Matrix shear model for elastomers containing rigid platelets embedded in a soft matrix: 1. Orientation properties and stress-strain behaviour

Abstract

The finite deformational behaviour of materials containing rigid platelets embedded in an elastic matrix has been evaluated by assuming that the dominant microscopic deformation mechanism is shear of the matrix in a direction parallel to the plane of a platelet. The behaviour was determined for an initially isotropic sample undergoing uniaxial extension for the cases of uniform strain and uniform stress. The orientation distribution function of the platelet normals, the stress-strain diagram and orientation parameters such as Hermans' orientation factor were calculated. The predicted inclination of platelet normals for deformation at uniform stress gives an explanation for the observed ‘cross-like’ small angle X-ray scattering patterns found for diamine-extended polyurethane elastomers. For uniform strain, the retractive force diverges, whereas for uniform stress it is approximately proportional to the macroscopic extension ratio, with the slope showing a small minimum corresponding to a peak in the instantaneous compliance at an extension of about 10%. Hermans' orientation factor for the platelet normal distribution becomes strongly negative with increasing extension ratio for both cases.