Leveraging yield buckling to achieve ideal shock absorbers

Abstract

The ideal shock absorber combines high stiffness with high energy absorption whilst retaining structural integrity after impact and is scalable for industrial production. So far no structure meets all of these criteria. Here, we introduce a special occurrence of plastic buckling as a design concept for mechanical metamaterials that combine all the elements required of an ideal shock absorber. By striking a balance between plastic deformation and buckling, which we term yield buckling, these metamaterials exhibit sequential, maximally dissipative collapse combined with high strength and the preservation of structural integrity. Unlike existing structures, this design paradigm is applicable to all elastoplastic materials at any length scale and hence will lead to a new generation of shock absorbers with enhanced safety and sustainabilty in a myriad of high-tech applications.

Figures (18)

• Figure 1: Ideal shock absorbers.A, (bottom-right) stretching-dominated materials are stiff but do not exhibit a force plateau. Bending-dominated materials exhibit a force plateau a low stiffness and are reusable (top-left). Ideal shock absorbers exhibit a high stiffness before impact for load bearing, show a stable plateau during impact for maximum energy absorption, are reusable multiple times while retaining their initial stiffness (top-right) and can be mass-manufactured. B, a cylindrical metamaterial with multiple layers strip mode designed for such ideal shock absorption enabled by yield buckling.
• Figure 2: Yield buckling.A. Stress $\sigma$ vs. strain $\varepsilon$ for a bilinear elastoplastic model with Young modulus $E$, yield stress $\sigma_y$ and tangent modulus $E_t$. Inset: unit cell consisting of a pair of rotating squares and connecting ligaments buckling at a load $F_{cr}$. The green (before yielding), red (at yielding), and blue (after yielding) markers denote three stress states of the ligaments when the unit starts to buckle. B. Force (thick lines) and lateral deflection (thin lines) vs. displacement in the elastic (green), plastic (blue), and yield (red) buckling regimes from finite elements simulations (see SI for details). $F_{cr}$ is the critical load at buckling and $S$ is the slope right after the onset of buckling. Inset: unit cell at self-contact reached at a load $F_{sc}$. C. Post-buckling stiffness $S$ vs. aspect ratio of the unit cell $t/\ell$ and ratio between tangent and Young's moduli $E_{t}/E$. The red triangles denote the yield buckling regime defined by $S<0$ and $F_{sc}<F_{cr}$. D, E, F A six-step sequential yield buckling is achieved in a six-layer structure with sliding constraints on its side. D. Snapshots at each buckling step. The colors denote the horizontal displacement field. E. Lateral deflection of the center of each ligament $w_{i}$ vs. compressive stroke $u/6\ell$. F. Load vs. compressive stroke $u/6\ell$. The reaction load is normalized by the initial yield buckling load, $F_{cr}=\sigma_{y}t$.
• Figure 3: Yield buckling in a metamaterial with line modes.A. Snapshot of a finite element simulation of a metamaterial unit cell buckles along lines under compression. B. Force (thick lines) and lateral deflection (thin lines) vs. displacement in the elastic (green), plastic (blue), and yield (red) buckling regimes from finite elements simulations (see Appendix B for details). $F_{cr}$ is the critical load at buckling and $S$ is the slope right after the onset of buckling. Inset: unit cell at self-contact reached at a load $F_{sc}$. C. Post-buckling stiffness $S$ vs. aspect ratio of the unit cell $t/\ell$ and ratio between tangent and Young's moduli $E_{t}/E$. The red triangles denote the yield buckling regime defined by $S<0$ and $F_{sc}<F_{cr}$. DEF. Force (top) and deflection of the central ligament (bottom) in a finite element simulation of two unit cells in series in the elastic (D), plastic (E) and yield buckling (F) regimes.
• Figure 4: Experimental demonstration of ideal shock absorbers. The ligament thickness of the metacylinder is $t=0.5$ mm and the compression speed is 0.2 mm/s unless indicated otherwise. A. Snapshots of the metacylinder under uniaxial compression at different strokes $u/L$. B. Number of buckled line modes $N_\textrm{buckled}$ vs. compressive stroke $u/L$ for various ligament thicknesses (top) and loading speeds (bottom). C. Force $F$ vs. compressive stroke $u/L$ for metacylinders with various ligament thicknesses. D. Force vs. compressive stroke $u/L$ under quasi-static compression (top) and deceleration vs. compressive stroke under impact (bottom) for the metacylinder (red) and crash can (gray). The impact speed is $4.7\; m/s$ with a weight of $15.5\; kg$. E. Force vs. compressive stroke displacement curve under six quasi-static compression cycles $C$ of increasing magnitude (top) and deceleration vs. compressive stroke under six distinct dynamic drops $D$ (bottom). See also Supplementary Movie 3.
• Figure 5: Ashby maps (A) Specific stiffness, $E^{*}/\rho$ vs. plateau strength, $\sigma_{pl}$ and (B) specific energy absorption at $20\%$ strain $SEA_{0.2}$, vs. specific stiffness, $E^{*}/\rho$ vs for our metacylinder (red disks) and optimised metamaterial (FEM only, red circle) and for existing metamaterials from references tancogne2016additivelymeza2014strongschaedler2011ultralightbauer2021tensegrityrafsanjani2015snappingpapka1998experiments.