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Proc Natl Acad Sci U S A
Proc Natl Acad Sci U S A
PNAS
Proceedings of the National Academy of Sciences of the United States of America
0027-8424
1091-6490
National Academy of Sciences

38527196
202317340
10.1073/pnas.2317340121
videoVideoresearch-articleResearch ArticleengEngineering416
Physical Sciences
Engineering
Intelligent electroactive material systems with self-adaptive mechanical memory and sequential logic
El Helou Charles a 1
Hyatt Lance P. a 1 https://orcid.org/0000-0002-1143-8003

Buskohl Philip R. b
Harne Ryan L. ryanharne@psu.edu
a 2
aDepartment of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802
bFunctional Materials Division, Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson AFB, OH 45433
2To whom correspondence may be addressed. Email: ryanharne@psu.edu.
Edited by Nicholas Boechler, University of California, San Diego, CA; received October 6, 2023; accepted February 9, 2024 by Editorial Board Member John A. Rogers

1C.E.H. and L.P.H. contributed equally to this work.

25 3 2024
2 4 2024
25 9 2024
121 14 e231734012106 10 2023
09 2 2024
Copyright © 2024 the Author(s). Published by PNAS.
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

Significance

An autonomous engineered system composed of soft matter components would more seamlessly operate in natural environments and enable decentralized intelligence in mechanical materials and structures. The challenge is to make this happen by endowing the system with the ability to sense, think, and remember information without central control. In this work, we demonstrate a soft, electroactive platform that integrates digital logic and memory to enable self-adaptive sequential behavior. The introduced framework is scalable to facilitate advanced computing operations such as solving linear algebraic equations through basic optimization algorithms. The underlying principles developed here establish a foundation for general intelligence that can be implemented in soft material systems across a myriad of applications.

By synthesizing the requisite functionalities of intelligence in an integrated material system, it may become possible to animate otherwise inanimate matter. A significant challenge in this vision is to continually sense, process, and memorize information in a decentralized way. Here, we introduce an approach that enables all such functionalities in a soft mechanical material system. By integrating nonvolatile memory with continuous processing, we develop a sequential logic-based material design framework. Soft, conductive networks interconnect with embedded electroactive actuators to enable self-adaptive behavior that facilitates autonomous toggling and counting. The design principles are scaled in processing complexity and memory capacity to develop a model 8-bit mechanical material that can solve linear algebraic equations based on analog mechanical inputs. The resulting material system operates continually to monitor the current mechanical configuration and to autonomously search for solutions within a desired error. The methods created in this work are a foundation for future synthetic general intelligence that can empower materials to autonomously react to diverse stimuli in their environment.

intelligent materials
mechanical material systems
mechanical computing
DOD | USA | AFC | CCDC | Army Research Office (ARO) 100000183 W911NF-23-1-0314 Ryan L Harne DOD | USAF | AMC | Air Force Office of Scientific Research (AFOSR) 100000181 n/a block grant to AFRL Philip Buskohl U.S. Air Force Research Lab Summer Faculty Fellowship n/a Ryan L Harne
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pmcRealizing intelligence in synthetic matter has been at the forefront of recent research. To be considered intelligent, a material system must integrate sensing, processing, memory, and actuation capabilities (1–3). Motivated to create synthetic embodiments of intelligence, researchers have proposed approaches such as brain-inspired neural networks modeled after learning processes found in living systems (4, 5). These efforts have been formulated via strictly mathematical constructs (4–6) and in physical models using interconnected analog components (7, 8). Lin et al. created diffractive neural network layers that are trained to passively classify optical signals (9). Mechanical beam networks are also shown to exhibit stiffness tuning to adapt and mimic neural network functionalities in engineered mechanical metamaterials (10, 11). Such metamaterials or material systems exhibit tailorable behaviors and properties not seen in natural materials (12). While these methods are a promising avenue for intelligence, the material systems lack intrinsic means to process complex information and update computation as required for intelligent matter.

Moreover, there are benefits to achieving intelligence in soft matter based on the potential for deformation modes (13, 14) and reversible shape configurations (15, 16) that afford functional versatility to the material system. Such characteristics are cultivated in elastomeric systems and coupled with other physics to integrate key functional elements of intelligent behavior (17–20). For instance, Kotikian et al. (21) developed self-sensing liquid crystal elastomer (LCE) actuators with embedded conductive elements that exhibit closed-loop feedback adaptation. Nonvolatile memory may also be realized in multistable soft structures through bistable unit cell designs (22, 23) and magnetic interactions (24, 25).

Unconventional computing techniques have also been investigated to embed information processing functionality in mechanical materials. Unlike the top–down neuromorphic embodiments, these methods abstract digital bits found in bistate material behaviors (26–28). Simple logic gates have been developed in embodiments including origami-based systems (29), serially connected bistable elastic structures (30), fluidic networks (31, 32), and acoustic transistors (33). El Helou et al. (34) coupled the mechanical logic found in reconfigurable soft structures with conductive integrated circuits to demonstrate a template for combinational logic information processing. The material senses and processes digitized mechanical stress, yet only possesses volatile memory and thus cannot adapt or change its output based on past inputs or states.

