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In this paper we present the homogenization for nonlinear viscoelasticsecond-grade non-simple perforated materials at large strain in the quasistaticsetting. The reference domain $\Omega_{\varepsilon}$ is periodically perforatedand is depending on the scaling parameter $\varepsilon$ which describes theratio between the size of the whole domain and the small periodic perforations.The mechanical energy depends on the gradient and also the second gradient ofthe deformation, and also respects positivity of the determinant of thedeformation gradient. For the viscous stresses we assume dynamic frameindifference and is therefore depending of the rate of the Cauchy-stresstensor. For the derivation of the homogenized model for $\varepsilon \to 0$ weuse the method of two-scale convergence. For this uniform a priori estimateswith respect to $\varepsilon$ are necessary. The most crucial part is toestimate the rate of the deformation gradient. Due to the time-dependent frameindifference of the viscous term, we only get coercivity with respect to therate of the Cauchy-stress tensor. To overcome this problem we derive a Korninequality for non-constant coefficients on the perforated domain. The crucialpoint is to verify that the constant in this inequality, which is usuallydepending on the domain, can be chosen independently of the parameter$\varepsilon$. Further, we construct an extension operator for second orderSobolev spaces on perforated domains with operator norm independent of$\varepsilon$.

Extension operators and Korn inequality for variable coefficients in  perforated domains with applications to homogenization of viscoelastic  non-simple materials