Inhomogeneous swelling in filled elastomers

An exact formulation is given for the inhomogeneous swelling of an elastomeric matrix containing a spherical inclusion, and is presented in a form amenable to solution for arbitrary free energy of mixing and network strain energy functions, rigid or soft inclusions, and finite or infinite matrix size. Specific examples of the deformation field, stress field, and composition variation are given as functions of distance from a rigid inclusion imbedded in an infinite matrix displaying Flory-Huggins/Gaussian swelling behavior. Interfacial stresses and extension ratios are given as functions of cross-link density and Flory-Huggins X parameter.

In a related study published elsewhere, Kotani and Sternstein have obtained experimental verification of the theory using birefringence techniques on model-filled elastomers. Stein and co-workers have found similar agreement of the theory with their light scattering measurements.