On the Role of Elastic Constants in Multiphase Contact Problems

For a plane composite body consisting of an arbitrary number of different linearly elastic constituents under conditions of plane deformation or plane stress, the minimum number of required elastic constants describing the stress field is determined. For conditions in accordance with the assumptions of Michell and Dundurs, i.e., for prescribed surface tractions and no net forces on internal boundaries, the state of stress in a body involving N different phases is found to be determined by only 2N-2 combinations of the elastic constants. This result holds for conditions of complete adhesion and frictionless slip at the interfaces of the materials.