Fused Deposition Modeling (FDM) offers significant design flexibility for creating 3D-printed parts. However, the mechanical performance of these components remains a critical challenge. This study aims to explore the behavior of 3D-printed thermoplastic materials under static and quasi-static loading conditions through both experimental and numerical methods. For this purpose, uniaxial tensile tests are performed to generate force-displacement curves for 3D-printed PETG materials. Additionally, stress relaxation tests are conducted to characterize the time-dependent viscoelastic behavior resulting from deviations from purely static deformation. A visco-hyperelastic constitutive model is then proposed to characterize the behavior of these materials. The experimental data are utilized to calibrate the model's parameters through curve-fitting within commercial finite element software, ABAQUS. The results reveal a high degree of correlation between experimental observations and numerical predictions, confirming the model's effectiveness in representing the nonlinear behavior of the 3D-printed polymeric materials. In fact, accurate mechanical characterization of additively manufactured materials supports performance-driven design optimization and ensures structural reliability in practical applications.