Asymmetric elastoplasticity of stacked graphene assembly actualizes programmable untethered soft robotics

There is ever-increasing interest yet grand challenge in developing programmable untethered soft robotics. Here we address this challenge by applying the asymmetric elastoplasticity of stacked graphene assembly (SGA) under tension and compression. We transfer the SGA onto a polyethylene (PE) film, the resulting SGA/PE bilayer exhibits swift morphing behavior in response to the variation of the surrounding temperature. With the applications of patterned SGA and/or localized tempering pretreatment, the initial configurations of such thermal-induced morphing systems can also be programmed as needed, resulting in diverse actuation systems with sophisticated three-dimensional structures. More importantly, unlike the normal bilayer actuators, our SGA/PE bilayer, after a constrained tempering process, will spontaneously curl into a roll, which can achieve rolling locomotion under infrared lighting, yielding an untethered light-driven motor. The asymmetric elastoplasticity of SGA endows the SGA-based bi-materials with great application promise in developing untethered soft robotics with high configurational programmability.

Upon heating by T, the PE layer expands laterally, resulting in the tensile force in the SGA layer and compressive force in the PE layer. (c) Upon cooling, the PE layer returns to its original configuration while the SGA layer's deformation cannot be fully recovered due to the plastic deformation in step (b), resulting in the residual tensile force in the PE layer and compressive force in the SGA layer. (d) After releasing the constraint of the plates, the SGA/PE bilayer film coils due to the internal residual stress.
Theoretical modeling (plane strain assumption) is carried out to predict the curling curvature of the SGA/PE bilayer after constrained tempering, as schematically shown in Fig. SN1-1. In our modeling, the PE layer is assumed as a purely elastic material, while the SGA layer is assumed as a continuum material with asymmetric elastoplastic behavior under tension and compression, namely elastic and ideally plastic under tension and purely elastic under compression as revealed by the MD simulation (see Fig. 4a). Given the negligible thermal expansion of the SGA layer, its deformation in the heating stage ( Fig. SN1-1b) mainly results from the stretching by the attached PE layer. For the PE layer, on the other hand, the deformation includes two portions. One is the thermal expansion and the other is the strain caused by the reaction forces (compression) from the SGA layer. Consider a segment of a bilayer strip. The forces experienced are shown in Fig. SN1  According to Hooke's law and plane strain condition, it is easy to demonstrate that the stress along zdirection is (SGA) = SGA (SGA) . The constraint applied along y-direction by glass slides mainly functions to restrain the bending deformation of bilayer strip, while the compressive stress exerted is negligible compared with the stresses along x and z directions. In our analysis, therefore, the stress along y-direction is neglected, i.e., (SGA) = 0. Based on the von Mises criterion, yielding will not happen until in which SGA t is the yield strength of SGA under tension. Substituting Eq. (SN1-2) into Eq. (SN1-3), the minimum temperature increment causing plastic deformation in the SGA layer is determined as At the critical moment of yielding, F saturates at its maximum value, which can be determined by When Δ > Δ * , temperature increment will only cause plastic strain ( p t ) in the SGA layer, while F remains constant. Therefore, when Δ > Δ * , the perfect bonding condition implies Eqs. (SN1-5) and (SN1-6) imply that the plastic strain p t can be written as After the heating stage, the temperature then is reduced to the initial value ( Fig. SN1-1c). The PE layer contracts and the tensile load applied to the SGA layer gets released. This causes the recovery of the elastic tensile strain in the SGA layer. Since the SGA layer has experienced permanent elongation during the heating stage, contraction of the PE layer would lead to compressive stress in the SGA layer and tensile stress in the PE layer. After removing the external constraint, the strain misfit between the SGA and PE layers, which is equal to the plastic strain ( p t ) of the SGA in the heating stage, causes the bilayer to curl with the PE layer being wrapped inside ( Fig. SN1-1d). Consider a segment of the bilayer 5 strip (see Fig. SN1-3). All the forces acting on the cross-section of the bilayer can be equivalently simplified as axial forces F plus a bending moment M ( Fig. SN1-3). Perfect bonding along the interface implies that being the compressive elastic modulus of the SGA layer.
The compressive elastic modulus of the SGA layer is used here since the stress in the SGA layer is Denote the radius of the curvature of the neutral surface as , as shown in Fig. SN1-3. The bendinginduced strain is given by where h is the distance from the SGA/PE interface to the neutral surface. The stresses along lateral direction caused by axial force and bending moment in both SGA and PE layers are given by In Eq. (SN1-11a), the whole SGA layer is assumed under compression along the lateral direction. This point will be verified later.
The resultant force on the entire cross-section of the bilayer is zero, which implies Taking where total refers to the total strain energy released by the SGA/PE bilayer due to unfolding, f is the work done by the friction force and k stands for the increment of the kinetic energy. The total released strain energy can be expressed as total = ∆ , where is the number of times that the propeller pushes the ground; ∆ is the average strain energy released from each touch; f can be described by f = − f ∫ 0 , where f is the rolling friction force between the roller and the ground.
Assume that the roller is a thin-walled cylinder. The kinetic energy can be expressed as k = 2 , where m stands for the mass of the roller.
For a curled bilayer film, the stored strain energy is proportional to 2 as the previous theory indicates 63 , where is the curvature. First-order approximation indicates that where 0 is the initial strain energy stored, S is the remaining strain energy after a sufficiently long time of heating by the IR light, ∆ is the change of strain energy near the initial state, and is the change of curvature near the initial curled configuration.
The above discussion on the prediction of curvature indicates that ∝ ∆ , where ∆ refers to the temperature increase. To predict the temperature change in the SGA/PE bilayer due to IR light illustration, a thermal equilibrium equation is established as follows where is a constant representing the energy reception rate from the IR light on a unit area, is the effective area that is exposed upon the IR light, e is the environmental temperature, ℎ and represent the surface heat transfer coefficient and heat capacity of the material, respectively. The