scholarly journals Effective properties of hierarchical fiber-reinforced composites via a three-scale asymptotic homogenization approach

2019 ◽  
Vol 24 (11) ◽  
pp. 3554-3574 ◽  
Author(s):  
Ariel Ramírez-Torres ◽  
Raimondo Penta ◽  
Reinaldo Rodríguez-Ramos ◽  
Alfio Grillo
Keyword(s):  
Composite Structures ◽  
Effective Properties ◽  
Elastic Solid ◽  
Asymptotic Homogenization ◽  
Linear Elastic ◽  
Homogenization Technique ◽  
Effective Coefficients ◽  
Out Of Plane ◽  
Mineralized Tissues ◽  
Homogenization Approach

The study of the properties of multiscale composites is of great interest in engineering and biology. Particularly, hierarchical composite structures can be found in nature and in engineering. During the past decades, the multiscale asymptotic homogenization technique has shown its potential in the description of such composites by taking advantage of their characteristics at the smaller scales, ciphered in the so-called effective coefficients. Here, we extend previous works by studying the in-plane and out-of-plane effective properties of hierarchical linear elastic solid composites via a three-scale asymptotic homogenization technique. In particular, the approach is adjusted for a multiscale composite with a square-symmetric arrangement of uniaxially aligned cylindrical fibers, and the formulae for computing its effective properties are provided. Finally, we show the potential of the proposed asymptotic homogenization procedure by modeling the effective properties of musculoskeletal mineralized tissues, and we compare the results with theoretical and experimental data for bone and tendon tissues.

scholarly journals Effective Complex Properties for Three-Phase Elastic Fiber-Reinforced Composites with Different Unit Cells

Technologies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 12
Author(s):  
Federico J. Sabina ◽  
Yoanh Espinosa-Almeyda ◽  
Raúl Guinovart-Díaz ◽  
Reinaldo Rodríguez-Ramos ◽  
Héctor Camacho-Montes
Keyword(s):  
Effective Properties ◽  
Elastic Fiber ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Effective Coefficients ◽  
Three Phase ◽  
Out Of Plane ◽  
Local Problems ◽  
Unit Cells

The development of micromechanical models to predict the effective properties of multiphase composites is important for the design and optimization of new materials, as well as to improve our understanding about the structure–properties relationship. In this work, the two-scale asymptotic homogenization method (AHM) is implemented to calculate the out-of-plane effective complex-value properties of periodic three-phase elastic fiber-reinforced composites (FRCs) with parallelogram unit cells. Matrix and inclusions materials have complex-valued properties. Closed analytical expressions for the local problems and the out-of-plane shear effective coefficients are given. The solution of the homogenized local problems is found using potential theory. Numerical results are reported and comparisons with data reported in the literature are shown. Good agreements are obtained. In addition, the effects of fiber volume fractions and spatial fiber distribution on the complex effective elastic properties are analyzed. An analysis of the shear effective properties enhancement is also studied for three-phase FRCs.

scholarly journals Asymptotic homogenization of metamaterials elastic plates

2021 ◽  
Vol 2015 (1) ◽  
pp. 012038
Author(s):  
David Faraci ◽  
Claudia Comi
Keyword(s):  
Shear Deformation ◽  
Effective Properties ◽  
Numerical Analyses ◽  
Thin Plates ◽  
Elastic Plates ◽  
Asymptotic Homogenization ◽  
Homogenization Process ◽  
Homogenization Technique

Abstract The asymptotic homogenization technique is applied to evaluate the effective properties of thin plates with periodic heterogeneity. The effect of shear deformation in the homogenization process is evidenced and the role of cell slenderness, besides that of the plate, is clarified by several numerical analyses.

Asymptotic Homogenization of Composite Materials and Structures

2009 ◽  
Vol 62 (3) ◽  
Author(s):  
Alexander L. Kalamkarov ◽  
Igor V. Andrianov ◽  
Vladyslav V. Danishevs’kyy
Keyword(s):  
Composite Materials ◽  
Composite Structures ◽  
Composite Shell ◽  
Effective Properties ◽  
Sandwich Composite ◽  
Asymptotic Homogenization ◽  
Random Composites ◽  
Analytical Formulas ◽  
Honeycomb Filler ◽  
Thin Walled

The present paper provides details on the new trends in application of asymptotic homogenization techniques to the analysis of composite materials and thin-walled composite structures and their effective properties. The problems under consideration are important from both fundamental and applied points of view. We review a state-of-the-art in asymptotic homogenization of composites by presenting the variety of existing methods, by pointing out their advantages and shortcomings, and by discussing their applications. In addition to the review of existing results, some new original approaches are also introduced. In particular, we analyze a possibility of analytical solution of the unit cell problems obtained as a result of the homogenization procedure. Asymptotic homogenization of 3D thin-walled composite reinforced structures is considered, and the general homogenization model for a composite shell is introduced. In particular, analytical formulas for the effective stiffness moduli of wafer-reinforced shell and sandwich composite shell with a honeycomb filler are presented. We also consider random composites; use of two-point Padé approximants and asymptotically equivalent functions; correlation between conductivity and elastic properties of composites; and strength, damage, and boundary effects in composites. This article is based on a review of 205 references.

