Buckling of a holey column

Abstract

We report the results from a combined experimental and numerical investigation of buckling in a novel variant of an elastic column under axial load. We find that including a regular line of centred holes in the column can prevent conventional, global, lateral buckling. Instead, the local microstructure introduced by the holes allows the column to buckle in an entirely different, internal, mode in which the holes are compressed in alternate directions, but the column maintains the lateral reflection symmetry about its centreline. The internal buckling mode can be accommodated within a smaller external space than the global one; and it is the preferred buckling mode over an intermediate range of column lengths for sufficiently large holes. For very short or sufficiently long columns a modification of the classical, global, lateral buckling is dominant.

On the buckling of an elastic holey column

“…( c ) The alternating mode with an odd number of holes, which does not break a reflection symmetry. In ( b ),( c ), the shading indicates the distribution of strain energy in the deformed state (as defined in [ 12 ]), from black (low strain) to yellow (maximum strain for that column). (Online version in colour.)…”

“…Pihler-Puzović et al [ 12 ] considered a fixed hole size and spacing relative to the column width, identified the buckling modes that occur in two- and three-hole columns, and quantified the transition between the alternating and Euler modes as the length of the column increased. They found good agreement between their finite-element numerical calculations and experiments on holey columns made of the hyperelastic material extra hard Sid AD Special (Feguramed GmbH).…”

Ultra-programmable buckling-driven soft cellular mechanisms

“…In particular, critical strains are usually geometry-dependent, meaning that it is impractical to drastically change the critical behavior once a specific type of geometry is chosen. 21,23,25 More importantly, the buckling patterns (i.e. the instability modes) have been limited to a few 19,23,24 without a clear strategy for reliable activation of the higher modes of instability that could support a much richer set of actuation modes.…”

Inverse Design of Mechanical Metamaterials That Undergo Buckling

“…We next focus on the buckling mode with the lowest critical strain, since this mode will occur upon compression of the beam. We find that for c < 0.075, the buckling mode of the beam is characterized by a typical macroscopic buckling mode with a wavelength of 2 nL that is equal to twice the length of the beam, while for c > 0.075 a microscopic buckling mode occurs characterized by a wavelength of 2 L equal to twice the size of the unit cell . When we would perform an optimization to maximize the lowest critical strain of the beam according to we find that the derivative of the objective function is discontinuous due to the change in buckling behavior (Figure ).…”

“…We find that for c < 0.075, the buckling mode of the beam is characterized by a typical macroscopic buckling mode with a wavelength of 2nL that is equal to twice the length of the beam, while for c > 0.075 a microscopic buckling mode occurs characterized by a wavelength of 2L equal to twice the size of the unit cell. [44,45] When we would perform an optimization to maximize the lowest critical strain of the beam according to max 1 cr ε c (2) we find that the derivative of the objective function d dc / 1 cr ε is discontinuous due to the change in buckling behavior ( Figure 1). While this specific problem can be tackled with gradient-based algorithms by rewriting Equation (2) using a bound formulation, [37,46] a perturbation-based sensitivity analysis should be performed for each individual eigenvalue by solving sub-optimization problems at each optimization step.…”