scholarly journals Semi-Analytical Method for Computing Effective Thermoelastic Properties in Fiber-Reinforced Composite Materials

2021 ◽  
Vol 11 (12) ◽  
pp. 5354
Author(s):  
Rodolfo Avellaneda ◽  
Suset Rodríguez-Alemán ◽  
José A. Otero
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Analytical Method ◽  
Effective Properties ◽  
Fibrous Composite ◽  
Transversely Isotropic ◽  
Homogenization Method ◽  
Elliptical Cross ◽  
Periodic Cell ◽  
Effective Coefficients

Effective elastic and thermal properties for isotropic or transversely isotropic thermoelastic fibrous composite materials are obtained. Fibers are distributed with the same periodicity along the two perpendicular directions to the fiber orientation. The periodic cell of the composite has a square or hexagonal distribution. Perfect contact between the fiber and the matrix is presented. The effective properties are calculated using a semi-analytical method. The semi-analytical method consists of obtaining the differential equations that describe the local problems using the Asymptotic Homogenization Method. Then, these equations are solved using the Finite Element Method. Effective elastic coefficient (C¯), effective thermal expansion coefficient (α¯) and the effective thermal conductivity (κ¯) are obtained. The numerical results are compared with the semi-analytical solution and with results reported by other authors. Additionally, the effective properties for a fiber with an elliptical cross section are calculated. Distributions of the fiber’s cross section with different orientations are also studied. A MATLAB program for computing the effective coefficients is presented.

scholarly journals Assessment of models and methods for pressurized spherical composites

2016 ◽  
Vol 23 (2) ◽  
pp. 136-147
Author(s):  
David Guinovart-Sanjuán ◽  
Raffaella Rizzoni ◽  
Reinaldo Rodríguez-Ramos ◽  
Raúl Guinovart-Díaz ◽  
Julián Bravo-Castillero ◽  
...  
Keyword(s):  
Transversely Isotropic ◽  
Homogenization Method ◽  
Heterogeneous Structure ◽  
Asymptotic Homogenization ◽  
Contact Conditions ◽  
Effective Coefficients ◽  
Asymptotic Homogenization Method ◽  
Perfect Contact ◽  
Periodic Components ◽  
Radial Axis

The elastic properties of a spherical heterogeneous structure with isotropic periodic components is analyzed and a methodology is developed using the two-scale asymptotic homogenization method (AHM) and spherical assemblage model (SAM). The effective coefficients are obtained via AHM for two different composites: (a) composite with perfect contact between two layers distributed periodically along the radial axis; and (b) considering a thin elastic interphase between the layers (intermediate layer) distributed periodically along the radial axis under perfect contact. As a result, the derived overall properties via AHM for homogeneous spherical structure have transversely isotropic behavior. Consequently, the homogenized problem is solved. Using SAM, the analytical exact solutions for appropriate boundary value problems are provided for different number of layers for the cases (a) and (b) in the spherical composite. The numerical results for the displacements, radial and circumferential stresses for both methods are compared considering a spherical composite material loaded by an inside pressure with the two cases of contact conditions between the layers (a) and (b).

scholarly journals EVALUATION OF EFFECTIVE PROPERTIES OF BASALT TEXTILE REINFORCED CERAMIC MATRIX COMPOSITES

2017 ◽  
Vol 13 ◽  
pp. 142
Author(s):  
Soňa Valentová ◽  
Vladimír Hrbek ◽  
Michal Šejnoha
Keyword(s):  
Effective Properties ◽  
Fibrous Composite ◽  
Ceramic Matrix Composite ◽  
Ceramic Matrix Composites ◽  
Ceramic Matrix ◽  
Homogenization Method ◽  
Matrix Composites ◽  
Fabric Composite ◽  
Textile Fabric

The present paper is concerned with the analysis of a ceramic matrix composite, more specifically the plain weave textile fabric composite made of basalt fibers embedded into the pyrolyzed polysiloxane matrix. Attention is paid to the determination of effective elastic properties of the yarn via homogenization based on the Mori-Tanaka averaging scheme and the 1st order numerical homogenization method adopting a suitable representative computational model. The latter approach is then employed to simulate the response of the yarn when loaded beyond the elastic limits. The required mechanical properties of individual material phases are directly measured using nanoindentation with in-build scanning probe microscopy. Applicability of the proposed computational methodology is supported by the analysis of a unidirectional fibrous composite, representing the yarn, subjected to a macroscopically uniform strain.

Interface Parameters of Composite Materials with an Elliptical Cross-Section Fiber Bundle

2013 ◽  
Vol 275-277 ◽  
pp. 1688-1692
Author(s):  
Zhi Min Xie ◽  
Dong Liang Chai ◽  
Hai Wen Du ◽  
Chang Qing Miao
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Fiber Bundle ◽  
Biaxial Tension ◽  
Pure Shear ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Plane Shear ◽  
Elliptical Cross ◽  
Interface Parameters

How to design the interfacial properties is a significant fundamental issue in the field of the composite materials, while little work was concerned with the mechanical design of the interface for the fiber reinforced polymer. In the present work, a fiber bundle embedded in the matrix was described as a transversely isotropic material. Based on the imperfect interface conditions, the interface parameters were derived to satisfy the neutral conditions for the composite materials reinforced by the elliptical cross-section fiber bundle. It is found that the interface parameter is not always associated with the applied loading in the case of the anti-plane shear. In the state of equal-biaxial tension, the normal interface parameter is merely related to the mechanical properties of components except for the shape of the fiber bundle, but independent of the loading magnitude. In the other cases of pure shear and uniaxial tension, the neutral interface does not exist except that the fiber bundle has a circular cross-section. It is also found that the interface parameters can be expressed in the forms similar to that for an isotropic inclusion by using Kolosov constant in the in-plane deformations.

