Complex Mechanical Memory and Training via Disorder and Multiple Fields

A wide variety non-equilibrium physical systems, from disordered magnets to crumpled pieces of paper, display memory, leading to rich phenomena that are induced not merely by the present state of of a system's environment but by its entire history. One such avenue of memory formation is return point memory, in which applied fields lead to highly reproducible complex response, indicating that the system consistently returns to exact microstates under particular loading protocols. Here, we generalize prior theories by relaxing certain assumptions in the zero-temperature random-field Ising model to demonstrate return-point memory in a much broader range of systems, including mechanical metamaterials such as the disordered rotating square system. These memory effects persist even in the face of individual hysteresis and the use of multiple control fields/actuators. We explore how these memory effects can be used to efficiently train a single system to display multiple target nonlinear response curves, and how different classes of control fields are either commutative or non-commutative.