Along with computing based on combinational logic, recent works have approached the use of sequential logic operations in material systems. Sequential logic incorporates the history or memory of previous states with new inputs to determine subsequent behaviors. Zeng et al. (35) introduced soft liquid crystal network actuators whose reaction to light can be adjusted based on conditioned responses to heat and light. Other works have showcased sequential logic components such as shift registers and D flip-flops in rigid mechanical systems (36) and microfluidic networks (37) to perform complex logic operations. While these innovative works incorporate some elements of sequential logic, a comprehensive integration of self-actuating behavior with the processing of new and stored information is yet to be established in a soft material system (38).

Here, we introduce an electroactive soft mechanical material system that can perform complex sequential logic operations with integrated mechanical memory and self-adaptive functionality. The system is implemented on a multistable platform composed of magnetoelastic bistable elements that convert analog displacement inputs into digital mechanical configurations and store the states in nonvolatile mechanical–electrical memory. Soft LCE electroactive actuators reconfigure the material shape through the electrically conductive network that interconnects signals from among the functional elements. By extensively building on the logic design model introduced by El Helou et al. (34) with the introduction of nonvolatile memory, self-actuation, and autonomy, here we present a template for materials that cultivate requisite functionalities for intrinsic intelligent behavior in inanimate soft matter.

Building Block of Sequential Logic in Mechanical Material Systems

An integration of the fundamental elements of intelligence is analogous to combinational logic with memory and sequential iterative timing capability. Such elements are connected as illustrated in the sequential logic computing loop in Fig. 1A. All systems in this research are built upon this architecture with a mechanical–electrical network (combinational logic) that electrically governs electroactive actuators to reconfigure a mechanical multistable platform (memory).

Fig. 1. Design of the mechanical 1-bit T flip-flop. (A) Fundamental sequential logic computing loop for a single T flip-flop system. (B) Design of the mechanical 1-bit T flip-flop material system. (C) Logic diagram of the T flip-flop. (D) Fabrication process for electroactive liquid crystal elastomer (LCE) actuators. (E) Schematic of bistable rows to obtain nonvolatile memory through magnetic insert alignments.

A 1-bit building block of this computing architecture is demonstrated through the toggle T flip-flop material design in Fig. 1B. The T flip-flop mechanical–electrical network (Fig. 1A, light blue block) is programmed with a constant high input (T=1) based on the logic that is described by the characteristic table in Fig. 1C. This network recognizes the present mechanical configuration as a digital input, Qn, and outputs two types of digital electrical signals that are categorized as output signals (LED1, LED0) and updating signals, (ΔQn,ΔQn′), The present state of the updating signals governs the electroactive actuators to reach the next mechanical configuration, Qn+1. The integer n is a state index and an iterative representation of the sequential cycle (Fig. 1A).

Electroactive LCEs are utilized for the self-actuating functional element (Fig. 1A, yellow block). Fig. 1D demonstrates the LCE fabrication process and standardized length scale of all actuator units utilized in this report. Each unit is composed of a silver thermoplastic polyurethane (Ag-TPU) heating element that is embedded between two partially cross-linked LCEs as seen in step (i) of Fig. 1D. To create an anisotropic alignment of the LCE mesogens, the material is stretched to 100% strain (ε100%) and then exposed to ultraviolet (UV) irradiation in step (ii). The standard actuator units seen in step (iii) are obtained with a width, length, and average resistance of 10 mm, 50 mm, and 1.63 Ohm (SD 0.53 Ohm), respectively. When power is applied across the Vcc terminals, the material temperature increases due to Joule heating. As a result, the material reduces in length and exerts a toggle force when molded into the multistable material system. See the Materials and Methods for details about the elastomeric platform and LCE fabrication method.

Shown in Fig. 1E the nonvolatile memory results from the multistable mechanical constituent (Fig. 1A, gray block). Multistability is realized through repelling force interactions between adjacent unit cells with alternating magnetic insert alignments. See Supporting Information for more details on the magnetic inserts, SI Appendix, Fig. S1. The serial connection of bistable rows, or bits, determines the quantity of possible states (28). Thus, a single bistable row is required for a 1-bit T flip-flop platform (Fig. 1B). The digital “0” and “1” state of each bit is abstracted from the clockwise and counterclockwise orientation of each row, respectively (Fig. 1E).

For a 1-bit T flip-flop, the information processing capabilities are exhibited as a toggling state behavior (Fig. 1C). An experimental realization of such a system is shown in Fig. 2A. See supplementary text for details on the material fabrication and experimental methods. When the Vcc is electrically powered, the 1-bit material autonomously toggles between the two mechanical states. For instance, with an initial ‘0’ digital mechanical state (n=0, the initial cycle), the conductive network for ΔQ0 is connected through self-contact and the updating signal is ΔQ0=1 as indicated by the red path. Similarly, the green path is connected which powers the output signal LED0 displaying a 0. The red path powers the left electroactive actuator to exert a toggle force on the 1-bit row and switch the digital mechanical state to a 1, Fig. 1E. At such state (n=1), the output signal is ΔQ1′=1 as seen by the blue connected path. The magenta path shows the connection of the LED1 to display a 1. In this state, the electrical signal sent to the blue LCE exerts an opposing toggle force to switch the system into a 0 state.

