A party balloon is made from a rubber whose Mooney-Rivlin constants are and

PHYSICS · Subjective · 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

A party balloon is made from a rubber whose Mooney-Rivlin constants are C1=0.18 MPaC_1 = 0.18\,\mathrm{MPa} and C2=0.09 MPaC_2 = 0.09\,\mathrm{MPa}, so that the nominal stress in uniaxial tension is σeng=(2C1+2C2λ)(λ−λ−2).\sigma_{\rm eng} = \left(2C_1 + \frac{2C_2}{\lambda}\right)\left(\lambda - \lambda^{-2}\right). Calculate σeng\sigma_{\rm eng} at a stretch λ=4\lambda = 4.

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