A semi-rigid method of rotating triangular auxetic mechanical metamaterials

The rotating triangular auxetic structure is a mechanical metamaterial characterized by a pronounced negative Poisson's ratio and nonlinear stiffness, with wide-ranging applications in energy harvesting and absorption. Existing analyses of its mechanical performance primarily rely on finite element methods (FEM), which are hindered by lengthy computation times and accuracy sensitivity to mesh quality. To overcome these challenges, we introduce an innovative semi-rigid solution method that conceptualizes the auxetic structure as a series of rigid rods and plates connected by torsional springs. By establishing the relationship between equivalent torsional spring parameters and the geometrical characteristics of the auxetic structure, the static analysis is transformed into an efficient multi-rigid-body system evaluation. This method reveals the intrinsic influence of geometric parameters on the mechanical behavior of the auxetic structure and enables accurate numerical evaluation of rotating triangular auxetic metamaterials under arbitrary deformation lengths, geometric configurations, and material parameters—completely independent of FEM simulations. Validation through FEM simulations and experimental tests confirms that the discrepancy between the proposed method's predictions and experimental data remains typically below 10 %. In contrast to FEM, the approach substantially decreases the number of elements and degrees of freedom by several orders of magnitude and reduces computation time by one to three orders of magnitude, thereby drastically lowering computational costs and obviating the need for mesh independence verification. Moreover, this method and framework can be extended to auxetic structures composed of arbitrary rotating polygons, offering an efficient means of generating large datasets essential for machine learning-based inverse design, thereby facilitating enhanced performance of auxetic structures in energy harvesting and absorption applications.