Fig. 2. Operation and characterization of the 1-bit T flip-flop. (A) Experimental photographs of autonomous toggle behavior between state 0 (top) and state 1 (below). (B) Experimental mechanical characterization of the 1-bit bistable platform with varying magnetic strength. The solid magenta and dotted cyan curves represent systems with 4 and 2 magnets per unit cell, respectively. The red and blue dotted lines show the maximum force of the LCE actuators, with illustrated SD. (C) Experimental voltage (solid blue) and temperature (dashed red) characterization of the 1-bit clock timing and LCE Joule heating thermal behavior.

To understand the underlying mechanics of such behavior, mechanical characterization of the electroactive LCE actuators and bistable platform are experimentally studied and shown in Fig. 2B. See SI Appendix for more details on the mechanical characterization. It is evident that the platform mechanical response is a bistable behavior as an opposing critical force is required to retrieve the original state. The critical force is tailored through the magnetoelastic properties of each unit cell. Here, the maximum forces required to toggle the bistable state are 1.0 N and 1.6 N for 2 (dotted cyan) and 4 (solid magenta) magnets per unit cell, respectively. Therefore, the effective horizontal 2.5 N (SD 0.44 N) average maximum force exhibited by a LCE actuator in its 60° orientation is sufficient to toggle/set the memory state of each bit.

By constantly powering the Vcc with (T=1), a periodic oscillating behavior that represents the intrinsic system clock is realized. Movie S1 demonstrates the 1-bit toggling behavior. An experimental characterization of the voltage cycle period Pn for the 1-bit T flip-flop material determines the steady-state period to be 27.2 s, Fig. 2C, when the driving voltage is about 2.8 V. It is evident that the transient cycles (n<3) demonstrate longer periods between switch events due to the Joule heating initially required to approach operating temperature. Once the 1-bit clock is at operating temperature, the steady-state energy consumption is 5.5 W (at 1.96 A). Increasing or decreasing the driving voltage results in a corresponding decrease or increase in the period of the 1-bit clock cycles. SI Appendix, Fig. S3 shows a comparison of the periodic operation at different input voltages. The 1-bit T flip-flop and the intrinsic clock behavior illustrated here are fundamental for the development of advanced sequential logic operations.

Multibit Counting Operation

With the constituents outlined in the T flip-flop material, the autonomous toggling capability can be extended to higher bit materials to facilitate counting. To create a counter with j-bits, multiple T flip-flop circuits can be connected in series as seen in Fig. 3A. By connecting the outputs of previous T flip-flops to the inputs of subsequent elements, the resulting outputs are consecutive binary numbers for each time step n. The design of a 2-bit counter mechanical material system is presented in Fig. 3 B and C. The urethane rubber platform is composed of two serially connected bistable rows Q1n and Q2n that correspond to the bits in the binary number (Q2n,Q1n)2. The state of each bit is controlled by two LCE actuators that apply antagonistic toggling forces on each row, as commanded through the conductive network. As shown in Fig. 3B, the 1-bit T flip-flop in Fig. 1B is contained within the 2-bit counter network as outlined in green. Powered by the Vcc, electrical current is distributed through the open or closed Ag-TPU conductive paths to the updating signals (ΔQ2n,ΔQ2n′,ΔQ1n,ΔQ1n′) to reconfigure to the next digital mechanical state (Q2n+1,Q1n+1)2 via Joule heating of the LCE actuators.

Fig. 3. Design of the mechanical 2-bit counter. (A) Logic diagram illustrating the structure of higher bit counter circuits. (B) Material design of the mechanical 2-bit counter material system. (C) Photograph of the 2-bit counter material. (D) Configuration cycle for the 2-bit counter with timing diagram below. The solid blue curve indicates the state of Q1, and the dotted green curve indicates the state of Q2.

The design of the Ag-TPU processing network is undertaken using a technique developed here that expands on methods outlined by El Helou et al. (34). Instead of truth tables for combinational logic, here we introduce characteristic tables to compose the sequential logic network connectivity. Characteristic tables are initially determined for Q2n+1 and Q1n+1 of the 2-bit counter by analyzing the outputs of two serially connected T flip-flops as outlined in the dotted red box in Fig. 3A. The changes (Δ) in state are determined by comparing the outputs calculated for the next state (Q2n+1,Q1n+1) to the present state of the bits (Q2n,Q1n). Minimized characteristic Boolean functions are then extracted in the sum of product form to determine the updating signal functions (ΔQ2n,ΔQ2n′,ΔQ1n,ΔQ1n′). These functions are outlined in SI Appendix, Eqs. S1–S4. Such functions are utilized to design the network shown in Fig. 3B. It is essential to note that (ΔQ2n′,ΔQ1n′) are not the true negated terms of (ΔQ2n,ΔQ1n) since the digital outputs are a representation of the change (Δ) in present state n. This significantly improves the electrical efficiency of the material because the LCE actuators are only powered when a change in state is required. In other words, once the next mechanically stable state is achieved, the LCE actuator that pulled the material row into that state is thereafter disconnected from electrical current. An automated design tool is developed to design all of the sequential logic networks found in this report. See SI Appendix, section S3 for details on the Boolean characteristic method and functions.

