The Elastic Moduli of Fiber-Reinforced Materials

1964 ◽  
Vol 31 (2) ◽  
pp. 223-232 ◽  
Author(s):  
Zvi Hashin ◽  
B. Walter Rosen
Keyword(s):  
Variational Method ◽  
Cross Sections ◽  
Elastic Moduli ◽  
Numerical Results ◽  
Exact Results ◽  
Effective Elastic Moduli ◽  
Fiber Reinforced ◽  
Random Array ◽  
Fiber Reinforced Materials ◽  
Hexagonal Arrays

Bounds and expressions for the effective elastic moduli of materials reinforced by parallel hollow circular fibers have been derived by a variational method. Exact results have been obtained for hexagonal arrays of identical fibers and approximate results for random array of fibers, which may have unequal cross sections. Typical numerical results have been obtained for technically important elastic moduli.

scholarly journals Optimization of elasticity of unidirectionnal non-overlapping fiber reinforced materials

2019 ◽  
Vol 286 ◽  
pp. 03004
Author(s):  
L. Lakhal ◽  
Y. Brunet ◽  
T. Kanit
Keyword(s):  
Elastic Properties ◽  
Elastic Moduli ◽  
Volume Averaging ◽  
Distribution Functions ◽  
Fiber Reinforced Composites ◽  
Effective Elastic Moduli ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Fiber Reinforced Materials ◽  
Local Stresses

The aim of this work is to efficiently select samples of non-overlapping parallel fiber reinforced composites with regard to their elasticity and their fiber distribution in the composite cross-section. The samples were built with the help of the simulated annealing technique according to chosen Radial Distribution Functions. For each sample the fields of local stresses were simulated by finite element method, then homogenized by volume averaging in order to investigate their elastic properties. The effect of RDF shape on elastic properties was quantified. The more the fiber distributions deviate from Poisson’s Law the higher the effective elastic moduli are. A method to select samples of real fiber reinforced composites according to their elasticity is proposed.

Evaluation of second-order correlations adjusted with simulated annealing on physical properties of unidirectional nonoverlapping fiber-reinforced materials (UD Composites)

2019 ◽  
Vol 30 (02n03) ◽  
pp. 1950017 ◽  
Author(s):  
L. Lakhal ◽  
Y. Brunet ◽  
T. Kanit
Keyword(s):  
Thermal Properties ◽  
Simulated Annealing ◽  
Physical Properties ◽  
Cross Sections ◽  
Volume Averaging ◽  
Distribution Functions ◽  
Heat Fluxes ◽  
Mechanical And Thermal Properties ◽  
Fiber Reinforced ◽  
Fiber Reinforced Materials

The focus of this paper is on aligned fiber-reinforced composites, where fiber centers were randomly distributed in their cross-sections. The volume fractions of fibers were [Formula: see text]% and [Formula: see text]%. Samples were built with the help of the simulated annealing technique according to the chosen Radial Distribution Functions (RDFs). For each sample, the fields of local stresses and heat fluxes were simulated by finite element method. Then, homogenization by volume averaging was performed in order to investigate both the effective mechanical and thermal properties. The effect of RDF shape on elastic and thermal properties was quantified along with the influence of the probability of near neighbors of fibers on the physical properties. The more the fiber distributions deviate from Poisson’s Law, the higher the results compared to the lower bound of Hashin–Shtrikman.

Effective Elastic Moduli of Fiber-Reinforced Polymer Matrix Composites Filled with Nanoparticle

2013 ◽  
Vol 811 ◽  
pp. 32-38
Author(s):  
Hui Zhang ◽  
Zong Fu Zhang ◽  
Jia Chu Xu
Keyword(s):  
Polymer Matrix ◽  
Elastic Moduli ◽  
Polymer Matrix Composites ◽  
Fiber Reinforced Polymer ◽  
Inclusion Problem ◽  
Matrix Composites ◽  
Effective Elastic Moduli ◽  
Effective Moduli ◽  
Fiber Reinforced ◽  
Reinforced Polymer

Effective moduli of fiber-reinforced polymer matrix composites filled with nanoparticle considering the effect of linear change of interphase are presented in this paper. The three-phase inclusion problem for matrix-interface-particle is equivalent to the Eshelby two-phase inclusion problem. According to the result of the Eshelby inclusion problem, the effective modulus tensor of unit cell of equivalent particle is derived. The effective moduli of equivalent matrix are given based on Mori-Tanaka method. Using two fundamental equation of micromechanic theory, the three-dimensional bridged formulation of unidirectional composites is derived. The quantitative relationship between the macroscopic elastic parameters and the structural parameters of the fiber-reinforced polymer composites filled with nanoparticles is investigated. Effects of the thickness of interfacial layer, the particle size and the volume fraction of nanoparticles on the effective elastic moduli of the composites are also discussed.

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