Elastic-plastic mechanical properties of cross-shaped honeycomb materials using Timoshenko bending theory and Hill failure criterion

Resumo

Honeycomb materials are characterized by a periodic structure composed of unit cells that exhibit interesting properties such as a high stiffness-to-weight ratio, functional versatility, and structural efficiency. Due to these characteristics, these materials are employed in various fields including architecture, engineering, and biomedicine. The mechanical properties of such materials are intrinsically influenced by the topology of the cells, which determines the overall response of the cellular medium. Therewith, the modeling and characterization of the mechanical behavior of cellular materials have intensified in recent decades, emphasizing nonlinear responses under different loading conditions. Numerical models are usually based on the theories of elasticity and plasticity. Therefore, the present study aims to investigate the mechanical properties of two-dimensional cellular materials, focusing on unit cells with cross-shaped topology. The proposed model uses planar frame members based on Timoshenko bending theory combined with a plasticity analysis. The classic Hill criterion characterizes the failure modes. For the analyzed problems, the global response was obtained through numerical homogenization. The results showed good agreement with the available experimental data.