Micromechanical analysis of a lamina

The engineering properties of interest are the elastic constants in the principal material coordinates. If we restrict ourselves to transversely isotropic materials, the elastic properties needed are Ei, Ei, v, and G23, i.e. the axial modulus, the transverse modulus, the major Poisson s ratio, the in-plane shear modulus and the transverse shear modulus, respectively. All the elastic properties can be obtained from these five elastic constants. Since experimental evaluation of these parameters is costly and time-consuming, it becomes important to have analytical models to compute these parameters based on the elastic constants of the individual constituents of the composite. The goal of micromechanics here is to find the elastic constants of the composite as functions of the elastic constants of its constituents, as 

The superscripts/and m over the elastic constants stand for fibre and matrix, respectively. The theoretical formulas to compute the elastic properties of a lamina are also dependent on fibre and matrix volume fractions. The fibre volume fraction and the matrix volume fraction are noted as Vf and respectively. The sum of volume fractions is 

As a consequence of the manufacturing process of a composite, voids are created in the composite. This causes the theoretical volume of the composite to be lower than the actual volume. Moreover, the void content of a composite decreases the matrix-dominated strengths and the compression strength. 

Approximate formulae for four E, E, v i, G12) of the five elastic properties of a transversely isotropic composite can be developed using simple approaches based on the strength of materials concepts. These concepts do not necessarily satisfy in full all the elasticity requirements. The RVE considered consists of a uniform arrangement of straight, continnons fibres. 

Let us assume a transversely nnidirectional lamina nnder uniform axial loading Cj, as depicted in Fignre 11.9. Assnming that the fibres and matrix are perfectly bonded with no slip, i.e. the axial strain of the composite is uniform. 

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