Modular and programmable material systems drawing from the architecture of skeletal muscle

The passive attributes of skeletal muscle “material” often have origins in nanoscale architecture and functionality where geometric frustrations directly influence macroscale mechanical properties. Drawing from concepts of the actomyosin network, this study investigates a modular, architected material system that leverages spatial constraints to generate multiple stable material topologies and to yield large adaptability of material mechanical properties. By exploiting the shearing actions induced on an actomyosin-inspired assembly of modular material constituents, intriguing material behaviors are cultivated, including strong metastability and energy-releasing state transitions. Experimental, numerical, and analytical studies reveal that such passive attributes can be tailored by geometric constraints imposed on the modular material system. The geometric parameters can also introduce a bias to the deformations, enabling a programmable response. By invoking the spatial constraints and oblique, shearlike motions inherent to skeletal muscle architecture, this research uncovers potential for architected material systems that exploit locally tunable properties to achieve targeted macroscopic behaviors.

Figure 1

(a) Muscle fibers are composed of bundles of rodlike myofibrils (b), which consist of actin and myosin proteins arranged in a lattice and sectioned into units called sarcomeres (c). These filaments are connected by cross bridges (d), with power stroke mechanics influenced by lattice geometry. (e) A section of the proposed architected modular material system subject to compression (f), resulting in local buckling of constituent modules (g). Application of a shear load causes a state switch (h) in the void pattern.

Figure 2

Architected material systems highlighting a four-void constituent module exhibiting local buckling under compression. (a) Two serially connected sets of two modules in parallel. (b) Three-module system under transverse confinement, where each of the three modules exhibits a different deformation pattern despite being subject to the same confinement.

Figure 3

(a) Photo and (b) schematic of a unit module considered in this research, indicating important dimensions. (c) Transverse compression ${\delta }_x$ applied by aluminum plates. The plate on the left side is clamped to the base of a tensile testing machine, while the plate on the right side is clamped to the upper fixture and load cell.

Figure 4

Stress-strain relationship of Mold Star 15 Slow silicone rubber from tension and compression tests. Linear-elastic and neo-Hookean approximations are also presented. Inset: Bulk material specimens used in (left) compression and (right) tension tests.

Figure 5

Force displacement results from a full loading cycle when the module has an initial deformed configuration characterized by (a) voids pointed downward and (b) voids pointed upward.

Figure 6

Responses from compression and extension tests where the initial configuration is characterized by (a), (b) vertical and (c), (d) horizontal deformations of the upper left void. The thick curve segments represent the portions in which the module retains the starting configuration, while the thin segments denote portions following a transition to one of the states shown in Fig. 5. (e) A half cycle with the same starting conditions as in (c) followed immediately by a full cycle. This indicates that following a transition to one of the states in Fig. 5, subsequent loading cycles remain in that configuration. (f) A half cycle repeated from the end condition of (d).

Figure 7

(a)–(d) Experimentally measured vertical reaction force-displacement responses for four levels of transverse compression ${\delta }_x/w$ for a module with $d_1=d_2=4.12\mathrm{mm}$. Thin vertical dotted lines marked with arrows at the boundaries of the shaded strongly metastable range indicate discrete state transitions. Line styles correspond to the aligned and polarized topologies presented in (e), (f). The polarized topologies are not observed for the lowest level of transverse compression.

Figure 8

Numerical results of a module with uniform void geometry subject to oblique displacements under four different levels of transverse compression. (a)–(d) Trends in reaction force responses show reasonable agreement with the experimental results shown in Figs. 7–7. (g)–(j) Strain energy curves reveal the large strain energies stored in the polarized states within the shaded highly metastable regions. (e), (f) Images showing aligned and polarized topologies as predicted by the finite element model, with line styles corresponding to the curves in (a)–(d), (g)–(j).

Figure 9

(a) Module highlighting deformations of central horizontal member in polarized and aligned deformed topologies. (b) Schematic of a flexible beam with boundaries clamped at an angle $\beta$.

Figure 10

Nondimensionalized (a)–(c) reaction force and (d)–(f) strain energy for the clamped elastica, with bias reflected by introducing a nonzero clamp angle $\beta$. Numerical results and the elastica model show that the polarized or three-inflection states are at higher strain energy levels than the aligned or two-inflection states.

Figure 11

Illustration of a module with nonuniform void diameters and approximation of this geometry with nonzero clamp angle $\beta$ of the flexible beam.

Figure 12

Force and energy responses of modules with nonuniform void diameters. (a)–(c) Experimental results showing vertical reaction force-displacement responses and (d)–(f) numerical results showing strain energies as void diameters $d_1$ and $d_2$ are varied, demonstrating a bias toward one of the polarized states as the difference between $d_1$ and $d_2$ increases.

Figure 13

Multimodule specimens. (a) The 16 possible metastable configurations for a material section composed of two modules. (b) Programmable response in an arrangement of modules with different void geometries. The upper module has $d_1=d_2$, the central module has $d_1=0.9d_2$, and the lower module has $d_1=0.8d_2$. If the initial configuration is such that all three modules are the polarized state characterized by a vertical shape of the upper left void, prescribing shear motions will result in different thresholds for which sudden polarized-to-aligned transitions occur. These transitions are indicated by vertical jumps in reaction force. Results from three trials are presented, indicating repeatability.