Critical scaling of shear modulus for particle-filled soft elastomers in the jamming limit

Soft composite solids are composed of stiff particles dispersed within a soft polymeric matrix. They form the basis of many multi-phase materials in nature and industries, including biological tissues and field-responsive soft devices. While the mechanics of dilute composites has been well-understood by the Eshelby framework, the governing mechanical principles of dense soft composites remain unclear. Dense soft composites often display novel nonlinear behaviors that are determined by the complex multiscale interactions within soft composites. In this work, we focus on revealing the role of granular jamming in the strain-stiffening behaviors of soft composites. For composites with different particle volume fractions and matrix shear moduli, we systematically characterized their shear responses to varying uni-axial compressive strains. We uncovered the underlying connections between composite mechanics and the jamming rheology of granular suspensions. In particular, we demonstrate a critical scaling collapse of the composite modulus near the shear-jamming transitions of granular systems. In addition, we constructed a phenomenological model that quantitatively predicts the strain-stiffening of dense soft composites.