Return Point Memory Research Articles

Modeling the interaction between instabilities and functional degradation in shape memory alloys

Localization of the stress-induced martensitic phase transformation plays an important role in the fatigue behavior of shape memory alloys (SMAs). The phenomenon of return-point memory that is observed during the subloop deformation of a partially-transformed SMA is a clear manifestation of the interaction between localized phase transformation and degradation of the functional properties. The present study aims to demonstrate this structure–material interaction in the modeling of return-point memory. It seems that this crucial aspect has been overlooked in previous modeling studies. For this purpose, we developed a gradient-enhanced model of pseudoelasticity that incorporates the degradation of functional properties in its constitutive description. The model is employed to reproduce the hierarchical return-point memory in a pseudoelastic NiTi wire under isothermal uniaxial tension with nested subloops. Additionally, a detailed analysis is carried out for NiTi strip with a more complex transformation pattern. Our study highlights the subtle morphological changes of phase transformation under different loading scenarios and the resulting implications for return-point memory.

Controlled pathways and sequential information processing in serially coupled mechanical hysterons

The complex sequential response of frustrated materials results from the interactions between material bits called hysterons. Hence, a central challenge is to understand and control these interactions, so that materials with targeted pathways and functionalities can be realized. Here, we show that hysterons in serial configurations experience geometrically controllable antiferromagnetic-like interactions. We create hysteron-based metamaterials that leverage these interactions to realize targeted pathways, including those that break the return point memory property, characteristic of independent or weakly interacting hysterons. We uncover that the complex response to sequential driving of such strongly interacting hysteron-based materials can be described by finite state machines. We realize information processing operations such as string parsing in materia, and outline a general framework to uncover and characterize the FSMs for a given physical system. Our work provides a general strategy to understand and control hysteron interactions, and opens a broad avenue toward material-based information processing.

Effect of axial preloads on torsional behavior of superelastic shape memory alloy tubes – experimental investigation and simulation/predictions of intricate inner loops

Shape memory alloy (SMA) devices (utilizing wires/rods, springs or tubes) engage unique superelastic/pseudoelastic (SE) phenomenon for large stroke recovery, energy dissipation and damping applications. In particular, SMA components in torsion are also generally subjected to some pre-tension loads and hence understanding their combined effects on the torsional response is vital. In this work, some intricate internal loop and outer loop responses (large twists > 1500°) of SMA tubes under different twisting-untwisting scenarios are investigated to understand the effects of static pre-load on torsional responses. Key SMA hysteretic features like sink point memory (SPM) and return point memory (RPM) have not been well understood under torsion (with and without axial loads) have been investigated here. Further, a modified two variant thermodynamic Preisach modeling approach is proposed to simulate responses of twisted tubes with varying extents of twist and different axial loads. The central principle here is the use of a Gibbs Potential framework to separate the dissipative and thermoelastic parts of the SE responses using well established thermodynamic principles and then utilizing a non-ideal switching type disjunctive Preisach model to fit the nonlinear hysteretic dissipative section of the SE response. By using the outer loop response for model calibration, other complex loading unloading scenarios leading to intricate internal loops and effects of axial loads on these can be predicted. It is also shown that addition of a single interior loop detail for model calibration significantly enhances prediction of other more intricate internal loops. This approach dramatically simplifies the experimental data needed for the simulation of SMA components even under complex loading.

Rate-independent hysteretic energy dissipation in collagen fibrils.

Nanoindentation cycles measured with an atomic force microscope on hydrated collagen fibrils exhibit a rate-independent hysteresis with return point memory. This previously unknown energy dissipation mechanism describes in unified form elastoplastic indentation, capillary adhesion, and surface leveling at indentation velocities smaller than 1 μm s-1, where viscous friction is negligible. A generic hysteresis model, based on force-distance data measured during one large approach-retract cycle, predicts the force (output) and the dissipated energy for arbitrary indentation trajectories (input). While both quantities are rate independent, they do depend nonlinearly on indentation history and on indentation amplitude.

Parameters calculation method of energetic model for symmetrical static hysteresis loop and asymmetrical minor loop

PurposeThis paper aims to propose an energetic model parameter calculation method for predicting the materials’ symmetrical static hysteresis loop and asymmetrical minor loop to improve the accuracy of electromagnetic analysis of equipment.Design/methodology/approachFor predicting the symmetrical static hysteresis loop, this paper deduces the functional relationship between magnetic flux density and energetic model parameters based on the materials’ magnetization mechanism. It realizes the efficient and accurate symmetrical static hysteresis loop prediction under different magnetizations. For predicting the asymmetrical minor loop, a new algorithm is proposed that updates the energetic model parameters of the asymmetrical minor loop to consider the return-point memory effect.FindingsThe comparison of simulation and experimental results verifies that the proposed parameters calculation method has high accuracy and strong universality.Originality/valueThe proposed parameter calculation method improves the existing parameter calculation method’s problem of relying on too much experimental data and inaccuracy. Consequently, the presented work facilitates the application of the finite element electromagnetic field analysis method coupling the hysteresis model.

