Permanently Reversible Adaptive Materials (PRAM)

• PRAM is a class of adaptive materials defined by their ability to undergo reversible state changes with non-volatile retention after a transient programming stimulus.
• They utilize mechanisms such as reversible lamination, photochemical memory, dynamic covalent reconfiguration, and thermal gating to modulate properties like stiffness and magnetization.
• PRAM systems have practical applications in aerospace, robotics, RF metamaterials, and trainable matter, offering energy-efficient and durable functionality.

Permanently Reversible Adaptive Materials (PRAM) are material systems and architected structures whose functional state can be programmed by a transient stimulus, retained after that stimulus is removed, and later reprogrammed reversibly. Across the cited literature, PRAM is associated with non-volatile state retention, repeated switching without continuous holding power or electrical bias, and adaptive behavior encoded directly in material state variables such as stiffness, adhesion state, magnetization distribution, geometry, conductivity, or internal learning parameters (Chen et al., 2023, Georgiou et al., 2019, Kuang et al., 2020, Vasudevan et al., 2022, Kergariou et al., 5 Jun 2026).

1. Defining characteristics

In the cited works, PRAM is defined less by a single constituent chemistry than by a set of operational criteria. The first is reversibility: the material must switch between functional states and later return to prior states. The second is permanence, or non-volatility: after programming, the selected state is maintained without continuous power, external bias, or sustained holding field. The third is adaptivity: the material response is not fixed at fabrication, but can be altered post-fabrication or in service. In several formulations, a fourth criterion is implied or stated explicitly: repeated programming should occur without performance degradation across cycles (Georgiou et al., 2019, Kergariou et al., 5 Jun 2026).

This framing distinguishes PRAM from variable-property systems that require continuous pressure, magnetic field, or electrical drive to hold a state. Gecko-inspired laminated structures, for example, use dry adhesion so that all stiffness states are passively maintained, with electrostatic or magnetic actuation applied for approximately $1$ s only to reprogram stiffness (Chen et al., 2023). In RF metamaterials, photomechanical memcapacitors and meminductors hold their reactive state at zero electrical bias, so dense arrays can be written with momentary programming pulses and then left unbiased (Georgiou et al., 2019). In magneto-thermomechanical metamaterials, cooling below the glass transition temperature locks the deformed configuration without continued magnetic actuation, while reheating above $T_g$ unlocks recovery (Zou et al., 2022).

The literature also uses PRAM as a design target for trainable matter. In the Engineering Material Neural Networks perspective, PRAM are materials whose node parameters $\theta$ can be reconfigured reversibly and repeatedly, retain their trained values and function across many cycles, and return to earlier states under a deliberately applied counter-trigger (Kergariou et al., 5 Jun 2026). This suggests that PRAM is not confined to a single class of morphing or memory material, but functions as a cross-domain criterion spanning structural mechanics, RF metasurfaces, rheology, and physically learned metamaterials.

2. Physical mechanisms for non-volatile reversible adaptation

A major PRAM mechanism is reversible lamination. In gecko-inspired laminated structures, dry adhesives couple and decouple stiff laminates from a compliant base. Lamination activates composite bending and the parallel-axis effect; delamination returns layers to more independent bending. The reported system demonstrates hinges with up to four passively maintained reprogrammable states, decoupled from any shape reconfiguration, with an experimentally achieved stiffness modulation ratio of up to $14.4$ and simulations showing stiffness modulation ratios of at least $73.0$ (Chen et al., 2023).

A second mechanism is photochemical conformation memory. In Chua mem-components for adaptive RF metamaterials, the internal state $w(t)$ corresponds to the photomechanical expansion of an azobenzene polymer. The constitutive relations are

$q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$

for a memcapacitor, and

$\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$

for a meminductor. The polymer changes the plate spacing by up to $25\%$, and the authors report an overall capacitance variation of about $20\%$. Because the RF state is stored in photochemical metastability rather than a continuous bias condition, the device provides bias-free, nonvolatile tunability around $T_g$0 GHz (Georgiou et al., 2019).

A third mechanism is dynamic covalent network reconfiguration coupled to hard magnetism. In magnetic dynamic polymers, hard-magnetic NdFeB microparticles are embedded in a Diels–Alder network with two thermal windows. In the bond-exchange regime, targeted welding and stress relaxation occur without loss of cross-linked integrity; in the retro-Diels–Alder regime, viscosity drops sufficiently to allow particle rotation and selective magnetization reprogramming under fields as low as $T_g$1 mT. The resulting system supports targeted welding, magnetization reprogramming, and structural reconfiguration, while the field-driven morphing itself remains reversible at room temperature (Kuang et al., 2020).

