Buckling of Columns and Films: from Fundamental Mechanics to Functional Materials
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Buckling of Columns and Films: from Fundamental Mechanics to Functional Materials

  • Author(s): Chen, Yuzhen
  • Advisor(s): Jin, Lihua
  • et al.
Abstract

Buckling instabilities are traditionally regarded as failure modes. However, they can also be exploited to design functional materials. This dissertation focuses on investigating the buckling of columns and films, and on harnessing these buckling instabilities to design pneumatically actuated pattern-transforming metamaterials, design reusable energy-absorbing architected materials, and achieve complex 3D morphing of LCE thin films. Four major contributions are made: First, we propose a pneumatically actuated pattern-transforming metamaterials and reveal the mechanism of the pattern transformation. Metamaterials are carefully structured materials that exhibit unusual properties relying primarily on their geometries rather than their constitutive materials. The proposed metamaterial is composed of an elastomer with periodic circular holes sealed by elastomeric membranes. Subjected to negative pressures, it can undergo pattern transformation, yielding large transformation strains. Such pattern transformation is triggered by a buckling instability and can be broadly tuned by the geometry of the metamaterial. Here we numerically, analytically and experimentally investigate the effects of geometry on the pattern transformation. Our finite element simulations indicate that the thickness of the slenderest wall and the pattern of the holes play key roles in determining the critical load for the pattern transformation, the transformation strain, and the transformation type. To quantify the effects of these geometric parameters, we further analytically model the pattern transformation of the metamaterial by simplifying it to a network of rigid rectangles linked by deformable beams. Finally, we experimentally characterize the pattern transformation of the metamaterials with different geometric parameters. The experimental, numerical, and analytical results are in good agreement. Our work provides design guidelines for this metamaterial. Secondly, we numerically show that a straight hyperelastic column under axial compression exhibits complex buckling behavior. As its width-to-length ratio increases, the column can undergo transitions from continuous buckling, like the Euler buckling, to snapping-through buckling, and eventually to snapping-back buckling. In particular, we numerically and experimentally identify a new snapping-back mode of column buckling. We develop an analytical discrete model to reveal that snapping-back buckling results from strong coupling between stretching and bending. Besides, we analytically determine the critical width-to-length ratios for the transitions of buckling modes using a general continuum mechanics-based asymptotic post-buckling analysis in the framework of finite elasticity. A phase diagram is constructed to demarcate the different buckling modes of axially compressed columns. Thirdly, by harnessing the newly discovered snapping-back buckling, we design a new class of reusable energy-absorbing architected material. Subjected to an axial compression, a wide hyperelastic column can discontinuously buckle, snapping from one stable equilibrium state to another, leading to energy dissipation, while upon unloading, it can completely recover its undeformed state. Making use of this property, we design an energy-absorbing architected material by stacking layers of wide hyperelastic columns, and fabricating it by multi-material 3D printing and sacrificial molding. Characterized by quasi-static and drop tests, the material shows the capability of energy dissipation and impact force mitigation in a reusable, self-recoverable, and rate-independent manner. A theory is established to predict the energy-absorbing performance of the material and the influence of the column geometry and layer number. Wide tunability of the peak force, energy dissipation and stability of the material is further demonstrated. Our work provides new design strategies for developing reusable energy-absorbing materials and opens new opportunities for improving their energy dissipation capacities. Finally, we achieve well-defined 3D shapes by buckling flat liquid crystal elastomer (LCE) thin sheets subjected to in-plane nonuniform stresses. Shape morphing of flat thin sheets to well-defined 3D shapes is an effective method of fabricating complex 3D structures, and LCEs are an attractive platform for shape morphing due to their ability to rapidly undergo large deformations. Here we model the buckling-induced 3D shape formation from a thin LCE sheet with prescribed in-plane stretch profiles. The sheet is modeled as a non-Euclidean plate, in which the prescribed metric tensor cannot be realized in a flat configuration and thus no stress-free configuration exists even in the absence of external loads or constraints. Under the thin plate limit, when the stretching energy dominates, we solve both the forward and inverse problems, i.e. determine the 3D shapes under prescribed stretch profiles, and determine the stretch profiles for desired 3D shapes, respectively. In the condition of a finite thickness of the sheet, the resulting 3D shapes are determined by the interplay between both the stretching and the bending energies. For a sheet with a small but finite thickness, we predict the 3D shapes for prescribed stretch profiles, and identify the critical thicknesses at which the transition from the flat to buckled configurations occurs. The theoretical predicted 3D shapes agree closely with the ones from both finite element simulations and experiments. Our analysis sheds light on the design of the shape morphing of LCE sheets, and provide quantitative predictions on the 3D shapes of programmed LCE sheets upon stimuli for various applications.

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