Hysteresis and return point memory in the random-field Blume-Capel model.

We study the zero-temperature steady-state of the random-field Blume-Capel model with spin-flip Glauber dynamics on a random regular graph. The magnetization m as a function of the external field H is observed to have double hysteresis loops with a return point memory. We also solve the model on a Bethe lattice in the approximation that the spin relaxation dynamics is abelian and find good agreement between simulations on random regular graphs and Bethe lattice calculations for negative values of H.

Memory from coupled instabilities in unfolded crumpled sheets

Crumpling an ordinary thin sheet transforms it into a structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and memory retention. A central challenge in explaining these behaviors lies in understanding the contribution of the complex geometry of the sheet. Here we combine cyclic driving protocols and three-dimensional (3D) imaging to correlate the global mechanical response and the underlying geometric transformations in unfolded crumpled sheets. We find that their response to cyclic strain is intermittent, hysteretic, and encodes a memory of the largest applied compression. Using 3D imaging we show that these behaviors emerge due to an interplay between localized and interacting geometric instabilities in the sheet. A simple model confirms that these minimal ingredients are sufficient to explain the observed behaviors. Finally, we show that after training, multiple memories can be encoded, a phenomenon known as return point memory. Our study lays the foundation for understanding the complex mechanics of crumpled sheets and presents an experimental and theoretical framework for the study of memory formation in systems of interacting instabilities.

Delicate memory structure of origami switches

While memory effects emerge from systems of wildly varying lengthscales and timescales, the reduction of a complex system with many interacting elements into one simple enough to be understood without also losing the complex behavior continues to be a challenge. Here, we investigate how bistable cylindrical origamis provide such a reduction via tunably interactive memory behaviors. We base our investigation on folded sheets of Kresling patterns that function as two-state memory units. By linking several units, each with a selected activation energy, we construct a one-dimensional material that exhibits return-point memory. After a comprehensive experimental analysis of the relation between the geometry of the pattern and the mechanical response for a single bit, we study the memory of a bellows composed of four bits arranged in series. Since these bits are decoupled, the system reduces to the Preisach model, and we can drive the bellows to any of its 16 allowable states by following a prescribed sequence of compression and extension. We show how to reasonably discriminate between states by measuring the system's total height and stiffness near equilibrium. Furthermore, we establish the existence of geometrically disallowed defective stable configurations that expand the configuration space to 64 states with a more complex transition pattern. Using empirical considerations of the mechanics, we analyze the hierarchical structure of the corresponding diagram, which includes Garden of Eden states and subgraphs. We highlight two irreversible transformations, namely shifting and erasure of defects, leading to memory behaviors reminiscent of those observed with more complex glassy systems.3 MoreReceived 29 June 2021Revised 4 November 2021Accepted 21 January 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.013128Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFunctional materialsMechanical metamaterialsOrigami & KirigamiShape memory effectTechniquesGeometryGraph theoryMechanical testingCondensed Matter, Materials & Applied PhysicsGeneral PhysicsPolymers & Soft MatterStatistical Physics

Profusion of transition pathways for interacting hysterons.

The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.

Degeneracy and hysteresis in a bidisperse colloidal ice

We use numerical simulations to investigate the low-energy states of a bidisperse colloidal ice, realized by confining two types of magnetic particles into double wells of different lengths. For this system, theoretical calculations predict a highly degenerate ground state where all the vertices with zero topological charge have equal energy. When raising the applied field, we find a re-entrant transition where the system passes from the initial disordered state to a low-energy one and then back to disorder for large interaction strengths. The transition is due to the particle localization on top of the central hill of the double wells, as revealed from the position distributions. When we decrease the applied field, the system displays hysteresis in the fraction of low-energy vertices, and a small return point memory by cycling the applied field.

State transition graph of the Preisach model and the role of return-point memory.

