Nonlinear Lattice Structures
: A Numerical and Analytical Study on their Stability

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Advances in both structural analysis and (meta-)material engineering has allowed previously uncharted (and often highly nonlinear) areas of the response space of elastic structures to be systematically explored. In efforts to maximise or even achieve a step change in performance, engineers and researchers voyage deeper into these uncharted nonlinear regimes. With a diverse catalogue of nonlinear behaviours and design freedoms, nonlinear cylindrical lattices have already been identified as an excellent candidate for elastic tailoring. This thesis expands the design space and response portfolio of these structures through exploiting increased geometric complexity.

Herein, geometric complexity is investigated in two complementary streams. Firstly, hierarchical assemblies of cylindrical lattices are explored and shown to exhibit a richness in response not available for single lattices in isolation. In addition, a step change in the tailorability of the response space is demonstrated, where, the energy of the lattice system is shown to approximate any polynomial energy, and thus, by Weierstrass approximation theorem, any continuous function.

Secondly, non-cylindrical lattice geometries are investigated. The added complexity warrants a modelling framework capable of describing spatially variable geometry, stiffness and pre-strain. A constitutive model is developed to describe laminated material architectures for one-dimensional continua, and subsequently employed in a finite element scheme to describe the mechanics of such lattices. The additional capability of the framework is showcased by investigating spatially variable pre-strain, where, it is demonstrated that the additional design freedoms allow for both geometric and elastic tailoring. A variety of geometrically variable lattice geometries are shown to exhibit exploitable response behaviours including snap-through and bi-stability.

Accordingly, this thesis reflects a burgeoning paradigm shift towards nonlinear elastic tailoring where enhanced functionality is achieved through subjugation of nonlinear phenomena previously deemed detrimental for structural performance; nonlinear elasticity is treated as a valuable design tool to be exploited rather than avoided.
Date of Award23 Jan 2020
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorAlberto Pirrera (Supervisor) & Isaac V Chenchiah (Supervisor)

Cite this

Nonlinear Lattice Structures: A Numerical and Analytical Study on their Stability
Dixon, M. D. X. (Author). 23 Jan 2020

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)