Jamming-controlled shear stiffening in particle-filled soft solids

Dispersing hard particles into a soft polymer gel forms a soft composite that is widely used in mechanical and biomedical applications. The global mechanics of such composites is strongly affected by the collective interactions among the embedded particles. Predicting the nonlinear mechanical features of such materials presents a great challenge. To address the problem, we performed a systematic experimental study on a model system consisting of micron-sized polystyrene spheres randomly dispersed in a crosslinked polydimethylsiloxane (PDMS) matrix. We found that the shear modulus of densely filled samples grows significantly, in some cases more than ten-fold, under small deformations. Inspired by the stress-controlled shear-thickening effects in dense suspensions, we proposed a phenomenological model that explains the stiffening effect through critical scaling laws near a stress-dependent jamming point. The model not only captured our observations but also predicted the emergence of mechanical instability for extremely dense samples. Our work provides the experimental evidence to support that jamming criticality controls the responses of soft composites, and revealed a similar role played by the particle contact networks in determining both the elasticity of dense particle-filled soft solids and the rheology of dense granular suspension.