Motion mem-converters: A paradigm shift in mechanical element modeling

From converters and mem-converters to an array of mechanical two-port elements

Abstract

Since the introduction of memristors, memory element theories have advanced significantly, yet their application in mechanical systems remains limited due to the dominance of force-based linear modeling thinking. This paper proposes a mem-nonlinear modeling paradigm by identifying the diamond-shaped mechanism as a motion mem-converter, a purely mechanical two-port memory element. It is demonstrated that displacement, as the across variable, should dominate the modeling of geometrically nonlinear mechanical elements, challenging the traditional force-dominated approach. Through a systematic port-variable selection method within the framework of the periodic table of mechanical elements, correct constitutive relations for diamond-shaped memory elements are derived. The validity of this paradigm is confirmed via self-consistency analysis, including conservation of co-evolution, co-action, and energy, as well as experimental validation on a diamond-shaped mem-inerter. Furthermore, the framework successfully identifies the relativistic mass as a nonlinear converter with memory properties via decomposition. Finally, converters and mem-converters are generalized to a two-port mechanical-element array, enabling the prediction of higher-order elements. This work establishes a fundamental shift from force-dominated linear modeling to an across-variable-dominated mem-nonlinear paradigm, providing a robust theoretical foundation for future mechanical memory systems.