RUC-based multi-scale model for braid-reinforced polymers: Application to coil springs

As fiber- and braid-reinforced polymer components exhibit a vast number of additional design parameters compared to components made of monolithic materials, simulation methods are indispensable in the design and optimization process, accompanying or substituting experimental approaches. In respect thereof, we present a multi-scale approach comprising three observation scales: (i) the yarn scale considering fibers embedded in polymer, (ii) the braid scale capturing interwoven yarns, and (iii) the component scale. Information from one scale is transferred to the next higher scale by means of effective properties determined by finite element analysis of repetitive unit cell (RUC) models, subsequently applied for the determination of elastic properties on the yarn and braid scale. The depicted procedure allows the consideration of different types of braids (balanced and unbalanced regular braids) exhibiting arbitrary braid angles. Therefrom obtained effective properties enter the numerical model of the respective structural component. Finally, the multi-scale model is applied to the analysis of braid-reinforced polymer coil springs highlighting the potential of the proposed numerical approach. The obtained simulation results show excellent agreement with the respective experimental measurements and provide additionally insight into the stress distribution/loading within the coil as well as the sensitivity of design parameters with respect to the spring performance.