The use of a simple composite element to describe the creep properties of fibre reinforced composites

The stress-strain relationship for a composite material is dependent on both the geometry and the stress-strain relationships of the component phases. This note describes a technique by which the stress-strain relationship can be calculated for any fibre reinforced composite where the matrix has linear viscoelastic properties and the fibres are linearly elastic. The distribution of fibres within the composite is assumed to be macroscopically homogeneous but the distribution of fibre orientation can take any configurations. The problem is solved initially for the case where both phases are linearly elastic. A simple composite element from which a composite can be built up is defined and the stress-strain relationship for this element is calculated using variational methods. By summing these elements assuming either uniform stress or uniform strain throughout the composite, upper and lower bounds to the stiffness matrix of the composite are obtained. Using the correspondence principle these bounds for the purely elastic case are transformed to give the bounds for the viscoelastic case. The theoretical answers obtained using this method are compared with those obtained using a more simple model for the mode of combination of the two phases.