Exponentially Graded Auxetic Structures: An Assessment of the Shear Correction Factor and Static Deflection

Abstract

This work aims to study the influence of the material and geometric parameters that characterize re-entrant hexagonal honeycomb auxetic structures in the maximum transverse static deflection of beams. In addition, this study considers the composition of the material through the thickness results from the mixture of a metallic phase and one of four different selected ceramics, using the exponential volume fraction law. The first-order shear deformation theory within an equivalent single-layer approach is used to assess the material and geometric parameters’ influence on the structures’ deflection. Considering this theoretical approach, the impact of the material and geometric parameters on the shear correction factors, calculated for each specific case, is also analyzed. The results allow us to conclude how the shear correction factors and the structures’ maximum static deflection are affected by the re-entrant hexagonal honeycomb auxetic cells’ aspect ratios, by the angle associated with the direction of the inclined members of the hexagonal cells and the use of materials with differentiated Poisson’s ratios.

Keywords

• re-entrant hexagonal honeycomb structures
• auxetic materials
• exponentially graded materials
• first-order shear deformation theory
• shear correction factor
• finite-element analysis