A fourth mechanism is thermally gated stiffness collapse with shape locking. In magneto-thermomechanical metamaterials built from PLA and embedded NdFeB magnets, the storage modulus drops from approximately $T_g$2 GPa at $T_g$3C to approximately $T_g$4 MPa near $T_g$5C, enabling magnetic torques to actuate deformation above $T_g$6, while cooling below $T_g$7 restores a glassy, load-bearing locked state. Magnetic fields of $T_g$8–$T_g$9 mT and temperatures of $\theta$0–$\theta$1C are sufficient for untethered, reversible, reprogrammable transformations with shape locking (Zou et al., 2022).

Across these mechanisms, the state variable differs—adhesion state, cis/trans fraction, bond topology, magnetization direction, or temperature-dependent prestress—but the PRAM logic is consistent: transient write, passive hold, reversible erase or rewrite.

3. Mechanics of stiffness modulation, multistability, and thermal reset

The mechanics of PRAM often reduces to deliberate reshaping of an energy landscape. In laminated stiffness control, a general beam formulation distinguishes the adhered and delaminated states: $\theta$2

$\theta$3

The stiffness modulation ratio is therefore

$\theta$4

The operative design rule is that increasing modulus contrast, laminate thickness, and centroidal offset increases $\theta$5, while keeping stiffness modulation decoupled from external shape change (Chen et al., 2023).

In thermally reversible lattices inspired by shape-memory alloys, bistability is generated not by crystallographic phase transformation but by thermoelastic mismatch in a spring network. The single-element free energy is written as

$\theta$6

with axial force

$\theta$7

At high temperature the lattice is monostable; below a critical temperature it becomes bistable or multistable. After Liapunov–Schmidt reduction, the local bifurcation is described by

$\theta$8

This gives a high-$\theta$9 single-well landscape and a low-$14.4$0 double-well landscape, with heating restoring a unique reference configuration (Vasudevan et al., 2022).

A related but experimentally distinct route is prestress-induced multistability in direct-ink-written reinforced thermosets. There, shear-aligned glass microfibers generate orthotropic laminae with $14.4$1 GPa and $14.4$2 GPa at room temperature, while above $14.4$3 the moduli drop to approximately $14.4$4 MPa and $14.4$5 MPa, respectively. Thermal strain enters through

$14.4$6

A one-time thermal programming step encodes mismatched thermal strains between layers, producing morphing on cooling and reversible snap-through between stable shapes near $14.4$7. Reversible snap-through is sustained for at least $14.4$8 cycles without cracking (Puthanveetil et al., 2021).

These examples show that PRAM mechanics is not limited to binary switching. It includes multistability, temperature-dependent topology of the energy landscape, and nonvolatile transitions between states whose accessibility is set by bifurcation structure, prestress, or composite action.

4. Learning, trainability, and material-level memory

Several recent works extend PRAM from reversible switching to trainable reversible switching. In non-equilibrium inverse design, periodically switching training targets teaches a material to perform incompatible functionalities with minimal changes in design parameters. In elastic allosteric networks, oscillatory training yielded designs in which as few as $14.4$9 bonds changed by more than $73.0$0 between two incompatible targets, whereas separately optimized networks differed in about $73.0$1 bonds. In heteropolymer folding, oscillatory training localized changes to a small set of affinity entries associated with nucleation barriers (Falk et al., 2022).

A physically implemented version appears in metamaterials that learn to change shape through local stiffness updates. For reciprocal learning, the update rules are

$73.0$2

For nonreciprocal learning,

$73.0$3

A chain with $73.0$4 learned a target “U” shape to below $73.0$5 mean-squared error in about $73.0$6 epochs, while nonreciprocity increased multi-target learning capacity to approximately $73.0$7 with nearest-neighbor couplings and up to $73.0$8 with next-nearest active couplings (Du et al., 21 Jan 2025).

The Engineering Material Neural Networks perspective generalizes this into a materials architecture in which trainable parameters $73.0$9 are embedded directly in nodes and links. The formal structure is

$w(t)$0

Within that framework, PRAM denotes materials whose node parameters $w(t)$1, $w(t)$2, $w(t)$3, $w(t)$4, or $w(t)$5 can be reconfigured reversibly and repeatedly, while retaining trained values across many cycles. The proposed metrics include reversibility ratio $w(t)$6, energy dissipation per cycle $w(t)$7, fatigue life $w(t)$8, and parameter degradation $w(t)$9 per cycle (Kergariou et al., 5 Jun 2026).

Not all trainable matter meets the permanent criterion. Dense suspensions with stress-activated memories can be trained to stiffen or soften depending on the training stress window. Their effective impact resistance can increase by approximately $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$0 at $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$1 mm/s or decrease to $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$2 of the initial value at $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$3 mm/s, but the trained state relaxes by about $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$4 toward baseline within approximately $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$5 s at rest. The material is therefore reversibly reprogrammable and multi-state, but does not satisfy strict PRAM permanence (Kim et al., 12 Mar 2025).

