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

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.