Modeling tri-field coupling in an innovative sport equipment: Electro-magneto-elastic response of a G-Ori metamaterial structure

Rong Qi , Mintao Li , Mostafa Habibi

Abstract

This study presents a theoretical framework for analyzing multi-field coupled behavior in shear deformable sandwich beams, targeting advanced sports equipment such as a functionally graded baseball bat. The structure comprises a graphene origami-reinforced copper matrix core sandwiched between piezoelectric (top) and piezomagnetic (bottom) face-sheets, enabling interaction with external electric and magnetic fields. A higher-order thickness-stretched theory is employed to overcome limitations of classical models, capturing transverse shear and normal strain effects essential for thick sandwich configurations. The formulation integrates two-dimensional constitutive relations for elastic, piezoelectric, piezomagnetic, and thermo-elastic responses, with appropriate field equations describing electric potential and magnetic induction distributions. Equilibrium equations are derived systematically via the principle of virtual work, incorporating mechanical, thermal, electrical, and magnetic contributions to yield the full set of governing equations and boundary conditions. The proposed model provides a foundational basis for designing smart baseball bats capable of vibration damping through applied electric potentials or impact energy harvesting via the piezomagnetic effect under thermal environments, supporting the development of sensor-integrated intelligent sports equipment.

Key Words

auxetic metamaterial; electro-magneto-elastic results; folding; graphene origami; initial electric/ magnetic potentials; shear and normal deformation theory

Address

Rong Qi — 1Institute of physical Education, Shanghai normal University, Shanghai 200234, China
Mintao Li — 2School of Intelligent Manufacturing, Wenzhou Polytechnic, Wenzhou 325000, Zhejiang, China
Mostafa Habibi — Technical Sciences, Chennai, India/ Department of Mechanical Engineering, Faculty of Engineering, Haliç University, Istanbul, Turkey/ Department of Biomaterials, Saveetha Dental College and Hospital, Saveetha Institute of Medical and Technical Sciences, Chennai, 600077, India

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