Overall properties of composites with physically non-linear discrete phase

The problem of constructing effective constitutive laws is solved for matrix composites with a physically non-linear discrete phase. The technique employed is a variant of the self-consistent method in which interaction between inclusions is described by disturbance of external field. The approach is based on generalisation of the Eshelby’s theorem. Use of a thermodynamic time scale leads to a reduction of this problem to the solution of four linear integral equations. This procedure presents the possibility of applying this averaging scheme to engineering problems of materials design. As an example the problem of designing artificial bio-composites is discussed. The material is modelled as a two-phase matrix composite with a brittle elastic matrix and visco-plastic inclusions. Dense hydroxyapatite is considered as the matrix material and recommended properties of the plastificator are derived under the condition that material should possess the mechanical properties as close to the human cortical bone as possible. The elastic constants and the yield stress for plastificator are obtained as functions of the volume concentration of phases. The application of the method to the design of artificial bio-composites is discussed.