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The Flory theory of rubber elasticity suggests that rubber elasticity has primarily entropic origins. By using the following basic equations for Helmholtz free energy and its discussion about entropy, the force generated from the deformation of a rubber chain from its original unstretched conformation can be derived.
The Gent hyperelastic material model [1] is a phenomenological model of rubber elasticity that is based on the concept of limiting chain extensibility. In this model, the strain energy density function is designed such that it has a singularity when the first invariant of the left Cauchy-Green deformation tensor reaches a limiting value .
Yeoh model prediction versus experimental data for natural rubber. Model parameters and experimental data from PolymerFEM.com. The Yeoh hyperelastic material model [1] is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber.
In continuum mechanics, an Arruda–Boyce model [1] is a hyperelastic constitutive model used to describe the mechanical behavior of rubber and other polymeric substances. This model is based on the statistical mechanics of a material with a cubic representative volume element containing eight chains along the diagonal directions.
Elastic response of rubber-like materials are often modeled based on the Mooney–Rivlin model. The constants , are determined by fitting the predicted stress from the above equations to the experimental data. The recommended tests are uniaxial tension, equibiaxial compression, equibiaxial tension, uniaxial compression, and for shear, planar ...
The polynomial hyperelastic material model is a phenomenological model of rubber elasticity. In this model, the strain energy density function is of the form of a polynomial in the two invariants , of the left Cauchy-Green deformation tensor. The strain energy density function for the polynomial model is
For rubber and biological materials, more sophisticated models are necessary. Such materials may exhibit a non-linear stress–strain behaviour at modest strains, or are elastic up to huge strains. These complex non-linear stress–strain behaviours need to be accommodated by specifically tailored strain-energy density functions.
In polymer science Flory–Rehner equation is an equation that describes the mixing of polymer and liquid molecules as predicted by the equilibrium swelling theory of Flory and Rehner. [1] It describes the equilibrium swelling of a lightly crosslinked polymer in terms of crosslink density and the quality of the solvent .