A multi-scale deformation analysis for a particulate composite at the rigidity threshold

The rigidity threshold in a two-phase soft-rigid material is linked to the formation of networks of the rigid phase, which supports a substantial fraction of overall load. Metal filled particulate polymer composites were used to characterize rigidity transition experimentally, as metals and polymers have contrasting mechanical properties enabling easy detection of the rigidity transition. A detailed analysis of the load transferring mechanisms was performed using in-situ synchrotron X-ray diffraction to directly verify the compressive loading of the rigid metal particles at a microscopic scale. Elastic buckling of the force chains was attributed to the non-affine deformation at the rigidity threshold at room temperature, using digital image correlation (DIC) technique at a mesoscopic length scale. However, beyond the glass transition temperature of the polymer, the deformation was homogeneous due to the low viscosity and high compressibility of the polymer and the absence of buckling of force chains. Macroscopically, an increasing Poisson ratio was observed as a function of elastic strains, which is quite unique for these composites. The criteria for having increasing Poisson ratio is discussed based on elastic buckling of force chains and polymer incompressibility, and a link is proposed between deformation at microscopic, mesoscopic and macroscopic scale for the composite.