An improved Flory's statistical-mechanics model of chain-molecular for compressible polymers

Existing hyperelastic models require a large number of material constants to fully describe the mechanical behavior of compressible polymers, indicating that existing hyperelastic models need to be improved. To address this fundamental problem, we modified the Flory's statistical mechanics model of chain molecular by introducing a generalized multivariate Gaussian distribution of cross-linked units and derived a new Helmholtz free energy expression and macroscopic constitutive equation for polymer networks. The improved Flory's model can not only adaptively describe linear elastic and nonlinear elastic materials, but also unify the form of the constitutive equation whether the material is compressible or not. The experimental results show that the improved Flory's model containing 6 parameters can well describe the mechanical behavior of foam silicone rubber with a volume change of 150 %. Compared with existing models, the improved Flory's model not only does not require the addition of complex volume terms to characterize compressibility, but also has fewer parameters in the constitutive equation. This also shows that the improved Flory's model captures the essence of statistical mechanics of chain molecule well and has better universality.