## 1 Introduction
The Prony model assumes a preliminary determination of the values of the material constants of the relaxation function. As traditionally, the data from the tests for uniaxial tension-compression, not for shear, are used to obtain experimental parameters, the shear constants are calculated through relations linking them to constants from the tension-compression experiment, which are found from the experiment to determine the complex modulus (Sections 2.2 and 2.2.1). Numerical values of the temperature dependence function of the complex relaxation modulus \(E\) can be calculated on the basis of experimental data from [7; 16; 17; 18] (Section 2.2.3). Experimental graphs of the amplitude of the complex relaxation \(E\) modulus at sample cooling rates of 1, 10, and 35 \({}^{\circ}\)C/s known from [7] demonstrate a sharp increase in the modulus from 5 \(\times\) 10\({}^{7}\) Pa to 3.2 \(\times\) 10\({}^{9}\) Pa at a temperature of 173 \({}^{\circ}\)C and from 5 \(\times\) 10\({}^{7}\) Pa to 2.7 \(\times\) 10\({}^{9}\) Pa at a temperature of 143 \({}^{\circ}\)C, respectively. The model for predicting the reaction of a material during technological cooling, described in these sources, includes temperature evolution, crystallization kinetics, and a viscoelastic model for predicting thermomechanical properties. The kinetics of crystallization in semi-crystalline thermoplastic composites is considered in connection with the influence of the degree of crystallinity on the mechanical properties and possible contribution of volumetric shrinkage deformation, and the model of the nucleation and growth of crystals of Velisaris and Seferis is used to describe it [16; 17]. To predict dynamic modules in [7], a modified form of the standard linear viscoelastic solid model was used. This model was expanded to account for the effect of crystallinity on the behavior of semi-crystalline thermoplastic matrices. Experimental data describing the process of crystallization of PEEK are known from [7; 16; 17]. Study [7] presents the results of modeling the dependence of the material crystallinity degree on temperature for cooling rates of 1, 10, and 35 \({}^{\circ}\)C/s. A sharp decrease in the degree of crystallinity of the material is observed from 0.27 to 0 at 280 \({}^{\circ}\)C, from 0.24 to 0 in the temperature range from 200 to 260 \({}^{\circ}\)C, and from 0.025 to 0 in the temperature range from 200 to 250 \({}^{\circ}\)C for the corresponding cooling rates. The experimental curves of the degree of material crystallinity for cooling rates of 9.4 \({}^{\circ}\)C/min, 19.2 \({}^{\circ}\)C/min, 37.1 \({}^{\circ}\)C/min, and 55.8 \({}^{\circ}\)C/min are given in [16; 17]. A decrease in the material crystallinity degree is observed from 0.32 to 0 in 250 s, from 0.3 to 0 in 100 s, from 0.28 to 0 in 70 s, and from 0.26 to 0 in 25 s for the corresponding cooling rates. Experimental curves describing the dependence of the material crystallinity degree on time at set temperatures of 307, 310, 312, and 315 \({}^{\circ}\)C are also given in [16; 17]. The material crystallinity degree reaches values of 0.3 per 1000 s, 0.34 per 1600 s, and 0.33 per 2100 and 3200 s, respectively, at the corresponding temperatures. The dependence of the elastic modulus of the material on the crystallinity degree of the material of the sample is also known from [19]. There is an increase in the elastic modulus of the material from 2.8 to 5.5 GPa with an increase in the material crystallinity degree from 0 to 35%, respectively. The numerical modeling of the process of layer-by-layer deposition of polymer materials is considered in [20; 21; 22; 23]. The existing solutions cover all stages of the extrusion deposition process of the material: the feeding, melting, extrusion, and deposition of the substance. Models of the material feeding process allow us to calculate the optimal feed rate of the solid filament and the pushing force, as well as to take into account and minimize the effect of slipping of the filament.