Reduced basis homogenization of viscoelastic composites

A reduced basis order-reduction based homogenization method for the constitutive behavior of viscoelastic composites is presented. The approach is based on a modification of the Nonuniform Transformation Field Analysis (NTFA) introduced by Michel and Suquet [1]. A new evolution law for the set of macroscopic internal variables of the homogenized material is derived based on dissipative considerations. The theoretical aspects of the method are extensively discussed including an explicit algorithm for the computation of the anisotropic complex moduli of the material. Details concerning the numerical implementation and a selection of representative numerical examples are provided. The method accurately captures the anisotropic transient mechanical response of composites for various loading conditions while offering numerical savings in the order of 106–1010 with respect to both, CPU time and memory requirements.