Instability-Induced Pattern Formations in Soft Magnetoactive Composites

Elastic instabilities can trigger dramatic microstructure transformations giving rise to unusual behavior in soft matter. Motivated by this phenomenon, we study instability-induced pattern formations in soft magnetoactive elastomer (MAE) composites deforming in the presence of a magnetic field. We show that identical MAE composites with periodically distributed particles can switch to a variety of new patterns with different periodicity upon developments of instabilities. The newly formed patterns and postbuckling behavior of the MAEs are dictated by the magnitude of the applied magnetic field. We identify the particular levels of magnetic fields that give rise to strictly doubled or multiplied periodicity upon the onset of instabilities in the periodic particulate soft MAE. Thus, the predicted phenomenon can be potentially used for designing new reconfigurable soft materials with tunable material microstructures remotely controlled by a magnetic field.

Figure 1

Schematic representation of MAE composite with rectangular unit cells subjected to a vertically applied magnetic field and horizontally applied prestress. Each unit cell is comprised of soft matrix and centered magnetoactive inclusion. An example of representative volume element (RVE) containing $N=3$ unit cells (right).

Figure 2

Numerically realized instability-induced periodic (b),(d),(f),(h) and nonperiodic (c),(e),(g) patterns in soft MAE composites at $\epsilon =50\%$ [47] and various levels of $\tilde{B}=0$, 6.7, 10.3, 11.2, 12.1, 12.6, 12.8 (b)–(d). (a) Undeformed state. The elements of strictly periodic patterns $N_p=2$ (b), $N_p=3$ (d), $N_p=4$ (f), and $N_p=5$ (h) are marked by green dashed rectangles, and base elements of nonperiodic $N_b=2$, 3 (c), $N_b=3$, 4 (e), and $N_b=4$, 5 (g) patterns are denoted by red dashed rectangles.

Figure 3

Dependence of critical strain on the applied magnetic field level. The numerically detected critical buckling points are denoted by circles corresponding to the periodic patterns from Figs. 2, 2, 2, and 2, and the connecting dashed curve illustrates the trend of the dependence of critical strain on the magnetic field. The continuous curve represents the long-wave instability prediction.

Figure 4

Dependence of the critical magnetic field required for the formation of the periodic patterns on $\eta$ ($\xi =0.309$). Continuous, dashed, and dash-dotted curves correspond to periodic patterns with $N_p=3$, 4, and 5, respectively.

Figure 5

Magnetic field triggers instability-induced patterns in soft MAE composites. (a),(b) Experimentally observed patterns for the applied compressive strain level 32% and for the magnetic fields $B=0$ (a) and $B=1.8\mathrm{T}$ (b), respectively. (c),(d) Numerically realized patterns for the applied compressive strain level 39% and for $B=0$ (c) and $B=1.8\mathrm{T}$ (d), respectively. The magnetic field is applied perpendicularly to the inclusion column direction.