scholarly journals Refinement of the Maxwell formula for a composite reinforced by circular cross-section fibres. Part II: using Padé approximants

2020 ◽  
Vol 231 (12) ◽  
pp. 5145-5157
Author(s):  
Igor I. Andrianov ◽  
Jan Awrejcewicz ◽  
Galina A. Starushenko ◽  
Vladimir A. Gabrinets
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Volume Fraction ◽  
Effective Properties ◽  
Circular Cross Section ◽  
The Novel ◽  
High Contrast ◽  
Asymptotic Results ◽  
Reinforced Composite ◽  
Coefficient Of Thermal Conductivity

Abstract The effective properties of the fiber-reinforced composite materials with fibers of circle cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For an analytical solution of the periodically repeated cell problem the Schwarz alternating process (SAP) was employed. Convergence of this method was proved by S. Mikhlin, S. Sobolev, V. Mityushev. Unfortunately, the rate of the convergence is often slow, especially for nondilute high-contrast composite materials. For improving this drawback we used Padé approximations for various forms of SAP solutions with the following additive matching of obtained expressions. As a result, the solutions in our paper are obtained in a fairly simple and convenient form. They can be used even for a volume fraction of inclusion very near the physically possible maximum value as well as for high-contrast composite constituents. The results are confirmed by comparison with known numerical and asymptotic results.

Matrix laminate composites: Realizable approximations for the effective moduli of piezoelectric dispersions

1999 ◽  
Vol 14 (1) ◽  
pp. 49-63 ◽  
Author(s):  
L. V. Gibiansky ◽  
S. Torquato
Keyword(s):  
Effective Properties ◽  
Matrix Material ◽  
Transversely Isotropic ◽  
Effective Moduli ◽  
Phase Volume ◽  
Laminate Composites ◽  
Effective Coefficients ◽  
The Matrix ◽  
Axis Of Symmetry ◽  
Free Parameters

This paper is concerned with the effective piezoelectric moduli of a special class of dispersions called matrix laminates composites that are known to possess extremal elastic and dielectric moduli. It is assumed that the matrix material is an isotropic dielectric, and the inclusions and composites are transversely isotropic piezoelectrics that share the same axis of symmetry. The exact expressions for the effective coefficients of such structures are obtained. They can be used to approximate the effective properties of any transversely isotropic dispersion. The advantages of our approximations are that they are (i) realizable, i.e., correspond to specific microstructures; (ii) analytical and easy to compute even in nondegenerate cases; (iii) valid for the entire range of phase volume fractions; and (iv) characterized by two free parameters that allow one to “tune” the approximation and describe a variety of microstructures. The new approximations are compared with known ones.

Computer-aided Analysis of Micromechanics and Damage of Composite Materials Based on Multiscale Homogenization Method

2013 ◽  
Vol 1535 ◽  
Author(s):  
Yuriy I. Dimitrienko ◽  
Alexandr P. Sokolov ◽  
Yulia V. Shpakova
Keyword(s):  
Finite Element ◽  
Composite Materials ◽  
Effective Properties ◽  
Homogenization Method ◽  
Software System ◽  
Computational Results ◽  
Composite Construction ◽  
Element Analysis ◽  
Object Oriented Design ◽  
Multiscale Homogenization

ABSTRACTResults of finite element analysis of linked two and three scale levels tasks are presented. Fields of components of stress concentration tensor function for several models of unit cells of textile composite materials are presented too. Comparison of experimental and computational results of obtained effective properties was carried out and results of this research are introduced. The basis of this phenomenological approaches was made by Prof. N.S. Bahvalov and Prof. B.E. Pobedriya in 80's and finally this method was renovated by Prof. Yu.I. Dimitrienko at Bauman Moscow State Technical University at «Computational mathematics and mathematical physics» department. Computational procedures and program implementation was made using object-oriented design and C/C++ language by A.P. Sokolov. All computational results have been performed using new-developed distributed high-perfomance software system GCD. Multiscale homogenization method was applied for single macroscopic level of composite construction and several connected microscopic levels. The task of stress-strain determination of composite construction was stated automatically by means of automatically defined plan based on certain computational problems. Architecture of software system and finite-element subsystem were developed too. Several practically important tasks were solved and some of its results are attached.

scholarly journals Semi analytical method for calculating Dean's vortex in Torus of elliptical cross section

2019 ◽  
Vol 286 ◽  
pp. 07004
Author(s):  
S. Ajgoun ◽  
J. Khalid Naciri ◽  
R. Khatyr
Keyword(s):  
Cross Section ◽  
Analytical Method ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Stationary Flow ◽  
Elliptical Cross Section ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Elliptical Cross ◽  
Curved Pipe

Based on the work of Dean (1927 and 1928) [1-2] and Cuming (1952) [3], the stationary flow of an incompressible Newtonian fluid through a curved pipe of uniform curvature and with elliptic cross section is studied. The Navier-Stokes equations are expressed in toroïdal coordinates system (s,r,θ). Following Dean’s approach, the governing equations for the fluid motion through a curved elliptical channel are solved by using an original semi analytical method for the resolution of a biharmonic equation. The main interest in this study is to test and validate in the case of an elliptical cross section the proposed semi-analytical method. The latter can then be used for other geometries for which explicit solutions are not available.

Sign in / Sign up

Export Citation Format

Share Document