Isogeometric homogenization of viscoelastic polymer composites via correspondence principle

We present an isogeometric homogenization theory (IGH) for efficiently identifying homogenized and local creep and relaxation response of linearly viscoelastic polymer composites with different microstructural parameters. The principal idea is to construct exact geometric representations of both two- and three-dimensional unit cell microstructures for periodic materials by utilizing multiple conforming NURBS patches that are also employed for the displacement field interpolation function at the local scale. The IGH-based unit cell formulation is then converted to the viscoelastic solution with the Laplace-Carson space parameters via the correspondence principle. Subsequently, we leverage the Zakian formula to reverse the transformed IGH solution and obtain the homogenized creep and relaxation response of the composite in the original time space. The modelling and predictive capabilities of the IGH theory have been extensively validated vis-à-vis the elasticity-based and conventional finite-element homogenization techniques, and the advantages of the proposed technique over the reference techniques were demonstrated.