Non-linear behaviour of gels under strong deformations

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Abstract
We consider a gel of flexible polymer chains in a good solvent : a strong constant stress σ is applied at time 0. We study the prompt elastic response at times t such that the chain/solvent fraction has not changed. The theory is based on the scaling laws established by various authors for a single chain under strong deformation. The stress-strain relation at large strain α is predicted to be σ ∼ α5/2 in longitudinal deformation and σ ∼ α3/2 in simple shear. We also present some tentative remarks on the neutron scattering patterns, the birefringence and the sedimentation coefficients, expected for the distorted sample. These considerations do not apply to pure rubbers