A generalized tube model of rubber elasticity

In the present paper, a new type of micro-mechanically motivated chain network model for rubber-like materials is proposed. The model captures topological constraints of polymer network chains, in particular, entanglements. The model demonstrates how the local molecular packing constraints modify under deformation and shows the impact of these changes on the macroscopic elasticity of the material. To this end, we combine concepts of a confining tube and a slip-link (reptation) model. In these models, entanglements of polymer chains play an important role. The nature of entanglements is discussed, and relationships governing entanglements are formulated in terms of molecular physics. In the context of nonlinear elasticity, we apply a non-affine concept which captures the liquid-like behavior of polymer networks at smaller scales in a more realistic way. Model predictions show good agreement with experimental results from uniaxial and biaxial tension tests.