The timing behavior of the LCE actuators governs the transitions between the 4 (22) possible states of the 2-bit counter, Fig. 3D. Starting from any configuration (Q2n,Q1n)2, the material autonomously counts up to decimal 3, which is the binary number (1,1)2, and then repeats the cycle from decimal 0, in other words the binary number (0,0)2. A challenge inherent in the counting operation of mechanical systems is the synchronization of bit transitions. Due to slight variations (SI Appendix, Fig. S2) in the resistance and fabrication of each LCE actuator, transitions that involve multiple transitions can introduce errors as highlighted by the fault regions in Fig. 3D. For example, as the material system transitions from (0,1)2 to (1,0)2, both bits need to toggle to the opposite state. If the second bit transitions first, the material enters the (1,1)2 configuration before reaching the correct state. To mitigate such challenges, alternative incrementing solutions can be implemented as reported in the following sections of this work.

Solving Linear Algebraic Equations

To illustrate the intelligent nature of this mechanical material foundation, we scale the design principles into a material system that can autonomously reconfigure itself to solve mathematical equations based on mechanical inputs. Specifically, the material system introduced in Fig. 4 solves a linear algebraic equation inspired by a neural network neuron using a directed optimization algorithm. In many conventional feedforward neural networks, a dot product relates an input X vector and weight vector Wn to an output scalar Yn. When compared to the desired output Yd, the weight vector is updated to approach a solution within an acceptable error threshold. In this study, a system with two independent integer inputs x1 and x2 are paired with unknown integer weights w1 and w2 as seen in Eq. 1.[1] Yn=x1w1n+x2w2n=XT·Wn=x1x2T·w1nw2n.

Fig. 4. Design of the linear algebraic equation solver. (A) Sequential logic computing loop to solve linear algebraic equations. (B) Schematic of the 3-layer, 8-bit material design. The top 4-bit passive rows (green) correspond to the mechanical input vector X. The bottom 4-bit active rows (red) correspond to the adaptive mechanical weight vector Wn. The conductive processing network with electrical output terminals ΔWn is highlighted via the blue paths. (C) Block logic diagram of the mechanical–electrical network with X, and Wn inputs, and Wn+1.

The objective of the material system is to autonomously identify a vector Wn that produces an output within an acceptable error threshold. For this study, the desired output Yd=9 and desired error Ed=3 are selected for integers x1, x2, w1, w2 between 0 and 3. Note that because Eq. 1 has two unknowns, there are an infinite number of possible values of Wn that result in an acceptable solution. To identify an appropriate combination, an iterative algorithm is needed. Fig. 4A illustrates the sequential logic computing cycle employed in this work. The present material state and processing cycle counter are represented by the integer n.

Here, the input vector X is obtained from a mechanical analog to digital converter (ADC) (39) which converts an analog displacement to a digital material configuration. The dot product of the input vector X and the weight vector Wn results in a present solution Yn. The present solution is compared to a programmed desired output Yd to identify the present error En in Eq. 2.[2] En=Yd-Yn.

If the present error is greater than the desired error Ed, the algorithm implements a conditional exhaustive search routine to provide the values of the subsequent weight vector Wn+1. By comparing Wn+1 to Wn, the vector for the change in weights ΔWn is determined. A Gray code incrementing scheme is employed to ensure that ΔWn only involves a single-bit state transition. The use of Gray code avoids the synchronization challenges seen in Fig. 3D. Additional details about the conditional Gray code algorithm are found in SI Appendix, Fig. S4. For the problem presented here, a conditional exhaustive search is feasible with the current solution space of 16 possible weight combinations. For larger systems with more rows or bits, a more efficient search algorithm may be necessary. Other search algorithms like simulated annealing or gradient descent may be implemented with the appropriate logic diagram structure using the methods described here and in previous work (34).

The resulting vector ΔWn is a set of electrical signals that control the electroactive actuators and multistable platform to update the digital mechanical weight values Wn. Such process is autonomously repeated until a solution Yn is found to satisfy the error inequality En≤Ed, at which time the updating electrical signals to the LCE actuators are ΔWn=0. At this point, the material system will idle in the resulting configuration until a new input is applied or the weight values are manually perturbed.

