Numerical and experimental predictions of the static behaviour of thick sandwich beams using a mixed {3,2}-RZT formulation

This paper presents a numerical and experimental assessment of the static behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory ($\text{RZ}{T}_{\left\{3,2\right\}}^{\left(m\right)}$). The displacement field of the $\text{RZ}{T}_{\left\{3,2\right\}}^{\left(m\right)}$ assumes a piecewise continuous cubic zigzag distribution for the axial contribution and a smoothed parabolic variation for the transverse one. At the same time, the out-of-plane stresses are assumed continuous a-priori: the transverse normal stress is given as a third-order power series expansion of the thickness coordinate, whereas the transverse shear one is derived through the integration of Cauchy's equation. The equilibrium equations and consistent boundary conditions are derived through a mixed variational statement based on the Hellinger-Reissner (HR) theorem and a penalty functional to enforce the strain compatibilities between the assumed independent stress fields and those obtained with the constitutive equations. Based on the proposed model, a simple C⁰-continuous two-node beam finite element is formulated ($2B-\text{RZ}{T}_{\left\{3,2\right\}}^{\left(m\right)}$). Firstly, the analytical and FE model accuracies of the presented formulation are addressed, and comparisons with the available three-dimensional elasticity solutions are performed. Subsequently, an experimental campaign is conducted to evaluate the static response of various thick sandwich beam specimens in three- and four-point bending configurations. The thick beam specimens are equipped with Distributed Fibre Optic Sensors (DFOS) embedded in the sandwich layup to measure axial deformation at the sandwich interfaces directly. Finally, the experimental data are compared with the available numerical models, highlighting the formulated numerical model's performances and limitations.