Micromechanical modelling of rubbery networks: The role of chain pre-stretch

Discrete Network (DN) models are a useful tool to investigate structure-property relationships in rubbery networks such as elastomers and hydrogels. In a DN model, polymer chains are represented by entropic springs connected at crosslinking points, and the partitioning of stretches among the chains is dictated by the condition of mechanical equilibrium at each crosslink. A key feature of these models is that springs have a zero natural length, and are therefore pre-stretched in the reference configuration. However, the role of chain pre-stretch distribution on the emerging mechanical properties has often been overlooked. In this work we investigate the elastic properties of DNs where the average chain pre-stretch, chain density and chain length distribution can be prescribed independently via a novel network generation algorithm. We show that increasing the average pre-stretch increases the network stiffness and decreases its extensibility limit. We also compare predictions of semi-analytical micromechanical models of rubber elasticity to DN predictions taken as reference. Deviations between analytical model and DN predictions are attributed to the combination of two factors: the loss of affinity at large strain and the initial pre-stretch distribution, which is not taken into account in analytical estimates. DN simulations further show that the assumption of one-to-one mapping between chain stretch and chain orientation on which microsphere models rely is not satisfied.