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TECHNICAL PAPERS

# Constitutive Model for Fiber-Reinforced Composite Laminates

[+] Author and Article Information
Bibiana M. Luccioni

CONICET, Structures Institute, National University of Tucumán, Av. Roca 1800, 4000 San Miguel de Tucumán, Tucumán, Argentina

J. Appl. Mech 73(6), 901-910 (Mar 27, 2006) (10 pages) doi:10.1115/1.2200654 History: Received May 21, 2005; Revised March 27, 2006

## Abstract

Nowadays, conventional materials have been progressively replaced by composite materials in a wide variety of applications. Particularly, fiber reinforced composite laminates are widely used. The appropriate design of elements made of this type of material requires the use of constitutive models capable of estimating their stiffness and strength. A general constitutive model for fiber reinforced laminated composites is presented in this paper. The model is obtained as a generalization of classical mixture theory taking into account the relations among the strains and stresses in the components and the composite in principal symmetry directions of the material. The constitutive equations for the laminated composite result from the combination of lamina constitutive equations that also result from the combination of fibers and matrix. It is assumed that each one of the components are orthotropic and elastoplastic. Basic assumptions of the proposed model and the resulting equations are first presented in the paper. The numerical algorithm developed for the implementation in a three-dimensional (3D) finite element nonlinear program is also described. The paper is completed with application examples and comparison with experimental results. The comparison shows the capacity of the proposed model for the simulation of stiffness and strength of different composite laminates.

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## Figures

Figure 1

Schematic representation of composite structure. (a) Simple structure, (b) more complex structure.

Figure 2

Numerical scheme for the solution of a nonlinear problem

Figure 3

Fiber reinforced laminated composite

Figure 4

Elastic properties of the lamina as a function of fiber fraction. (a) E1, (b) E2, (c) G12, (d) G23, (e) ν23.

Figure 5

Stress-strain behavior in the fiber direction. (a) kf=0.20, (b) kf=0.35.

Figure 6

Failure envelope for a unidirectional lamina (E-Glass/LY556/HT907/DY063)

Figure 7

Failure envelope for a unidirectional lamina (T300/BSL914C epoxy)

Figure 8

Failure envelope for a unidirectional lamina (Silenka E-Glass 1200 tex MY750/HY917/DY063 epoxy)

Figure 9

Failure envelope for a (90deg∕±30deg)s laminate (E-Glass/LY556/HT907/DY063). (a) σx versus σy; (b) τxy versus σx.

Figure 10

Failure envelope for (90deg∕±45deg∕0deg)s laminate (AS4/3501-6)

Figure 11

Failure envelope for (±55deg)s laminate (Silenka E-Glass 1200 tex MY750/HY917/DY063 epoxy)

## Errata

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