This PhD dissertation focuses on three distinct areas of study: Inconel Alloy 740H,polycrystalline graphene, and tetragraphene (TG). These materials each have their unique characteristics and applications, and this dissertation seeks to study and reveal their mechanical properties. The first project of this dissertation concentrates on the development and validation of a Chaboche constitutive model, incorporating combined nonlinear isotropic and kinematic hardening rules, to accurately predict the stress-strain behavior of Inconel Alloy 740H. Additionally, the material behavior of Inconel 740H is also predicted by only using the kinematic hardening rule to understand the difference in results. Inconel 740H is a high-temperature, nickel-based superalloy known for its exceptional mechanical strength, creep resistance, and corrosion resistance, making it highly suitable for extreme environmental applications. The research focuses on determining the material parameters of the unified Chaboche constitutive model and validating its accuracy using experimental data obtained from uniaxial strain-controlled loading tests. The experimental data covers a wide temperature range from the room temperature up to 600°C, with strain ranges spanning from 0.375% to 0.5%. The results, derived from both methods, demonstrate the model’s effectiveness in capturing the complex mechanical behavior of Inconel Alloy 740H under varying conditions, providing a valuable tool for design and engineering applications in high-temperature environments. The second project explores the mechanical properties of polycrystalline graphene, bridging the nanoscale to macroscale through a multiscale molecular dynamics (MD) finite element (FE) modeling approach. At the nanoscale, MD simulations are employed to study crack propagation and mechanical behavior. To address the limitations of atomic level simulations for large scale polycrystalline systems, FE analysis is used. To this aim, a multiscale modeling approach is adopted, initiating MD simulations on bicrystalline graphene sheets with different grain boundaries (GB) and atomic structures under uniaxial tension loading. These simulations provide insights into the local elastic properties of grain boundaries (GBs) using the cohesive zone model. Subsequently, the local properties derived using MD simulations are incorporated into FE simulations, which enables the modeling of large scale polycrystalline graphene sheets considering the effect of the grain boundaries. The grains are modeled as pristine graphene, and the simulations are repeated with varying grain sizes to investigate their impact on mechanical properties such as Young’s modulus and fracture stress. The results reveal a significant relationship between the grain size and the mechanical properties of polycrystalline graphene, indicating a crucial role of the grain size in its behavior. The final project of this dissertation investigates the mechanical properties of tetragraphene (TG), a quasi-2D semiconductor carbon allotrope composed of hexagonal and tetragonal rings, to address the limitations of graphene in electronic applications. MD simulations are employed to understand the fracture properties of triple-layered TG sheets with distinct atomic structures under mixed mode I and II loading. The effect of loading phase angle, temperature, crack edge chirality, and crack tip configuration on the crack propagation path and critical stress intensity factors are investigated. The findings indicate that the critical stress intensity factor and crack propagation path are influenced by these parameters, and their effect is discussed in detail.