Counting Metamaterials

In this dissertation, I ventured into one of the newest areas of metamaterials: memory.
My research was initially started with the question: ”can we make a block of rubber
that can count?”, which I set out to discover. Very quickly, I realized that counting
not only requires a retention of information, but a simple form of computation as
well. Thus, after developing an initial ’counting material,’ I investigated the essential
components required for such a material, its potential capabilities, and the limitations
of various configurations of these minimal components. Would these ingredients allow
us to learn more about memory, possibly even allow us to perform computations?
Chapter one serves as the introduction of this dissertation and it discusses the wide
variety of memory observed in materials and devices. I start by discussing footprints in
the sand and mechanical lap counters, two vastly different systems yet both featuring
a form of memory. We narrow down our definition of memory, introduce mechanical
metamaterials, and discuss the concept of materials as computers.
Chapter two discusses the beam counter metamaterial; a block of rubber with a
specific structure such that allows it to count how often it is compressed
Chapter three discusses the interaction that occurs between buckled beams in con-
tact, which is fundamental for the working of the beam counter metamaterial. As
two beams of equal length and unequal thickness are compressed, buckle and bump
in to each other, they collectively snap in either the direction of the thinner or the
thicker beam. We find that the direction is decided solely by the distance between
these two beams. We find that for every pair of unequal beams there is a certain
critical spacing: when the beams are closer together than this critical distance, the
beams snap in the direction of the thicker beam, and when the beams are further
apart, the beams snap in the direction of the thinner beam. This interaction is the
crucial ingredient for the working of the beam counter metamaterial.
Chapter four discusses the slitted beams used in the beam counter metamaterial.
These beams feature a partial slit cut into the beam, forming a hinge that opens
only towards one side. These elements play a crucial role in the function of the beam
counter metamaterial, as these beams behave equivalent to an uncut beam at small
compression, and a strongly asymmetric beam at large compression when the hinge
opens up. In the beam counter these are beneficial as they extend further towards one
side. This chapter however is concerned more with the hysteretic response that these
beams have when compressed; as a slitted beam is compressed and it snaps open, it
will remain open when decompressed below the compression where it initially opened.
These slitted beams therefore have a memory of the past.
Chapter five discusses twistbuckler metamaterials, which build on the beam counter
metamaterial by extending to two dimensions and allowing for interactions to occur
between two bistable elements in all four stable states. These metamaterials fea-
ture base elements that twist as they buckle and interact through rigid contact with
precisely shaped interfaces.