Determination of Neutral Axis and Effect of the Variation of Cross Sectional Area on the Mechanical Properties of Smart Meta-Structure

Abstract

In recent years, manufacturing has paved the way to enhance structural properties using 3D printed structures by constructing complex shapes. The properties of such structures depend on the arrangement of the internal lattices. Honeycomb is one such simple lattice struc ture that is widely used by researchers as it exhibits a high strength-to-weight ratio. However, the elastic properties of the lattice structures are intrinsic functions of the material properties and the geometric shape. Hence, it is impossible to modulate the elastic properties once constructed. Recent studies have shown that the active modulation of the elastic properties can be achieved by incorporating smart materials over the substrate layers of the lattice. The analytical expressions have been developed for honeycomb/ auxetic honeycomb lattice considering the Euler-Bernoulli bi-layer beam to determine its elastic properties. The expression is well valid for lattices where the thickness of the smart material is relatively less compared to the substrate thickness. How ever, it does not produce consistent results as the thickness of the smart material increases due to the shift of the position of the neutral axis, which was earlier assumed to be at the geomet ric centre of the substrate beam. This paper presents a modified formulation that considers the change in the position of the neutral axis as the thickness of the smart material patches varies. This modification allows the use of the analytical expression for beams with higher thickness ratios and can be used to understand the impact of forces in shear deformation. In addition, the variation in the elastic properties has also been investigated for different cross-sectional shapes such as I-section, T-section, and rectangular cross-section. The formulation presented here is generic, and the concept can be used in various futuristic multi-functional structural systems and devices across different length scales

Full Paper