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The purpose of this paper was to verify the possibility of applying differential calculus of incomplete order to describe relaxation of the material obtained using selective laser sintering (SLS) technology.

The samples were made using the incremental technology for three print directions. Relaxation tests were conducted. The theoretical curves, which are the solution of the equation describing the five-parameter Maxwell-Wiechert model for derivatives in relation to the total time of complete order and fractional order, were adjusted to the obtained experimental curves.

The SLS technology creates new possibilities regarding modelling polymeric elements which might be applied as functional models (products). Therefore, it is necessary to conduct an in-depth study of their properties, including relaxation properties, which is associated with the necessity to use proper mathematical tools to describe those properties. The differential calculus of incomplete order was applied herein to describe the anisotropy of relaxation properties because of the print direction in relation to the relaxation curves adjusted with the five-parameter Maxwell-Wiechert model.

As a result of the conducted considerations, the authors obtained the dependencies describing the anisotropy of relaxation properties with the use of coefficients alpha and beta, which stand for the derivative order of the differential equation, whereas coefficient kappa stands for the translation coefficient which is an innovative application of this type of mathematical apparatus.

The developed method might be applied to describe the anisotropy of a broader group of materials manufactured with the use of incremental technologies.

The application of the differential calculus of incomplete order to describe the anisotropy of the materials manufactured from polyamide powder using the SLS technology is a distinctive feature of this paper. A crucial cognitive element of the conducted research is the fact which confirms that the dynamic viscosity coefficients have the greatest impact on the anisotropy of material properties depending on the print directions.

This paper aims to investigate the suitability of additive manufacturing to produce O-ring seals.

The O-rings were made by the PolyJet-Matrix technology using four different digital materials and then tested for relaxation properties under static and dynamic (sliding) conditions. The approximation of the relaxation curves involved modelling with a Prony series.

The PolyJet-Matrix technology offers new opportunities to model elastomeric elements, with examples being the O-rings produced and tested for their relaxation properties. Describing the behaviour of the particular materials fabricated with this technology by using relaxation functions will extend the knowledge base on digital materials.

The four types of photopolymers used in the experiment differed in viscoelastic properties. The analysis of the stress relaxation of the O-ring models was performed at four different step displacements of the loading element.

The test results may be useful for the design of O-ring seals made of new elastomeric materials. The relaxation properties of the O-rings made of such materials can be applied to analyse the dynamics of seals, for instance, face seals.

The originality of the work lies in the use of digital materials to design and produce elastomeric elements with different relaxation properties, which was confirmed by the test results. This paper presents results of a relaxation analysis for a ring model and the material that the ring is made of. It also discusses how 3D printing and digital materials can be applied in practice.