On incompressibility of a matrix in naturally occurring composites

The work illustrates that a soft matrix, which has the Poisson ratio close to 0.5 and is reinforced with a rigid-line inclusion, possesses an interesting behavior at the inclusion/matrix interface. It experiences a hydrostatic stress state and behaves as an incompressible fluid under longitudinal and transverse loads. The stress singularities are eliminated ahead of the inclusion tips, and when interface defects are formed, their effect on the composite compliance is minimal. These observations have far reaching applications when one is interested in mechanisms of multifunctional property improvement of composites (such as toughness and stiffness) learned from naturally occurring composites.