Analysis of High Velocity Impact on Composite Structures

2014 ◽  
Vol 617 ◽  
pp. 104-109 ◽  
Author(s):  
Milan Žmindák ◽  
Zoran Pelagić ◽  
Maroš Bvoc
Keyword(s):  
Carbon Fibers ◽  
Composite Structures ◽  
Impact Resistance ◽  
Leading Edge ◽  
Layered Composite ◽  
Bird Strike ◽  
Out Of Plane ◽  
The Matrix ◽  
Composite Wing ◽  
Considerable Damage

In the recent years a big focus is subjected to the response of structures subjected to out-of-plane loading such as blasts, impact, etc. not only to homogenous materials, but also to heterogeneous materials, such as composites. Such form of loading can cause considerable damage to the structure. In the case of layered composite materials the damage can have several forms, starting from damage in layers up to delamination and full damage of the construction. This paper describes the investigation of shockwave propagation in composite structures caused by impact loading. The composite consists of carbon fibers in a polymer matrix, in which the fibers are much stiffer then the matrix. Finite element simulations were carried out for a “bird” strike impact on a composite wing leading edge. Results show a good impact resistance and good damping abilities of shockwaves.

Crack-Path Effect on Material Toughness

1990 ◽  
Vol 57 (1) ◽  
pp. 97-103 ◽  
Author(s):  
Asher A. Rubinstein
Keyword(s):  
Crack Path ◽  
Numerical Procedure ◽  
Crack Tip ◽  
Elastic Solid ◽  
Singular Integral Equations ◽  
Length Change ◽  
Curvilinear Crack ◽  
Linear Elastic ◽  
System Of Cracks ◽  
Remote Stress

The material-toughening mechanism based on the crack-path deflection is studied. This investigation is based on a model which consists of a macrocrack (semi-infinite crack), with a curvilinear segment at the crack tip, situated in a brittle solid. The effect of material toughening is evaluated by comparison of the remote stress field parameters, such as the stress intensity factors (controlled by a loading on a macroscale), to effective values of these parameters acting in the vicinity of a crack tip (microscale). The effects of the curvilinear crack path are separated into three groups: crack-tip direction, crack-tip geometry pattern-shielding, and crack-path length change. These effects are analyzed by investigation of selected curvilinear crack patterns such as a macrocrack with simple crack-tip kink in the form of a circular arc and a macrocrack with a segment at the crack tip in the form of a sinusoidal wave. In conjunction with this investigation, a numerical procedure has been developed for the analysis of curvilinear cracks (or a system of cracks) in a two-dimensional linear elastic solid. The formulation is based on the solution of a system of singular integral equations. This numerical scheme was applied to the cases of finite and semi-infinite cracks.

Analytical and Numerical Predictions of Thermoelastic Properties of Carbon Single-Walled Nanotubes

Aerospace ◽  
2005 ◽  
Author(s):  
Vinod P. Veedu ◽  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Graphene Sheet ◽  
Effective Properties ◽  
Constitutive Models ◽  
Thermoelastic Properties ◽  
Asymptotic Homogenization ◽  
Element Analysis ◽  
Single Walled Nanotubes ◽  
Numerical Predictions

The objective of this paper is to develop constitutive models to predict thermoelastic properties of carbon single-walled nanotubes using analytical, asymptotic homogenization, and numerical, finite element analysis, methods. In our approach, the graphene sheet is considered as a non-homogeneous network shell layer which has zero material properties in the regions of perforation and whose effective properties are estimated from the solution of the appropriate local problems set on the unit cell of the layer. Our goal is to derive working formulas for the entire complex of the thermoelastic properties of the periodic network. The effective thermoelastic properties of carbon nanotubes were predicted using asymptotic homogenization method. Moreover, in order to verify the results of analytical predictions, a detailed finite element analysis is followed to investigate the thermoelastic response of the unit cells and the entire graphene sheet network.

scholarly journals Influence of Gradual Damage on the Structural Dynamic Behaviour of Composite Rotors: Experimental Investigations

Materials ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 2421 ◽  
Author(s):  
Angelos Filippatos ◽  
Maik Gude
Keyword(s):  
Mechanical Properties ◽  
Composite Structures ◽  
Dynamic Behaviour ◽  
Experimental Investigations ◽  
Catastrophic Failure ◽  
Structural Dynamic ◽  
Delamination Growth ◽  
Reinforced Composite ◽  
Out Of Plane ◽  
Effective Mechanical Properties

Fibre-reinforced composite structures subjected to complex loads exhibit gradual damage behaviour with the degradation of the effective mechanical properties and changes in their structural dynamic behaviour. Damage manifests itself as a spatial increase in inter-fibre failure and delamination growth, resulting in local changes in stiffness. These changes affect not only the residual strength but, more importantly, the structural dynamic behaviour. In the case of composite rotors, this can lead to catastrophic failure if an eigenfrequency coincides with the rotational speed. The description and analysis of the gradual damage behaviour of composite rotors, therefore, provide the fundamentals for a better understanding of unpredicted structural phenomena. The gradual damage behaviour of the example composite rotors and the resulting damage-dependent dynamic behaviour were experimentally investigated under propagating damage caused by a combination of out-of-plane and in-plane loads. A novel observation is the finding that a monotonic increase in damage results in a non-monotonic frequency shift of a significant number of eigenfrequencies.

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