On Pattern-Switching Phenomena in Complex Elastic Structures

  • Stephen Willshaw

Student thesis: Phd


We investigate global pattern-switching effects in 2D cellular solids in which the voids are arranged in a square lattice. Uniaxial compression of these structures triggers an elastic instability which brings about a period-doubling transformation of the void shapes at a critical strain. Specifically, a square array of circular voids forms a pattern of mutually orthogonal ellipses and a similar effect is observed for diamond-shaped voids. The onset of instability is governed by the void fraction and size-effects are found for the experimental samples. We establish empirical laws which characterise the stiffness, strength and stability of cellular structures comprising square arrays of circular voids. A comparison of these with predictions from a discrete model implies underestimation of the resistance of the lattice to buckling, although the size effects are replicated. We find similar pattern-switching effects in the cubic lattice, which is a three-dimensional porous cube. The effect of buckling in this system is to produce a 2D pattern in one plane of voids. In two-phase granular crystals, rearrangement of a square lattice of particles results in a new, period-doubled, structural pattern. This switch can occur via an intermediate phase depending on the size ratio of the particles as shown in experiments and numerical simulations.
Date of Award31 Dec 2012
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorThomas Mullin (Supervisor)


  • cellular structure
  • bifurcation
  • elastic
  • instability

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