Fig. 3: Theoretical model for solvent and magnetic responsive behaviors of soft structures. | Nature Communications

Fig. 3: Theoretical model for solvent and magnetic responsive behaviors of soft structures.

From: Dynamic morphological transformations in soft architected materials via buckling instability encoded heterogeneous magnetization

Fig. 3

a Transformation of elastomer strip with length L, height H, and thickness T under solvent stimulus. \(\lambda\) represents the wavelength. A is the peak-to-peak value. b Transformation of elastic plate with free-to-rotate junctions under solvent stimulus. L is the distance between two junctions. The wavelength \({\lambda }_{{{{{{\rm{n}}}}}}}\) is determined by \({\lambda }_{{{{{{\rm{n}}}}}}}=L/{W}_{{{{{{\rm{n}}}}}}}\), where \({W}_{{{{{{\rm{n}}}}}}}\) represents the deformation mode of strip. c Comparison of the deformed shape of the free edge (z = H) of the strip structure with theoretical results. d The impact of the height of the strip on the wavelength and amplitude under solvent stimulus. e Schematic diagram of the magnetization process, the change of magnetization profile during the recovery process, and the magnetic actuation process. f The relationship between the normalized critical force \(\left(\frac{{H}^{2}{t}_{11}^{{{{{{\rm{c}}}}}}}}{E{T}^{3}}\right)\) and aspect ratio (L/H) under different deformation modes, where E and \({t}_{11}^{c}\) are Young’s modulus and critical membrane force, respectively. Discrete dots in orange color represents the experimental results, which can also be found in Fig. 3g. The intersection of the two curves indicates that mixed deformation modes would occur. g Theoretical and experimental results for the relationship between the \({W}_{{{{{{\rm{n}}}}}}}\) and the aspect ratio under solvent stimulus. When the aspect ratio reaches a critical value, the strip would exhibit mixed deformation modes. As the experimental results with L/H = 3.70, \({W}_{{{{{{\rm{n}}}}}}}\) can be equal to 1.0 or 1.5. When L/H = 7.41, \({W}_{{{{{{\rm{n}}}}}}}\) can be equal to 2.0 or 2.5. h Magnetization profile of the strip at z = 0 and z = H. i Validation of magnetic field distribution. j Comparison of experimental results and theoretical model for the deformation of the strip under magnetic actuation. The scale bar is 2 mm. Error bars stand for the standard error (n = 3).

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