A rubber seal has an initial (small-strain) shear modulus

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Rubber elasticity, swelling and gelation

Problem

G = 0.45\,\mathrm{MPa}

, measured directly. A Mooney-Rivlin fit to its stress-strain curve gives

C_1 = 0.125\,\mathrm{MPa}

and

C_2 = 0.100\,\mathrm{MPa}

, consistent with

2(C_1+C_2)=G

. ((a)) Calculate the nominal stress predicted by the simple affine law,

\sigma_{\rm eng}=G(\lambda-\lambda^{-2})

, at

\lambda = 5

. ((b)) Calculate the nominal stress predicted by the Mooney-Rivlin law,

\sigma_{\rm eng}=(2C_1+2C_2/\lambda)(\lambda-\lambda^{-2})

, at the same stretch. ((c)) State by what percentage the Mooney-Rivlin stress falls below the affine prediction at

\lambda=5