## 3 Methodology of Numerical Investigations  
To determine the effect of imperfections, shown in Figure 2, on the signal disturbances measured in SHPB experiments when a pulse-shaping technique was used, a 3D finite element model was built. A finite element model of the SHPB arrangement used in the numerical analyses corresponded to the experimental set-up presented in Paper 14. The model contains not only all important components of the arrangement (Figure 4), i.e., bars, sample, striker, but also a pulse shaper, slide bearings, and a barrel. The bars and the striker, which work within an elastic limit, are described by eight-node solid elements with single-point integration. Through numerical experiments, the size of the finite elements describing the bars and the striker was chosen such that they allow a very good mapping of not only the amplitude and duration of the propagating pulses but also the rise and fall time of the pulses and the Pochhammer-Chree high-frequency oscillations. The number of elements in the cross-section was 316, and the average dimension of the elements was 0.3 mm. In total, each of the bars is described by more than 2 M nodes and approximately 1.9 M elements, and the striker is modeled by more than 300,000 nodes and 280,000 elements. Due to the large deformation of the specimen, and particularly the shaper, fully integrated solid elements were used with element formulations applicable to poor aspect ratios and an accurate formulation [15]. The specimen is described by more than 3000 nodes and 2100 elements (91 elements in the cross-section). In turn, the shaper is described by more than 14,000 nodes and 10,700 elements (1380 elements in the cross-section). The deformation of the specimen and the shaper occurs along the bar axis; therefore, the size of the elements in this direction is larger at 0.05 mm, compared to 0.04 mm, which is the average size of the elements in the shaper cross-section. The full FEM included more than 4.4 million nodes and 4.1 million hexahedral elements. The use of symmetry of the analyzed SHPB set-up shortened the computational time, while maintaining the appropriately sized element without deteriorating the accuracy of the analyses. Between the interacting surfaces, contact was defined based on a contact-impact algorithm, the parameters of which were established based on the author's previous work [21]. A segment-to-segment method, namely the mortar method, was used to describe the contact between the surfaces. This approach is based on the projection of integration points onto the master segment with a penalty regularization of contact tractions [22; 23]. For the mortar method, the contact constraints are fulfilled in a weak way. It shows the optimal convergence behavior when compared to the node-to-segment methods. This type of contact even allows for an accurate analysis of phenomena in which interacting parts are described by finite elements with significantly different sizes [24; 25; 26]. Additionally, [PERSON]'s law was used to predict the friction between the interacting surfaces. The friction coefficient was equal to 0.06, which corresponds to greased surfaces [27]. Figure 4: A schematic diagram of the SHPB set-up used in the numerical analysis. The bars, striker, barrel, and slide bearings were given elastic material properties of maraging steel: [PERSON]'s modulus \(E_{B}=207\) GPa, [PERSON]'s ratio \(\
u=0.3\), and density \(\rho=7800\) kg/m\({}^{3}\)[28].