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Materials Science in Additive Manufacturing Bistable 3D-printed compliant structure

1. Introduction applicability of multi-stability has been demonstrated in
various engineering applications, encompassing the design
Compliant mechanisms, inspired by the ingenious designs of deployable structures, vibration isolators, dampers, and
in nature, have gained significant attention in engineering energy absorbers. 18-22
disciplines due to their high precision, accurate
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motion, and force control. These features of compliant Among the previous designs, the controllable snap-
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mechanisms are mainly attributed to their reversibility and through motion from curved-beam buckling is highlighted
bi-stability. In nature, compliant mechanisms often exhibit in structures of reversibility and bi-stability. A common
reversibility attributed to their mono-stability. On the compliant system involves a stress-free pre-curved beam
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other hand, some compliant mechanisms, for example, in the shape of buckling Mode 1 (Figure 1A). For a fixed-
the Venus flytrap, possess multi-stability, which describes end curved beam under vertical force at the mid-span,
the ability of the system to exist in and transit between it would deform into Mode 2 and recover to its initial
multiple stable states. The multi-stability of compliant shape after unloading (Figure 1B). The force-displacement
mechanisms provides versatility and adaptability, curve is characterized by a negative stiffness phase, as
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enabling it to switch between different functionalities or shown in Figure 1D. Early in 2004, Qiu et al. established
behaviors, offering advantages in reconfigurability and an analytical model for the curved beam to explain and
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energy-efficient actuation. By leveraging these principles predict its bistable behavior. According to their study, two
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observed in nature, researchers have started exploring the criteria should be satisfied for a curved beam to achieve
integration of reversibility and bi-stability into the design bi-stability: the ratio of beam apex height to thickness is
of metamaterials. 7 larger than 2.31, and the buckling Mode 2 is constrained.
According to the criteria, a double curved beam system
Elastic beams have widely been used in the design
of reversible compliant structures. 8-10 Correa et al. with a membrane connecting beams at the mid-span was
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proposed to exhibit bi-stability (Figure 1C). The force-
studied the compressive behavior of honeycomb- displacement curve for a bistable system is shown in
shaped structures employing negative stiffness beams. Figure 1E, which displays an identifiable negative force
The proposed honeycombs yielded higher stiffness and segment. While the bending energy consistently rises
excellent recoverability. Building on these early designs, throughout the downward deflection of the beam, the
a 3D structure was designed and demonstrated to exhibit compression energy exhibits a peak near the central point
effective damage mitigation from impact loadings.
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Besides, a structure utilizing sandwich beams was found and subsequently diminishes. When the beam is engineered
to exhibit negative stiffness when subjected to quasi- to facilitate a more rapid decrease in compression energy
static compression loads while maintaining a high level after surpassing the central point compared to the increase
in bending energy due to the snap-through phenomenon,
of recoverability throughout the loading and unloading it results in a negative force segment.
cyclic process. The reversibility of elastic beams provided
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a new avenue for designing protective metamaterials with The finding was further proved by Vangbo using
enhanced energy absorption and energy dissipation. the mathematical model. Moreover, Mehreganian et al.
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In recent years, research endeavors have expanded developed an analytical model using the Euler–Lagrange
beyond the exploration of reversible structures, theorem to predict the force-displacement curve of a
leading to the emergence of studies focused on the double-curve-beam structure. Other analytical works
creation of configurations with multiple stable states. have been done in this field in terms of different actuation
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For instance, Restrepo et al. presented an innovative motions, snap-through properties, and different
On the basis of the theoretical
boundary conditions.
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material characterized by the periodic arrangement of framework, Gan et al. used the curved beams as the
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unit cells with negative stiffness, comprising curved
beams, which exhibited the capability to exist in various core of a meta-sandwich structure to enhance the impact
stable configurations. Later, Rafsanjani et al. designed resistance under repeated impact loadings. Besides,
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metamaterials with curved beams that undergo substantial various optimization methods of the curved beam were
deformations and transition between two configurations also performed to meet the desired bistable performance
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under tensile loadings. Furthermore, it has been observed and constraints of size and material distribution.
that metamaterials featuring multiple stable configurations While most of the studies developed mathematical models
can effectively capture and store the input energy in the to explore reversibility and bi-stability by investigating the
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deformed beams. The mechanism underpinning energy geometry of the curved beam, experiments have rarely been
trapping relies on the reversible transition between complemented systematically to understand the compliant
two stable configurations of the proposed beams. The behavior. In addition, the boundary conditions and other
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Volume 3 Issue 4 (2024) 2 doi: 10.36922/msam.4960