A theoretical model for the estimate of plateau force for the crushing process of 3D auxetic anti-tetra chiral structures

Abstract

Auxetic, anti-tetra-chiral structures designed as tubes subjected to axial quasi-static crushing were investigated in this research. Experimental work was carried on samples manufactured by laser cutting from a pipe. At the same time, numerical simulations were performed using a parametric numerical model of the structure. The experimental results analysis revealed that the crushing force presents a plateau region that extends up to the densification phase defined by the close contact between the ligaments joining the nodes. Subsequently, based on the representative unit's deformation characteristics, theoretical calculation models were established to estimate the plateau force. According to Bernoulli's beam model, the force calculation model was developed from the plastic hinge's structural design and theory. Sametime, the length or crushing distance with a constant force (plateau), can be estimated to provide the complete set of parameters for design activities. The analytical solution was validated against results obtained numerical simulation for various configurations. There is a good agreement between experimental, numerical, and theoretical results that proves the proposed model's reliability to estimate plateau force. Furthermore, individual parts were stacked to define graded structures. It was found that the crushing force displays successive stages according to each individual part. There is a possibility to reconstruct the response for stacked structure from the individual response using the analytical solution's results for force and length of individual plateau stages.The set of equations can design this structure when the capable load is one of the input parameters.