## 4 Conclusions  
Mechanical properties of polystyrene-based composites filled with carbon particles of different dimensionality (0D, 1D, and 2D) and at different concentrations (0.1, 0.5, and 5 wt%) were analyzed using a set of static and dynamic tests. The stress-strain performance of composite samples was studied in tensile and three-point bending tests, and dynamic mechanical and ultrasonic analysis. At low concentrations of 0.1 wt% and 0.5 wt%, all nanofillers did not provide significant improvement in the elastic characteristics of composites. More efficient reinforcement was observed at the concentration of 5 wt%. Among the filler types, some increase in composite rigidity was observed with the addition of carbon particles with a high axial ratio (nanotubes). The introduction of the layered filler (graphene) led to the most pronounced increase in material rigidity in three-point bending tests, under static and dynamic loads, and in measurements of ultrasound velocity. Note that due to the observed existence of some amounts of filler aggregates in composite samples functionalization of filler particles or utilization of a masterbatch could improve reinforcement of composites. Filling of the polystyrene matrix with spherical or filamentary particles provided the formation of an isotropic structure of the composite, while two-dimensional particles formed an anisotropic structure. Depending on the expected type of loading of elements produced by these materials, it is possible to choose the most efficient dispersed filler.  
A comparison of the static and dynamic elastic properties of nanocomposites with carbon inclusions showed that the addition of nanoparticles provided an increase in the elastic properties at different frequencies. For all studied composites, the average value of the mechanical loss tangent in the frequency range from 20 Hz to 2 MHz was consistent with the DMA results in the range of 1-50 Hz, which corresponds to the weak frequency dependence of the mechanical loss tangent, that is characteristic for amorphous thermoplastics. The conclusions obtained on the value of mechanical loss tangent allow for a better understanding of the dynamics of polymeric materials and polymer-based composites and for applying the obtained values to describe nonlinear and viscoelastic effects in such materials. Nonlinear elastic moduli demonstrate much more pronounced variations with frequency than the mechanical loss tangent and, therefore, can provide additional important information needed to accurately describe and predict the viscoelastic behavior of polymer-based composite materials. The future direction of our work can be in the thorough analysis of nonlinear elastic properties of the composites with carbon allotropes.  
Conceptualization and methodology, O.A.M., A.V.B., Y.M.B. and I.V.S.; validation and investigation, O.A.M., A.V.B. and A.A.Z.; data curation and writing, O.A.M., A.V.B., Y.M.B. and I.V.S. All authors have read and agreed to the published version of the manuscript.  
The financial support from Russian Science Foundation under the grant # 22-72-10083 is gratefully acknowledged.  
Not applicable.  
Data Availability Statement: Data are available within the paper.  
Authors are grateful to Ioffe Institute for providing equipment used in experiments.  
The authors declare no conflict of interest.