Abstract
An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis.
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