To implement the presented sequential logic operations in a physical mechanical material system, an 8-bit mechanical material system is developed as seen in Fig. 4B. The information processing network that governs the 8 update signals ΔWn is designed through the Boolean characteristic method and the logic operation in Fig. 4C. The high-level logic block diagram in Fig. 4C identifies the general flow of information through logic components (multipliers, adders, subtractors, comparators) (34) and the integration of 4-bit counting operations that facilitate the sequential Gray code incrementation. The resulting characteristic equations are described in SI Appendix, Eqs. S5–S12. Such a network involves 36 columns that interconnect the 8-bit multistable platform. To increase the computing density, a 2-layer material system is utilized with 20 unit-cell columns each, Fig. 4B. To facilitate the input of two independent mechanical displacements, the eight layers are divided into three sections: two passive 2-bit input rows highlighted in green, and a 4-bit active updating material highlighted in red. The columns between the three units are electrically connected to complete the conductive processing network shown in blue. The passive 4-bit multistable rows of the 2-layer material correspond to the digital mechanical input vector X with 2-bit binary number capacity for x1:(x1,1,x1,2)2 and x2:(x2,1,x2,2)2. Through unique unit cell designs of such rows, a mechanical analog-to-digital converter (ADC) is realized based on techniques developed by Hyatt and Harne (39) to convert the input analog displacement into a digital, binary mechanical configuration. The input material rows convert bidirectional analog linear displacement (x1)10 and (x2)10 to sequential digital mechanical states (x1,1,x1,2)2 and (x2,1,x2,2)2. Additional details on the ADC materials are in SI Appendix, Fig. S5.

The 2-bit x1 and x2 passive, ADC rows are separated from the 4-bit active rows that correspond to the digital mechanical weight vector Wn. This involves two vector components w1n:(w1,1n,w1,2n)2 and w2n:(w2,1n,w2,2n)2 with 2-bit binary number capacity each. The Ag-TPU processing network governs the electrical updating signal vector ΔWn and the 8 LCE electroactive actuators through the 8 output terminals (Δw1,1n,Δw1,1n′,Δw1,2n,Δw1,2n′,Δw2,1n,Δw2,1n′Δw2,2n,Δw2,2n′). To visualize the present weight vectors Wn, an LED display grid is controlled by a third processing layer, whose operation is seen in Movie S2.

Operation of the Linear Algebraic Equation Solver

In Fig. 5, we exemplify the behaviors of the intelligent material system by investigating the operation of the material based on a given input. Fig. 5A is a photograph of the mechanical material system described in this work. The applied analog displacements represent an X input vector of 1,3 in Fig. 5B. The initial weight vector W0 is arbitrarily chosen to be 0,0.

Fig. 5. Operation of the linear algebraic solver for inputs X=(1,3). (A) Photograph of the linear algebraic solver mechanical material system. (B) Mechanical ADC configurations as inputs (C) Initial configuration of the material system with photographs of the transition event. (D) Updated configuration continuing to search for solution. (E) Configuration which indicates an acceptable solution. (F) Solution space showing all possible errors (red surface), desired solution (blue line), and acceptable error (blue surface). The red, yellow, and green dots correspond to the configurations in C–E.

Based on the input configurations and initial weight vector, the material autonomously searches for the solution when connected to a voltage supply of 4 V as outlined in Fig. 5 C–E. In the initial state (n=0), Fig. 5C, highlighted in red, the processing network outputs an electrical current to an LCE that transitions the top layer w1,20 to 1. Photographs of the transition event show how a previously disconnected electrical trace connects after the material system changes configuration. At the next state (n=1), Fig. 5D, highlighted in yellow, the error E1 is reduced to 7. The material system processes the updated configuration and outputs a signal to transition the second layer w2,20 to 1. At n=2, Fig. 5E, highlighted in green, the system settles at a solution with weight values of W2=(2,2) and an acceptable error E2=1. Note that with the conditional Gray code searching algorithm, the optimum solution is not guaranteed if an acceptable solution is found first.

The solution space for this configuration is visualized in Fig. 5F where the error En is shown for the inputs shown in Fig. 5B. The red surface represents the possible errors for all combinations of weight values w1 and w2. An acceptable solution is represented by any point on the red surface below the blue plane of desired error Ed. The solid blue line represents the desired output Yd where the error is 0. The red, yellow, and green points on the red surface indicate the error of the configurations in Fig. 5 C–E, respectively.

While the system is searching for a solution, the average power consumption of the updating layers is approximately 7.4 W. Once a solution is reached, no power is required because the multistable platform maintains the present configuration and remains in an idle state. If a user updates the input displacement to the ADC layers, the material automatically processes the updated configuration and searches for an acceptable solution. Movie S2 captures the sequence shown in Fig. 5 and the continued autonomous operation of the intelligent material system with two additional sequences of updated inputs. These sequences are explored in SI Appendix, Fig. S6. While the operations in this work highlight five states, the 8-bit mechanical material has a memory capacity of 256 (27) possible configurations of inputs X and weights Wn. Note that in the presented linear algebraic solver, there exist sets of input vectors such that there are no possible weight vectors that represent an acceptable solution. For example, for inputs x1=x2=0, the mechanical material will never find a solution as the error will always be greater than 3. In such cases, the weights will cycle through the solution space indefinitely due to the nature of the conditional Gray code algorithm. Alternate search algorithms may include termination criteria to prevent infinite operation.

