Micro-Mechanical Hyperelastic Modelling for (Un)Filled Polyurethane with Considerations of Strain Amplification

Polyurethane (PU) is a very versatile material in engineering applications, whose mechanical properties can be tailored by the introduction of active fillers. The current research aims to (i) investigate the effect of active fillers with varying filler loads on the mechanical properties of a PU system and (ii) develop a micro-mechanical model to describe the hyperelastic behavior of (un)filled PU. Three models are taken into consideration: without strain amplification, with constant strain amplification, and with a deformation-dependent strain amplification. The measured uniaxial stress–strain data of the filled PU nanocomposites reveal clear reinforcement due to the incorporation of carbon black at 5, 10 and 20 wt%. In low concentration (1 wt%), for two different grades of carbon black and a fumed silica, it results in a reduction in the mechanical properties. The micro-mechanical model without strain amplification has a good agreement with the measured stress–strain curves at low concentrations of fillers (1 wt%). For higher filled concentrations (5–15 wt%), the micro-mechanical model with constant strain amplification leads to a better prediction performance. For samples with a larger filler volume fraction (20 wt%) and for a commercial adhesive, the model with a deformation-dependent strain amplification effect leads to the best predictions, i.e., highest R2 regarding curve fitting.