Realizable effective fractional viscoelasticity in heterogeneous materials

•Fractional viscoelasticity can be obtained by homogenization with purely elastic and viscous constituents.•2D hierarchical checkerboard microstructures allow to achieve different fractional orders.•Microstructures which attain the Hashin–Shtrikman estimates present classical effective viscoelasticity. This note addresses the overall viscoelastic behaviour of composite materials made of elastic and viscous phases. By considering different microstructures, it is shown that classical or fractional viscoelasticity can be achieved. Hierarchical checkerboard microstructures are proposed to build fractional viscoelastic materials.