fused filament fabrication 3D printing, less attention has been paid in using computational models to predict the mechanical properties of these parts. In the present paper, a numerical homogenization technique is developed to predict the effect of printing process parameters on the elastic response of 3D printed parts with cellular lattice structures. The development of finite element computational models of printed parts is based on a multi scale approach. Initially, at the micro scale level, the analysis of micro-mechanical models of a representative volume element is used to calculate the effective orthotropic properties. The finite element models include different infill densities and building/raster orientation maintaining the bonded region between the adjacent fibers and layers. The elastic constants obtained by this method are then used as an input for the creation of macro scale finite element models enabling the simulation of the mechanical response of printed samples subjected to the bending, shear, and tensile loads. Finally, the results obtained by the homogenization technique are validated against more realistic finite element explicit microstructural models and experimental measurements. The results show that, providing an accurate characterization of the properties to be fed into the macro scale model, the use of the homogenization technique is a reliable tool to predict the elastic response of 3D printed parts. The outlined approach provides faster iterative design of 3D printed parts, contributing to reducing the number of experimental replicates and fabrication costs.

Verification of asymptotic homogenization method developed for periodic architected materials in strain gradient continuum.

Abstract: Strain gradient theory is an accurate model for capturing size effects and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of such theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS.

Longitudinal compression failure of 3D printed continuous carbon fiber reinforced composites: An experimental and computational study

Abstract: Fused filament fabrication (FFF) with continuous carbon fiber filaments has proven to be a promising manufacturing technique in engineering applications. To provide guidance in the design of 3D printed carbon fiber reinforced polymer (CFPR) components, the longitudinal compression failure of continuous CFPR composites using the FFF technique is investigated systematically. First, longitudinal compression tests are performed for 3D printed continuous CFRP composites with and without designed waved filaments. The degradation of the failure strength is remarkable when the waved filaments are introduced. Nevertheless, further degradation is limited when more waved filaments are adopted. Next, the fracture morphologies are analyzed, and in-plane and out-of-plane kink-bands are observed in the microscopic images. For the specimens with waved filaments, fracture occurs at the cross-section with the contact region of the waved and regular filaments, as well as the cross-section with the maximum misalignment angle. Correspondingly, a computational framework for 3D printed continuous CFPR composites is established to explore the longitudinal compression failure mechanisms. The meso-scale computational models are reconstructed according to the geometric features of the deposited continuous CFRP filaments and the actual void volume fraction. The elastic properties of the filament are calculated by a micro-scale representative volume element (RVE) model, which is based on the fiber random distribution algorithm. The plastic deformation and failure is described by a filament constitutive model which is established by the Liu-Huang-Stout yield criterion and a simplified Tsai-Wu failure criterion. The experimental validation demonstrates the feasibility of the computational models to predict the stress-strain curves of 3D printed materials, and also capture the realistic longitudinal compression failure behavior.