Fourth-order shear elastic constant assessment in quasi-incompressible soft solids

In isotropic quasi-incompressible media, an expression of the elastic energy density has been developed as a function of the second-, third-, and fourth-order elastic constants (respectively μ, A, D). Thus the shear nonlinearity parameter βS depends only on these coefficients. In this letter βS is measured using finite amplitude plane shear waves in agar-gelatin based phantoms. Combining the results with recently published measurements of μ and A on the same phantoms, the fourth-order shear elastic constant D is found to be of the order of 10kPa and thus of the same order of magnitude as μ and A.