5. Representative platforms and application domains

PRAM has been demonstrated or proposed in structural, electromagnetic, rheological, and robotic settings. In stiffness-programmable laminates, the stated motivation is adaptation in aerospace and robotics applications, where energy requirements and design complexity are reduced by passive state retention (Chen et al., 2023). In adaptive RF metamaterials, PRAM behavior enables metasurfaces whose unit cells are reconfigured optically and then left unbiased, with direct implications for wavefront manipulation, beam steering, focusing, and surface impedance control around microwave frequencies (Georgiou et al., 2019).

Magnetic dynamic polymers broaden the application space to modular assembly and reconfigurable morphing architectures. The same material supports targeted welding efficiencies of $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$6 after $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$7 min at $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$8C and $q(t) = C(w,V,t)V(t), \qquad \dot{w}=f(w,V,t),$9 after $\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$0 min at $\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$1C, magnetization reprogramming at $\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$2–$\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$3C under $\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$4 mT, and room-temperature magnetic morphing in modular actuators, arrays, and 3D kirigami. Demonstrated field amplitudes include $\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$5 mT for large twisting in a “Z”-shape, $\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$6 mT for pop-up deformation in an “H”-shape, and $\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$7–$\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$8 mT for kirigami actuation (Kuang et al., 2020).

Thermally reversible architected composites extend PRAM to load-bearing morphing components. Direct-ink-written glass-fiber composites exhibit a density of $\varphi(t)=L(w,i,t)i(t), \qquad \dot{w}=g(w,i,t),$9 g·cm$25\%$0, operate reversibly near $25\%$1C, and couple shape state to electrical conductivity through a near-percolation CNT/CB network, with measured conductivity spanning approximately $25\%$2–$25\%$3 $25\%$4 across branches and states. The cited uses include aerospace morphing, deployable structures, and haptics (Puthanveetil et al., 2021).

Magneto-thermomechanical active metamaterials target flexible yet stiff soft robots and multimodal morphing structures. Shape changes are untethered and reversible, locked without continuous power, and reprogrammable either by changing magnet placement or by changing field direction in asymmetric bistable units. Demonstrated actuation times are approximately $25\%$5 s at $25\%$6C, $25\%$7 s at $25\%$8C, and $25\%$9 s at $20\%$0C, with at least $20\%$1 reversible cycles reported (Zou et al., 2022).

In the trainable-matter literature, the application horizon is wider still: protective gear and impact mitigation, vibration damping, soft robotics, load-bearing engineering materials, and animate or intelligent machines whose adaptation, reversibility, and learning are embedded into the material structure itself (Kim et al., 12 Mar 2025, Kergariou et al., 5 Jun 2026).

6. Boundaries, misconceptions, and unresolved issues

A recurring misconception is that any reversible adaptive material is automatically a PRAM. The literature does not support that equivalence. Variable-stiffness media based on jamming, magnetorheological control, or externally driven actuation may be reversible, yet often require continuous pressure, continuous field, or sustained power to hold a state. By contrast, PRAM emphasizes non-volatile retention after the programming stimulus is removed (Chen et al., 2023, Georgiou et al., 2019).

A second misconception is that trainability implies permanence. Dense suspensions with dynamic chemical bridging and frictional contact networks demonstrate multiple stress-activated memories, targeted viscosity, and tunable energy dissipation, but those memories relax rapidly at rest. The cited system is explicitly described as not meeting the strict “permanent” criterion of PRAM, even though it satisfies the “reversible” and “adaptive” aspects (Kim et al., 12 Mar 2025).

A third issue concerns the gap between algorithmic reversibility and physical reversibility. In non-equilibrium design protocols for adaptable materials, some training procedures identify very small switching sets, but one case study uses irreversible bond removal. The resulting designs are highly informative for discovering minimal switching subsets, yet direct PRAM operation would require those subsets to be implemented with reversible actuators or switchable interactions (Falk et al., 2022).

Several platform-specific limitations also recur. Gecko-inspired lamination must manage adhesive fouling, unexpected peel, hinge fatigue, and dielectric breakdown if voltages are too high (Chen et al., 2023). Photomechanical mem-components require quantification of retention times, fatigue, RF loss, linearity, and environmental stability in packaged devices (Georgiou et al., 2019). Magnetic dynamic polymers rely on heating windows between approximately $20\%$2C and $20\%$3C for welding, stress relaxation, and magnetization reprogramming, and excessive exposure near the retro-Diels–Alder regime temporarily weakens the network (Kuang et al., 2020). Thermally reversible lattices require tight control of diagonal or body-diagonal defects because these can drastically alter bifurcation behavior (Vasudevan et al., 2022).

Taken together, these limits indicate that PRAM is best understood not as a completed materials class but as a stringent operational standard: reversible switching, non-volatile state retention, repeated reprogramming, and useful functionality under realistic cycling. The cited works show that this standard is already achievable in selected systems and, just as importantly, clarify where present adaptive materials remain only partially PRAM.