This section computes the elastic moduli for various general models of random closed-cell cellular solids and relates them to various simple analytical theories and existing elastic moduli data for similar materials. This section develops a differential effective medium theory for the linear elastic properties for materials with composite inclusions. An example of this is concrete, where the composite inclusion is the aggregate plus the surrounding interfacial transition zone. The theory is then tested with accurate finite element simulations of random systems. The agreement is quite good.
Discussion is given of how to properly isotropically average the results of simulations.
A.P. Roberts and E.J. Garboczi, J. Mech.