Future of metamaterial-computer interaction: The combination of graphene origami and piezoelectric intelligent for application in sport pole vault

This study presents a comprehensive multi-physics analysis of wave propagation characteristics in a shear-deformable sandwich beam, employing a novel higher-order thickness-stretched model. The physical system comprises a graphene origami-reinforced copper matrix core, integrated with piezoelectric and piezomagnetic face-sheets, operating under combined thermal, electrical, and magnetic excitations. The formulation rigorously incorporates two-dimensional constitutive relations for the shear-deformable structure, coupled with the governing electric potential and magnetic induction equations. Hamilton's principle is applied to derive the system's governing equations, explicitly accounting for the interdependent effects of thermal gradients, applied electric potentials, and magnetic inductions. The results of this analysis and proposed structure can be used for application in sport equipment such as pole vault. The constitutive behavior of the innovative GOri-copper composite core is critically modeled using temperature-dependent modifier functions within the Halpin-Tsai micromechanical framework. This captures the influence of key parameters—including graphene volume fraction, origami folding degree, and thermal load—on the effective modulus of elasticity, Poisson's ratio, thermal expansion coefficient, and density of the core material. An analytical methodology is developed for the multi-field (thermal-electro-magneto-mechanical) and multi-material analysis of the composite beam structure. This approach enables systematic investigation of wave propagation sensitivity to variations in core morphology (folding degree, volume fraction), environmental conditions (temperature), and excitation parameters (electric potential, magnetic induction). A detailed verification study establishes the validity and accuracy of the proposed higher-order model and analytical solution by benchmarking against established theories and available results. The derived numerical results demonstrate significant potential for the application of this smart sandwich structure in both sensor and actuator systems. The integrated face-sheets, coupled with the tailored GOri core, provide a robust platform for real-time measurement of mechanical deformation, strain, or stress states within composite structures via the embedded electromagnetic response. Furthermore, the model offers critical insights for the design and optimization of advanced multifunctional sandwich composites operating in complex thermal and electromagnetic environments, particularly for structural health monitoring and adaptive structural control applications.