Mean field model of cellular materials

Modelling of the overall stiffness of the cellular materials indicates appropriateness of developed techniques for modelling cellular structures. A model of cellular material is obtained by equating the stiffness of one of the phases to zero. The theory was compared to experimental results from structured PVC foam and good agreement was observed for the normalized Young's modulus and the normalized shear modulus as a function of the cell volume fraction. Furthermore, good agreement was seen for the normalized stiffness of microcellular polycarbonate. The procedure to obtain the stress-strain diagram has been developed taking into account the changes in the microstructure i.e. change of the shape and volume fraction of the elliptical voids. The development of a stress-strain analysis method, which will be used in conjunction with statistical distributions of inclusions (cells), is in progress. The first step in this analysis is to find a solution to many inclusion interaction problems. Interaction between inclusions is calculated using equivalent eigenstrains and Eshelby`s solution. This gives a set of coupled singular integral equations, which are solved using Gauss quadrature to give the equivalent eigenstrains in the inclusion. The solution has been found for a model dispersion of inclusions that correspond to FCC and BCC lattice configurations. Partly financed by Statens Teknisk-Videnskabelige Forskningsråds Rammeprogram Structurally Graded Polymeric Materials.... (Jan Schjødt-Thomsen, Ryszard Pyrz)