Bounds of the expansion coefficients of composites reinforced by spherically isotropic particles

The present paper is devoted to the study of expansional behaviours of a composite reinforced by spherically isotropic particles. An exact relation is derived between the effective expansion coefficient and bulk modulus of the composite by using the concept of uniform fields in the matrix which is proposed here. Through obtaining the Paul-type bounds of the bulk modulus by using the extreme principle of energy, bounds of the effective expansion coefficient are also derivded