Discussion

The presented mechanical material systems here illustrate the capability of a mechanical material system to memorize past physical configuration to complete complex sequential logic operations. The 8-bit material introduced in this research, Fig. 4, exemplifies a versatile approach to autonomously processing and memorizing information in a mechanical material system to solve linear algebraic equations. These linear equations form the basis of conventional neural networks. Our design framework can be used to increase the memory capacity and information processing density to potentially approach deep neural network functionality. Moreover, considering the combinational logic integrated circuit formulation in the sequential logic operations embodied through the electroactive material circuits presented here, any integrated circuit may be realized in soft material systems (34). In other words, in applications with numerous sensor-actuator pairs, such as in haptics devices, our foundation may facilitate a future for self-sufficient, self-updating sensor-actuators that no longer require central information processing.

The implementation of autonomous materials capable of processing information can enable advancements in fields such as soft robotics with the ability to control complex gait sequences for improved locomotion (40) and offer greater adaptability in unstructured environments. In aerospace and automotive industries, such autonomous material systems can lead to the development of adaptive aerodynamic surfaces that can adjust based on dynamic loading conditions. Ultimately, these advancements represent a significant step toward practical, intelligent material systems with wide-ranging applications.

Certainly, our soft computing platform is not comparable to the speed of conventional, microprocessor-based computers. For example, the average clock period of 27.2 seconds indicates our material has a computing speed of 36.8 mHz, which pales to modern microprocessors operating in the GHz range. Yet, the principles developed here provide a scalable approach and foundation to realize soft intelligent matter in an integrated material system. Expanding on the requirements outlined in ref. 34, the functionality of the presented material system is dependent on the presence of independent bistate configurations integrated with a mechanical–electrical network, stability or memory, and a self-actuation electroactive element that allows the material system to autonomously reconfigure. The principles introduced here can be generalized to other mechanical material systems at any scale provided that the specified elements are present.

In summary, we introduce an approach to enable intelligent behavior in inanimate soft matter. This class of material system combines all the elements of intelligence: sensing, information processing, memory, and actuation (1). This type of narrow intelligence enables the mechanical material system to independently carry out specialized tasks (41). As multiple intelligent behaviors are integrated and nested using diverse stimuli as inputs, a future platform for synthetic general intelligence is possible, empowering broad adaptation to the environment (42).

Materials and Methods

Material Substrate Fabrication.

The elastomeric substrate is cast in a two-part mold that is 3D printed (FlashForge Creator Pro) with acrylonitrile butadiene styrene. The assembled, two-part mold creates the negative of the material shape with channels for the conductive traces and holes for the inserted magnets. Liquid urethane rubber (Smooth-On VytaFlex 60) material is mixed by hand for 3 min. A black dye (Smooth-On So-Strong) is added to the liquid urethane (1 to 3% of total urethane mass) for visual contrast with the conductive network of ink. The liquid urethane is poured into the mold and cures for 16 h at room temperature. Once cured, the material substrate is demolded and prepared for conductive ink deposition. The fabrication technique is reported in previous studies (28, 34).

Conductive Ink Fabrication for Electrical Network and Heating Elements.

The composition of the AgTPU conductive ink is 35% (volume % (v%)) Ag microflakes (Inframat Advanced Materials, 47MR-10F) and 65% (v%) TPU elastomer (BASF Elastollan Soft 35A). The Ag microflakes are added to a vial with sufficient N-Methyl-2-pyrrolidone (NMP) solvent and sonicated (Branson M2800 Ultrasonic Cleaner) for 60 min. The TPU is added to the Ag-NMP mixture and planetary mixed (KK 300SS Mazerustar) at 225 × g for 2 min. The planetary mixing process is repeated three times with gentle hand-stirring in between to ensure that the walls of the vial do not collect aggregates. This Ag-TPU fabrication procedure can be found in previous studies (28, 34).

After the urethane rubber substrate is demolded, enamel-coated copper wire (22 gauge) is passed to each terminal surface by piercing the urethane rubber from the rear-facing surface opposite the network channels. The enamel is removed from the extremities of the wires, and they are utilized to power the networks (Vcc) and connect the outputs to the LCE actuators. Similar wires are used to connect the networks of the weight (Wn) and input (X) rows which are separated as shown in Fig. 5A. Using a 3.0-cc dispensing syringe with a 27-gauge needle, the Ag-TPU ink is then deposited in the channels and allowed to cure around the copper wires for 24 h.

To create the heating elements for the LCE actuators outlined in Fig. 1D, a mask with a 1.5-mm serpentine path is laser cut (Epilog Mini Helix) in cardstock (0.3mm thick). An aluminum plate is polished with grade #00 steel wool and cleaned by acetone and isopropanol to remove unwanted particulates. A release agent (Smooth-On Ease Release 200) is then sprayed on the aluminum plate. The cut mask is fixed to the prepared plate and Ag-TPU is spread onto the masked surface. Once the serpentine pattern is filled, the mask is removed. Segments of copper wire (28 gauge) are placed on each of the ends of the pattern, and a drop of Ag-TPU ink is added to create an electrical connection between the wire and pattern. The plate with Ag-TPU patterns is placed in an oven at 100 °C for 45 min to accelerate the evaporation of the NMP solvent. The pattern is removed from the oven and allowed to cool to room temperature. The heating element is then gently scraped from the aluminum plate.

Liquid Crystal Elastomer Actuators.

