Damping Properties Evaluation of Viscoelastic Lattice Structures

Viscoelastic polymers are increasingly employed in lattice structures for their absorption and damping capabilities, particularly in applications involving vibration suppression or impacts. These structures exhibit remarkable properties, such as high specific stiffness, specific strength and energy absorption capacity, making them highly attractive for applications in aerospace, automotive, and biomedical fields. However, the accurate modeling by taking into account frequency-dependent behavior, especially for applications involving damping, remains challenging due to the interplay between geometric complexity and material viscoelasticity. To address this challenge, this study makes use of a general numerical homogenisation method enhanced for frequency-dependent material properties in order to predict the damping of the lattice structure at the macroscopic scale. A fractional derivative constitutive model is used to describe the frequency-depend behaviour of the bulk material, while a custom Ansys APDL code is developed to adapt the homogenisation method to the case of material with frequency-dependent properties. The results demonstrate that, for lattice structures made of a single material phase, it is possible to perform the homogenisation process at an arbitrary frequency. The resulting stiffness tensor of the equivalent homogeneous anisotropic material that replaces the structure at the macroscopic scale varies with frequency according to the same law used for the bulk material at a lower scale. Furthermore, the results show that even if the stiffness tensor of the lattice structure at the upper scale exhibits elastic symmetry depending on the topology of the unit cell, the damping matrix at the upper scale is unaffected by the lattice topology.