The Preisach model has been useful as a null model for understanding memory formation in periodically driven disordered systems. In amorphous solids, for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by Mungan etal. [Phys. Rev. Lett. 123, 178002 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.178002], the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between soft spots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying soft-spot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return-point memory in organizing thegraphinto a hierarchy of loops and subloops. Our analysis reveals that the topology of a large portion ofthisgraph is actually not governed by the values of the switching fields that describe the hysteretic behavior of the individual elements but by a coarser parameter, a permutation ρ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states |R| constituting the main hysteresis loop and its nested subloops. We find that |R| is equal to the number of increasing subsequences contained in the permutation ρ.

Dynamic Hysteresis Loops Modeling of Electrical Steel With Harmonic Components

The broad application of electronic device in the power systems requires a practical model to characterize the hysteresis loops of electrical steel excited with harmonic components. However, the existing dynamic models may not be appropriate for application because of their complexity and neglect of the minor loops caused by harmonics. This article proposes a new algorithm that updates model parameters with magnetization history to modify Tellinen model. The improved model can consider the return-point memory effect to describe the static hysteresis loops containing minor loops. Also, a new dynamic model is built to characterize dynamic loops with harmonic components by combining the improved model with the thin sheet model. The new model only requires the quasi-static major hysteresis loops and dynamic major hysteresis loops under sinusoidal excitation to identify parameters. A comparison between the measured and calculated results under both sinusoidal and harmonic excitations shows good agreement and validates the accuracy of the proposed model.

Global memory from local hysteresis in an amorphous solid

A disordered material that cannot relax to equilibrium, such as an amorphous or glassy solid, responds to deformation in a way that depends on its past. In experiments we train a 2D athermal amorphous solid with oscillatory shear, and show that a suitable readout protocol reveals the shearing amplitude. When shearing alternates between two amplitudes, signatures of both values are retained only if the smaller one is applied last. We show that these behaviors arise because individual clusters of rearrangements are hysteretic and dissipative, and because different clusters respond differently to shear. These roles for hysteresis and disorder are reminiscent of the return-point memory seen in ferromagnets and many other systems. Accordingly, we show how a simple model of a ferromagnet can reproduce key results of our experiments and of previous simulations. Unlike ferromagnets, amorphous solids' disorder is unquenched; they require "training" to develop this behavior.

Networks and Hierarchies: How Amorphous Materials Learn to Remember.

We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions joined by occasional one-way transitions. The highly connected regions include hierarchically organized hysteresis cycles and subcycles. At small to moderate strains this organization leads to near-perfect return point memory. The transitions in the network can be traced back to localized particle rearrangements (soft spots) that interact via Eshelby-type deformation fields. By linking topology to dynamics, the network representations provide new insight into the mechanisms that lead to reversible and irreversible behavior in amorphous solids.

Memory formation in matter

Memory formation in matter is a theme of broad intellectual relevance; it sits at the interdisciplinary crossroads of physics, biology, chemistry, and computer science. Memory connotes the ability to encode, access, and erase signatures of past history in the state of a system. Once the system has completely relaxed to thermal equilibrium, it is no longer able to recall aspects of its evolution. Memory of initial conditions or previous training protocols will be lost. Thus many forms of memory are intrinsically tied to far-from-equilibrium behavior and to transient response to a perturbation. This general behavior arises in diverse contexts in condensed matter physics and materials: phase change memory, shape memory, echoes, memory effects in glasses, return-point memory in disordered magnets, as well as related contexts in computer science. Yet, as opposed to the situation in biology, there is currently no common categorization and description of the memory behavior that appears to be prevalent throughout condensed-matter systems. Here we focus on material memories. We will describe the basic phenomenology of a few of the known behaviors that can be understood as constituting a memory. We hope that this will be a guide towards developing the unifying conceptual underpinnings for a broad understanding of memory effects that appear in materials.

Minimal descriptions of cyclic memories

Many materials that are out of equilibrium can ‘learn’ one or more inputs that are repeatedly applied. Yet, a common framework for understanding such memories is lacking. Here, we construct minimal representations of cyclic memory behaviours as directed graphs, and we construct simple physically motivated models that produce the same graph structures. We show how a model of worn grass between park benches can produce multiple transient memories—a behaviour previously observed in dilute suspensions of particles and charge-density-wave conductors—and the Mullins effect. Isolating these behaviours in our simple model allows us to assess the necessary ingredients for these kinds of memory, and to quantify memory capacity. We contrast these behaviours with a simple Preisach model that produces return-point memory. Our analysis provides a unified method for comparing and diagnosing cyclic memory behaviours across different materials.

