Improved model of nonaffine strain measure

A new calculation of the strain measure for entangled polymers is presented, in which the entanglement network is modeled as a set of entanglement points to which are attached four entanglement strands, randomly oriented in equilibrium. The network deforms nonaffinely to maintain a net zero force on each entanglement point, following a recent suggestion of Marrucci. The resulting strain measure in the case of uniaxial and biaxial extension as well as simple shear is well described by $Q=C−α/tr(C−α)$ with $α=0.7,$ where $C−1$ is the Finger tensor. The resulting second normal stress ratio $Ψ=−N2/N1$ is $(1−α)/2=0.15.$ The original Doi–Edwards strain measure is well described except for the second normal stress by this same function with $α=0.8.$