In recent years, manufacturing has paved the way to advance structural properties using 3D printed structures by constructing complex shapes. The elastic properties of such structures depend on the periodic arrangement of the internal lattices. Honeycomb is one such lattice structure 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 like magnetostrictive or piezoelectric patches over the substrate layers of the lattice. The analytical expressions have been developed for honeycomb/ auxetic honeycomb lattice considering the Euler-Bernoulli beam bi-layer 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. However, it does not produce consistent results as the thickness increases, due to the shift of the position of the neutral axis, which was earlier assumed to be at the geometric centre of the substrate beam. This paper presents a modified formulation and introduces a correction factor 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.