Elasticity Solutions with Contiguity

For the elasticity approach in which the contiguity is considered, T aiJ3 r1] obtains for the modulusJransyerse to the fibers 

For the modulus in the direction of the fibers. Tsai modified the rule of mixtures to cqunt for imperfectiorisanjioer ajignment  

The fiber misalignment fantnr k nrriinarilY varies from so 

Equation (3.68) does not represent a very significant departurerom the rule of mixtures. Of course, k is an experimentally determined constant and is highly dependent on the manufacturing process. 

The contiguity factor, Cj is actually a so-called fudge factor used to make sense out of the comparison of experimental dataTwitlirtheore-tical predictions. This correlation factor is useful only when the data fall between the theoretical bounds. The concept of a contiguity factor, i.e.. 

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The mechanics of materials approach to the micromechanics of material stiffnesses is discussed in Section 3.2. There, simple approximations to the engineering constants E., E2, arid orthotropic material are introduced. In Section 3.3, the elasticity approach to the micromechanics of material stiffnesses is addressed. Bounding techniques, exact solutions, the concept of contiguity, and the Halpin-Tsai approximate equations are all examined. Next, the various approaches to prediction of stiffness are compared in Section 3.4 with experimental data for both particulate composite materials and fiber-reinforced composite materials. Parallel to the study of the micromechanics of material stiffnesses is the micromechanics of material strengths which is introduced in Section 3.5. There, mechanics of materials predictions of tensile and compressive strengths are described. 

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