The aim of this research is to determine the relaxation and creep modulus of 3D printed materials, and the numerical research is based on the finite volume method. The basic material for determining these characteristics is ABS (acrylonitrile butadiene styrene) plastic as one of the most widely used polymeric materials in 3D printing. The experimental method for determining the relaxation functions involved the use of a creep test, in which a constant increase of the stress of the material was performed over time to a certain predetermined value. In addition to this test, DMA (dynamic mechanical analysis) analysis was used. Determination of unknown parameters of relaxation functions in analytical form was performed on the basis of the expression for the storage modulus in the frequency domain. The influence of temperature on the values of the relaxation modulus is considered through the determination of the shift factor. Shift factor is determined on the basis of a series of tests of the relaxation function at different constant temperatures. The shift factor is presented in the form of the WLF (Williams-Landel-Ferry) equation. After obtaining such experimentally determined viscoelastic characteristics with analytical expressions for relaxation modulus and shift factors, numerical analysis can be performed. For this numerical analysis, a mathematical model with an incremental approach was used, as developed in earlier works although with a certain modification. In the experimental analysis, the analytical expression for relaxation modulus in the form of the Prony series is used, and since it is the sum of exponential functions, this enables the derivation of a recursive algorithm for stress calculation. Numerical analysis was performed on several test cases and the results were compared with the results of the experiment and available analytical solutions. A good agreement was obtained between the results of the numerical simulation and the results of the experiment and analytical solutions.

Linear viscoelastic materials whose characteristics are suitable for description by the Prony series use experimental data to obtain the so-called “master” curve. The analysis of experimental results with the Prony model sometimes requires prior knowledge of the time parameters of the model ,, in order to make the corresponding module more suitable for use in analytical form. In this way, the existing model is optimized to some extent, while in this paper the approach is used that all parameters in the Prony series for (E i , τ i ) were determined using the well-known least squares method and its variations. The number of members in Prony’s series is initially smaller and increases proportionately. To determine the relaxation modulus using the Prony model, an example from an available article [1] was selected in this paper, while the performed experiment was used to determine the creep modulus. During the performance of the load experiment, the function of constant increase (ramp-test) was used. The previous experiment was done for the actual material ABS plastic (Acrylonitrile butaden styrene).