Multilayered folding with voids

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers results in geometrically-induced curvature singularities. When voids are penalized by external pressure, the system is forced to trade off these competing effects, leading to sometimes striking periodic patterns. In this paper we construct a simple model of geometrically nonlinear multi-layered structures under axial loading and pressure confinement, with non-interpenetration conditions separating the layers. Energy minimizers are characterized as solutions of a set of fourth-order nonlinear differential equations with contact-force Lagrange multipliers, or equivalently of a fourth-order free-boundary problem. We numerically investigate the solutions of this free boundary problem, and compare them with the periodic solutions observed experimentally

Self-similar voiding solutions of a single layered model of folding rocks

In this paper we derive an obstacle problem with a free boundary to describe the formation of voids at areas of intense geological folding. An elastic layer is forced by overburden pressure against a V-shaped rigid obstacle. Energy minimization leads to representation as a nonlinear fourth-order ordinary differential equation, for which we prove their exists a unique solution. Drawing parallels with the Kuhn-Tucker theory, virtual work, and ideas of duality, we highlight the physical significance of this differential equation. Finally we show this equation scales to a single parametric group, revealing a scaling law connecting the size of the void with the pressure/stiffness ratio. This paper is seen as the first step towards a full multilayered model with the possibility of voiding

Electrocatalyst Degradation in Polymer Electrolyte Membrane Water Electrolysers

Polymer electrolyte membrane water electrolysis (PEMWE) is predicted to become one of the backbone technologies of the future ‘hydrogen economy’, but for this to be realized several obstacles must be overcome. Importantly, an understanding of PEMWE system lifetime is incomplete as the various degradation routes have not been fully characterized or quantified. In this thesis several improvements to this understanding are presented. Firstly, time-based in situ open circuit voltage (OCV) data under a range of relevant ambient pressure conditions are presented. The impact of aqueous and gaseous environments has been elucidated, and it has been shown that potential change during OCV may proceed on either the anode, cathode or neither. These practical results have been enhanced with a basic model of OCV which shows that there is no universal OCV profile that can be applied to all PEMWE conditions. The impact of cathode potential change during OCV on the degradation of platinum has also been established. By the coupling of a 3-electrode PEM electrolyser cell, and using a differential pulse voltammetry technique, Pt dissolution from the cell was detected when the cathode potential rose above 0.85 V versus the normal hydrogen electrode (NHE). This reached a maximum dissolution rate at the highest cathode potential of 1.02 V NHE, and gradually decayed over an approximately 100 h period. This was established during OCV both on Pt black (PtB) and Pt on carbon (Pt/C) electrocatalysts. It was demonstrated that, in the case of Pt/C, the dissolution phenomenon may impact the lifetime of the PEMWE system to less than 5 years. It has been clearly shown that OCV conditions cause degradation of the cathode electrocatalyst, and so must be considered when evaluating PEMWE lifetime

A survey of vote slacking in five communities with implications for social studies curriculum

Thesis (Ed.M.)--Boston University, 1947. This item was digitized by the Internet Archive

Complexity in phase transforming pin-jointed auxetic lattices

This is the author accepted manuscript. The final version is available from The Royal Society via the DOI in this record.We demonstrate the complexity that can exist in the modelling of auxetic lattices. By introducing pin-jointed members and large deformations to the analysis of a re-entrant structure, we create a material which has both auxetic and non-auxetic phases. Such lattices exhibit complex equilibrium behaviour during the highly nonlinear transition between these two states. The local response is seen to switch many times between stable and unstable states, exhibiting both positive and negative stiffnesses. However, there is shown to exist an underlying emergent modulus over the transitional phase, to describe the average axial stiffness of a system comprising a large number of cells.Engineering and Physical Sciences Research Council (EPSRC