The liquid crystal elastomers (LCE) are synthesized with two monomers 1,4-Bis-[4-(6-acryloyloxyhexyloxy)benzoyloxy]-2-methylbenzene (RM82) and 1,4-Bis-[4-(3-acryloyloxypropyloxy)benzoyloxy]-2-methylbenzene (RM257), a chain extender 2,2′-(ethylenedioxy) diethanethiol (EDDT), a cross-linker 1,3,5-triallyl-1,3,5-triazine-2,4,6(1H,3H,5H)-trione (TATATO), an inhibitor butylated hydroxytoluene (BHT), a catalyst triethylamine (TEA), and photoinitiator Irgacure I-369. All materials are purchased from Sigma-Aldrich.

A mixture of 51.1% [weight% (wt%) of total mixture] RM82 and 17.0% (wt%) RM257 is heated and vortexed for homogenous mixing until melted. The chain extender 23.9% (wt%) EDDT, cross-linker 4.4% (wt%) TATATO, and inhibitor 1.0% (wt%) BHT are added to the monomer mixture, heated, and vortexed. The catalyst 1.0% (wt%) TEA, and photoinitiator 1.5% (wt%) I-369 are added while shielded from fluorescent light to prevent premature photocuring of the elastomer. The mixture is then poured into silicone molds (25 mm × 12.5 mm × 0.4mm) and transferred to an oven at 70 °C for 3 h. The molded samples are removed from the oven and allowed to cool to room temperature while shielded from the light.

The fabrication process is illustrated in Fig. 1D. The Ag-TPU heating element is sandwiched between two partially cross-linked cooled samples. The assembly is pressed together and stretched longitudinally to a length of 50 mm (100% strain). The stretched assembly is photocured under UV irradiation (385 nm) for 10 min to obtain the LCE actuator.

Supplementary Material

Appendix 01 (PDF)

Movie S1. Operation of a 1-bit T flip-flop material system. The material automatically toggles between ‘0’ and ‘1’ states. Electrical signals are sent to an LED display to show the current state of the material.

Movie S2. Operation of the linear algebraic equation solver. The design of the material is summarized, and three sequences are shown. Analog displacement inputs are applied, and the material autonomously updates its configuration to search for a solution of a linear algebraic equation with two unknown values.

We acknowledge helpful conversations with Ms. Haley Tholen, Dr. Taylor Ware, Dr. Christopher E. Tabor, and Ms. Yoo Jin Lee over the duration of this work. This research is supported in part by funds from a U.S. Air Force Research Lab Summer Faculty Fellowship, the Air Force Office of Scientific Research, and the Army Research Office.

Author contributions

C.E.H., L.P.H., and R.L.H. designed research; C.E.H. and L.P.H. performed research; C.E.H., L.P.H., P.R.B., and R.L.H. analyzed data; and C.E.H., L.P.H., P.R.B., and R.L.H. wrote the paper.

Competing interests

The authors declare no competing interest.

Data, Materials, and Software Availability

All study data are included in the article and/or supporting information.

