A Study on the Elastic Properties of Reinforced Solids

Abstract

A mathematical model for the elastic behaviour of two phase composite body has been formulated. The distribution of stresses for various cases have been dis cussed together with their corresponding elastic energies. It has been shown that a great deal of knowledge can be obtained even without analysing the interaction mechanism of composite. The mixture is assumed to be homogeneous on a macroscopic scale but not necessarily isotropic. However, two phases themselves are assumed to be homogeneous and isotropic. Further, no condition is placed on the shape of the inclusions which may for example be fibrous or plate like.

Young's Modulus of a Composite: Reinforced with (n - 1) Different Inclusions

“…The strain energy per unit volume, E, stored in a material is equal to the area under the stress-strain curve from the zero strain to the elastic strain, E, Equation (1) applies to both linear and non-linear cases. For linear case Q = LE, Equation (1) can be rewritten as or, alternatively So, for n arbitrary structures with respective stresses a, (i = 1,2,...,n), the corresponding strain energies E, (i = 1,2,...,n) are is the total energy of the system before composition.…”

“…Many such theories have been obtained by constructing suitable mathematical models, such as the model presented in Reference [1] to describe the elastic behaviour of a two-phase composite body. A special feature of this kind of model, based on a well-posed physical problem, is that it not only explains the posed problem, but may also explain the other processes occurring in the same system which initially were not considered.…”