Conclusions

Conservation of deformation energy, volume and mass lead to a general formulation for finding the static homogeneous equivalent of an arbitrary heterogeneous medium. While applying exterior surface forces and displacements the stress and stain components at points on interior discontinuity surfaces have to be continuous according to the specified boundary conditions. For a homogeneous equivalent medium forces and displacements on the exterior boundaries will be averages of the ones observed on the heterogenous medium. The heterogeneous and homogeneous equivalent have identical integral properties and on a large scale, show the same average behavior in displacements and stresses.