The Structure of State Transition Graphs in Systems with Return Point Memory: I. General Theory

We consider the athermal quasi-static dynamics (AQS) of disordered systems driven by a slowly varying external field. Our interest is in an automaton description (AQS-A) that represents the AQS dynamics in terms of the graph of state transitions triggered by the driving field. A particular feature of these systems is return point memory (RPM), a tendency for the system to return to the same microstate upon cycling the field. It is known that the existence of three conditions, (1) a partial order on the set of configuration; (2) a no-passing property; and (3) an adiabatic response to monotonous driving fields, implies RPM. When periodically driven, such systems settle into a cyclic response after a transient of at most one period. However conditions (1)-(3) are only sufficient but not necessary. In fact, we show that the AQS dynamics naturally provides a more selective partial order which, due to its connection to hysteresis loops, is a natural choice for establishing RPM. This enables us to consider AQS-A exhibiting RPM without necessarily possessing the no-passing property. We call such automata $\ell$AQS-A and work out the structure of their state transition graphs. Our central finding is that RPM constrains the {\em intra-loop} structure of hysteresis loops, namely its hierarchical organization into sub loops, but not the {\em inter-loop} structure. We prove that the topology of the intra-loop structure has a natural representation in terms of an ordered tree and that the corresponding state transition graph is planar. On the other hand, the RPM property does not significantly restrict inter-loop transitions. A system exhibiting RPM and subject to periodic forcing can thus undergo a large number of transient cycles before settling into a periodic response. Such systems can even exhibit subharmonic response.

Phase Coexistence and Kinetic Arrest in the Magnetostructural Transition of the Ordered Alloy FeRh

In materials where two or more ordering degrees of freedom are closely matched in their free energies, coupling between them, or multiferroic behavior can occur. These phenomena can produce a very rich phase behavior, as well as emergent phases that offer useful properties and opportunities to reveal novel phenomena in phase transitions. The ordered alloy FeRh undergoes an antiferromagnetic to ferromagnetic phase transition at ~375 K, which illustrates the interplay between structural and magnetic order mediated by a delicate energy balance between two configurations. We have examined this transition using a combination of high-resolution x-ray structural and magnetic imaging and comprehensive x-ray magnetic circular dichroism spectroscopy. We find that the transition proceeds via a defect-driven domain nucleation and growth mechanism, with significant return point memory in both the structural and magnetic domain configurations. The domains show evidence of inhibited growth after nucleation, resulting in a quasi-2nd order temperature behavior.

Scanning of Adsorption Hysteresis In Situ with Small Angle X-Ray Scattering.

Everett’s theorem-6 of the domain theory was examined by conducting adsorption in situ with small angle x-ray scattering (SAXS) supplemented by the contrast matching technique. The study focuses on the spectrum differences of a point to which the system arrives from different scanning paths. It is noted that according to this theorem at a common point the system has similar macroscopic properties. Furthermore it was examined the memory string of the system. We concluded that opposite to theorem-6: a) at a common point the system can reach in a finite (not an infinite) number of ways, b) a correction for the thickness of the adsorbed film prior to capillary condensation is necessary, and c) the scattering curves although at high-Q values coincide, at low-Q values are different indicating different microscopic states. That is, at a common point the system holds different metastable states sustained by hysteresis effects. These metastable states are the ones which highlight the way of a system back to a return point memory (RPM). Entering the hysteresis loop from different RPMs different histories are implanted to the paths toward the common point. Although in general the memory points refer to relaxation phenomena, they also constitute a characteristic feature of capillary condensation. Analogies of the no-passing rule and the adiabaticity assumption in the frame of adsorption hysteresis are discussed.

Energy landscape scheme for an intuitive understanding of complex domain dynamics in ferroelectric thin films

Fundamental understanding of domain dynamics in ferroic materials has been a longstanding issue because of its relevance to many systems and to the design of nanoscale domain-wall devices. Despite many theoretical and experimental studies, a full understanding of domain dynamics still remains incomplete, partly due to complex interactions between domain-walls and disorder. We report domain-shape-preserving deterministic domain-wall motion, which directly confirms microscopic return point memory, by observing domain-wall breathing motion in ferroelectric BiFeO3 thin film using stroboscopic piezoresponse force microscopy. Spatial energy landscape that provides new insights into domain dynamics is also mapped based on the breathing motion of domain walls. The evolution of complex domain structure can be understood by the process of occupying the lowest available energy states of polarization in the energy landscape which is determined by defect-induced internal fields. Our result highlights a pathway for the novel design of ferroelectric domain-wall devices through the engineering of energy landscape using defect-induced internal fields such as flexoelectric fields.