Multistable structures have a promising potential in a wide range of engineering and
scientific applications, such as shock absorption, soft robotics, superelastic structures,
vibration mitigation, foldable structures, configurable structures, programmable
materials, and tunable shape-memory structures. In addition, they are directly
relevant to the study of materials undergoing martensitic phase transformations,
macromolecular networks, and the development of new metamaterials. In this paper,
we study the quasistatic behavior of 2-D bistable lattices subjected to shear, with
emphasis on the multitude of equilibrium configurations, overall stress-strain relation,
sequence of phase transition, and statistics of stress jumps. In particular, the
influence of material (properties of the individual bistable interaction) and
microstructure geometry (architecture of the lattice) on the above mentioned
characteristics of the overall behavior is investigated. To this end, we perform
extensive numerical simulations with four different periodic lattice geometries. We
find that, for the same loading conditions, different lattice geometries or
different material (bistable) properties of the building block may result in
fundamentally different overall (macro) behaviors. This is manifested both in the
overall stress-strain relation and also in the evolution of the phase-transition
patterns. Also, hysteresis, which is a macroscopic manifestation of the energy
dissipated during change of configuration, is significantly affected by the
lattice architecture. Similar effects of geometrical incompatibility, but at the
level of the atomic lattice, have been observed in shape-memory alloys. Our
results also reproduce stress peaks, associated with nucleation of a new phase.
The magnitude of these nucleation peaks, their location, and number is
dictated by the geometry of the lattice and boundary effects that lead to stress
concentrations.
