Abstract

Additive manufacturing enables creation of complex geometries. Particularly, the material extrusion (MEX) based three-dimensional printing technique, often used for thermoplastic polymers, extrudes molten material through a nozzle to form a part layer-by-layer. This process creates a complex internal structure leading to nonlocal elastic properties often called mechanical metamaterials. In the case of incorporating viscous properties, due to the wide distribution of time scales within their complex internal structures, fractional calculus offers a promising approach to incorporate the whole history for accurately describing the rheological behavior of such materials with an inherent structure. However, its adoption within the scientific community remains limited due to the unconventional notation and complex properties of the fractional operators. This study aims at providing a more accessible overview of some basic fractional rheological models, highlighting their ability to provide a unified approach to the characterisation of polymeric metamaterials. The inverse analysis is achieved by generating various fictitious datasets and fitting them to the three models. We compare three rheological models to predict the material’s response. Our findings show that even the simplest fractional rheological model effectively predicts the time-dependent behavior in many cases within one-dimensional linear viscoelasticity.

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