Shear modulus G12 of unidirectional composites: a boundary element evaluation
The early micromechanical modelling techniques for describing composite behaviour considered the material as a two-phase medium with a perfect bonding between the components. At present, the development of modelling techniques is slightly more complex as there are some studies that consider that there is a zone surrounding the fibre with different properties from either the fibre itself or the matrix. Normally, this zone is artificially introduced as a thin coating. In cases of very thin coating, the thickness can be neglected, but the effect is taken into account using an appropriate coefficient of interface h. With this approximation, the evaluation of shear modulus G12 can be obtained by solving the boundaries of two bodies only. As shown in this paper, the BEM is a very efficient method for this purpose. The analysis is based on the analogy between the longitudinal shear loading and the transverse heat conduction in the unidirectional composite. Two models of boundary elements are proposed. The simpler model uses constant boundary elements. The second one uses two types of elements: linear elements, at the external boundaries, and cubic elements (with only two nodes), at the interface boundaries. All the results obtained can be compared with a similar model using MEF. A classic model is used for comparing under certain hypothesis. In all cases the results are in agreement.
shear modulus unidirectional composites boundary elements method effective thermal conductivity