Modelling mechanical behaviour of continuously graded vulcanised rubbers

Tailoring the spatial distribution of material properties is a well-established concept in materials engineering and referred as functional grading. Vulcanised rubbers have been graded very recently using a construction-based (layering) method. Although these studies have indicated the possibility of continuously grading the mechanical and chemical properties, there is little information available in the literature regarding the mechanical behaviour of so-produced rubbers. The present study attempts to close this knowledge gap via mathematical modelling of the stress-strain fields in graded rubbers. Rectilinear shearing of graded rubber slabs is theoretically analysed as it allows us to obtain closed-form analytical solutions. It is found that the slabs can develop highly localised stress-strain fields depending on the spatial variation of the shear modulus. The results indicate the need for a design code to grade rubbers with a mechanical functionality and the potential risks in the absence of such a code.