Supporting Information

This article is a PNAS Direct Submission. N.B. is a guest editor invited by the Editorial Board.
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1 C. Kaspar, B. J. Ravoo, W. G. van der Wiel, S. V. Wegner, W. H. P. Pernice, The rise of intelligent matter. Nature 594 , 345–355 (2021).34135518
2 M. A. McEvoy, N. Correll, Materials that couple sensing, actuation, computation, and communication. Science 347 , 1261689 (2015).25792332
3 C. A. Aubin , Towards enduring autonomous robots via embodied energy. Nature 602 , 393–402 (2022).35173338
4 Y. LeCun, Y. Bengio, G. Hinton, Deep learning. Nature 521 , 436–444 (2015).26017442
5 D. Silver , Mastering the game of Go with deep neural networks and tree search. Nature 529 , 484–489 (2016).26819042
6 K. Hornik, M. Stinchcombe, H. White, Multilayer feedforward networks are universal approximators. Neural Netw. 2 , 359–366 (1989).
7 L. G. Wright , Deep physical neural networks trained with backpropagation. Nature 601 , 549–555 (2022).35082422
8 L. Mennel , Ultrafast machine vision with 2D material neural network image sensors. Nature 579 , 62–66 (2020).32132692
9 X. Lin , All-optical machine learning using diffractive deep neural networks. Science 361 , 1004–1008 (2018).30049787
10 R. H. Lee, E. A. Mulder, J. B. Hopkins, Mechanical neural networks: Architected materials that learn behaviors. Sci. Robotics 7 , eabq7278 (2022).
11 L. Jin , Guided transition waves in multistable. Proc. Natl. Acad. Sci. U.S.A. 117 , 2319–2325 (2020).31969454
12 P. Jiao, J. Mueller, J. R. Raney, X. Zheng, A. H. Alavi, Mechanical metamaterials and beyond. Nat. Commun. 14 , 6004 (2023).37752150
13 A. Bossart, D. M. Dykstra, J. Van der Laan, C. Coulais, Oligomodal metamaterials with multifunctional mechanics. Proc. Natl. Acad. Sci. U.S.A. 118 , e2018610118 (2021).34001603
14 C. El-Helou, R. L. Harne, Exploiting functionally graded elastomeric materials to program collapse and mechanical properties. Adv. Eng. Mater. 21 , 1900807 (2019).
15 A. Pal, V. Restrepo, D. Goswami, R. V. Martinez, Exploiting mechanical instabilities in soft robotics: Control, sensing, and actuation. Adv. Mater. 33 , 2006939 (2021).
16 L. P. Hyatt, R. L. Harne, Rapid pneumatic control of bimodal, hierarchical mechanical metamaterials. Adv. Eng. Mater. 24 , 2101375 (2022).
17 X. Xia, C. M. Spadaccini, J. R. Greer, Responsive materials architected in space and time. Nat. Rev. Mater. 7 , 683–701 (2022).35757102
18 S. Jiang , Flexible metamaterial electronics. Adv. Mater. 34 , 2200070 (2022).
19 C. Coulais, E. Teomy, K. De Reus, Y. Shokef, M. Van Hecke, Combinatorial design of textured mechanical metamaterials. Nature 535 , 529–532 (2016).27466125
20 X. Xia , Electrochemically reconfigurable architected materials. Nature 573 , 205–213 (2019).31511685
21 A. Kotikian , Innervated, self-sensing liquid crystal elastomer actuators with closed loop control. Adv. Mater. 33 , 2101814 (2021).
22 Q. Zhang, K. Barri, Z. L. Wang, A. H. Alavi, “Digital information storage mechanical metamaterials” in Smart Materials, Adaptive Structures and Intelligent Systems (American Society of Mechanical Engineers, V001T01A004, 2022).
23 Y. Chi , Bistable and multistable actuators for soft robots: Structures, materials, and functionalities. Adv. Mater. 34 , 2110384 (2022).
24 T. Chen, M. Pauly, P. M. Reis, A reprogrammable mechanical metamaterial with stable memory. Nature 589 , 386–390 (2021).33473228
25 A. Pal, M. Sitti, Programmable mechanical devices through magnetically tunable bistable elements. Proc. Natl. Acad. Sci. U.S.A. 120 , e2212489120 (2023).37011212
26 L. J. Kwakernaak, M. van Hecke, Counting and sequential information processing in mechanical metamaterials. arXiv [Preprint] (2023). 10.48550/arXiv.2302.06947 (Accessed 12 February 2023).
27 H. Yasuda , Mechanical computing. Nature 598 , 39–48 (2021).34616053
28 C. El Helou, P. R. Buskohl, C. E. Tabor, R. L. Harne, Digital logic gates in soft, conductive mechanical metamaterials. Nat. Commun. 12 , 1633 (2021).33712597
29 B. Treml, A. Gillman, P. Buskohl, R. Vaia, Origami mechanologic. Proc. Natl. Acad. Sci. U.S.A. 115 , 6916–6921 (2018).29915077
30 J. R. Raney , Stable propogation of mechanical signals in soft media using stored elastic energy. Proc. Natl. Acad. Sci. U.S.A. 113 , 9722–9727 (2016).27519797
31 D. J. Preston , Digital logic for soft devices. Proc. Natl. Acad. Sci. U.S.A. 116 , 7750–7759 (2019).30923120
32 A. Rajappan , Logic-enabled textiles. Proc. Natl. Acad. Sci. U.S.A. 119 , e2202118119 (2022).35994641
33 O. R. Bilal, A. Foehr, C. Daraio, Bistable metamaterial for switching and cascading elastic vibrations. Proc. Natl. Acad. Sci. U.S.A. 114 , 4603–4606 (2017).28416663
34 C. El Helou, B. Grossmann, C. E. Tabor, P. R. Buskohl, R. L. Harne, Mechanical integrated circuit materials. Nature 608 , 699–703 (2022).36002486
35 H. Zeng, H. Zhang, O. Ikkala, A. Priimagi, Associative learning by classical conditioning in liquid crystal network actuators. Matter 2 , 194–206 (2020).31984376
36 T. Mei, C. Q. Chen, In-memory mechanical computing. Nat. Commun. 14 , 5204 (2023).37626088
37 S. Ahrar, M. Raje, I. C. Lee, E. E. Hui, Pneumatic computers for embedded control of microfluidics. Sci. Adv. 9 , eadg0201 (2023).37267360
38 C. D. Santangelo, Making smarter materials. Nat. Mater. 22 , 3–4 (2023).36333610
39 L. P. Hyatt, R. L. Harne, Programming metastable transition sequences in digital mechanical materials. Extreme Mech. Lett. 59 , 101975 (2023).
40 Q. He , Electrically controlled liquid crystal elastomer-based soft tubular actuator with multimodal actuation. Sci. Adv. 5 , eaax5746 (2019).31646178
41 M. Haenlein, A. Kaplan, A brief history of artificial intelligence: On the past, present, and future of artificial intelligence. California Manag. Rev. 64 , 5–14 (2019).
42 B. Goertzel, Artificial general intelligence: Concept, state of the art, and future prospects. J. Artifi. Gen. Intell. 5 , 1–46 (2014).
