Emergent elasticity relations for networks of bars with sticky magnetic ends

Abstract

Magneto-elastic materials have unique mechanical properties arising from the coupling between the magnetic and elastic components, which can be used in many engineering applications, such as waveguide systems, impact mitigation, and soft robotics. Traditional designs of magneto-elastic materials embed magnets or magnetic particles in a monolithic body. Under extreme conditions, the elastic matrices are prone to permanent damage and loss of functionality. An alternative framework was previously proposed by the authors in which 2D magneto-elastic networks were created through vibration-driven self-assembly from a dilute system of elastic bars with sticky magnetic ends. While these networks were demonstrated to fail gracefully under extreme loading and re-assemble under random excitation, how their emergent elasticity depends on magnet and elastic member characteristics remains to be fully understood. In this paper, to calculate the 2D bulk modulus of a given magneto-elastic network, particle dynamics simulations are first performed. An analytical framework is then developed to predict the bulk modulus of derived networks with varying design parameters, such as bar length and magnetic strength, based on the Cauchy–Born approximation. Through dimensional analysis, we demonstrate that 2D bulk modulus is linearly proportional to a composite variable that combines magnet strength, elastic member length, and wall thickness of the magnet holder, as evidenced by the collapse of 120 systems onto a single line. The numerical and analytical investigation of the bulk modulus of this architected magneto-elastic material demonstrates the broad tunability of its emergent elasticity, thereby enabling a myriad of promising applications of these systems.