Specific restitution in cases of vitiated consent

This piece was given at the SLS 2012 in the Restitution sub-section. It was one of two finalists for the best paper at the Restitution section that year.

The availability of proprietary restitution in cases of mistaken payments

This article is concerned with the availability of “proprietary restitution” in cases of mistaken payments. It is argued that the mistake of the claimant is an insufficient justification for proprietary restitution, however a close analysis of the case law demonstrates that the presence of additional factors can justify the availability of proprietary restitution in specific circumstances. The basis of proprietary restitution is to be found in the breach of a duty which arises separately from the claim for unjust enrichment. The significant contribution of this article is the analysis that knowledge merely creates a duty to maintain the fund until restitution is made, and that knowledge cannot establish the breach of this duty. Importantly, breach of this duty is established by a second condition which is demonstrated by the wilful misconduct of the recipient. It is this conduct which justifies the imposition of the constructive trust. By adopting this analysis, the proprietary claim in the context of mistaken transfers can be classified as forming part of the law of wrongs, rather than the law of unjust enrichment.

Finite element analysis of particle impact problems

Particle impacts are of fundamental importance in many areas and there has been a renewed interest in research on particle impact problems. A comprehensive investigation of the particle impact problems, using finite element (FE) methods, is presented in this thesis. The capability of FE procedures for modelling particle impacts is demonstrated by excellent agreements between FE analysis results and previous theoretical, experimental and numerical results. For normal impacts of elastic particles, it is found that the energy loss due to stress wave propagation is negligible if it can reflect more than three times during the impact, for which Hertz theory provides a good prediction of impact behaviour provided that the contact deformation is sufficiently small. For normal impact of plastic particles, the energy loss due to stress wave propagation is also generally negligible so that the energy loss is mainly due to plastic deformation. Finite-deformation plastic impact is addressed in this thesis so that plastic impacts can be categorised into elastic-plastic impact and finite-deformation plastic impact. Criteria for the onset of finite-deformation plastic impacts are proposed in terms of impact velocity and material properties. It is found that the coefficient of restitution depends mainly upon the ratio of impact velocity to yield Vni/Vy0 for elastic-plastic impacts, but it is proportional to [(Vni/Vy0)*(Y/E*)]-1/2, where Y /E* is the representative yield strain for finite-deformation plastic impacts. A theoretical model for elastic-plastic impacts is also developed and compares favourably with FEA and previous experimental results. The effect of work hardening is also investigated.

Elasto-plastic impact of fine particles and fragmentation of small agglomerates

Surface deposition of dense aerosol particles is of major concern in the nuclear industry for safety assessment. This study presents theoretical investigations and computer simulations of single gas-born U3O8 particles impacting with the in-reactor surface and the fragmentation of small agglomerates. A theoretical model for elasto-plastic spheres has been developed and used to analyse the force-displacement and force-time relationships. The impulse equations, based on Newton's second law, are applied to govern the tangential bouncing behaviour. The theoretical model is then incorporated into the Distinct Element Method code TRUBAL in order to perform computer simulated tests of particle collisions. A comparison of simulated results with both theoretical predictions and experimental measurements is provided. For oblique impacts, the results in terms of the force-displacement relationship, coefficients of restitution, trajectory of the impacting particle, and distribution of kinetic energy and work done during the process of impact are presented. The effects of Poisson's ratio, friction, plastic deformation and initial particle rotation on the bouncing behaviour are also discussed. In the presence of adhesion an elasto-plastic collision model, which is an extension to the JKR theory, is developed. Based on an energy balance equation the critical sticking velocity is obtained. For oblique collisions computer simulated results are used to establish a set of criteria determining whether or not the particle bounces off the target plate. For impact velocities above the critical sticking value, computer simulated results for the coefficients of restitution and rebound angles of the particle are presented. Computer simulations of fracture/fragmentation resulting from agglomerate-wall impact have also been performed, where two randomly generated agglomerates (one monodisperse, the other polydisperse), each consisting of 50 primary particles are used. The effects of impact angle, local structural arrangements close to the impact point, and plastic deformation at the contacts on agglomerate damage are examined. The simulated results show a significant difference in agglomerate strength between the two assemblies. The computer data also shows that agglomerate damage resulting from an oblique impact is determined by the normal velocity component rather than the impact speed.