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

A finite deformation Cosserat continuum model for uncured carbon fibre composites

A new three-dimensional, finite deformation Cosserat continuum model for the elastic response of uncured carbon fibre composites is presented. The new composite process model captures the bending contribution of bundles of fibres at the microscale within a mesoscale continuum description of a composite ply. This is achieved by introducing higher-order, independent rotational degrees of freedom into the continuum formulation. This paper demonstrates the inclusion of such mechanics is essential to accurately model various bending responses induced during typical composite manufacturing processes. This includes large deformation forming, finite strain consolidation and wrinkling (the formation of an unwanted defect). If such mechanics are not included, the literature demonstrates the resulting finite element solutions have a pathological dependence on the mesh size. As a result, simulations require users to fit mesh-dependent material parameters, which limits confidence in their predictive capabilities. The Cosserat continuum, which can be seen as a form of the regularised continuum model, overcomes these challenges. In particular, this paper presents details of the finite element formulation of the new continuum model within a nonlinear Taylor–Hood Cosserat Element. Implementation details of embedding this new element within the commercial code Abaqus are given, alongside a series of increasingly complex validation simulations. Notably, the examples include modelling the formation of internal fibre wrinkles and large deformation forming, which involves complex ply-to-ply and tool-to-ply contact. The paper concludes by describing: (1) how the elastic Cosserat model can be integrated into existing large deformation process models in the literature. The approach set out readily allows researchers to include the important effects of resin flow, cure kinetics and temperature distribution, not considered in this contribution, and (2) how it is envisaged that the ply scale model can be naturally scaled up to large laminate scale simulation using mathematical upscaling techniques

Chevron folding patterns and heteroclinic orbits

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We present a model of multilayer folding in which layers with bending stiffness EI are separated by a very stiff elastic medium of elasticity k2 and subject to a horizontal load P. By using a dynamical systems analysis of the resulting fourth order equation, we show that as the end shortening per unit length E is increased, then if k2 is large there is a smooth transition from small amplitude sinusoidal solutions at moderate values of P to larger amplitude chevron folds, with straight limbs separated by regions of high curvature when P is large. The chevron solutions take the form of near heteroclinic connections in the phase-plane. By means of this analysis, values for P and the slope of the limbs are calculated in terms of E and k2.We would like to acknowledge the support of the FP7 Marie-Curie ITN FIRST, the Pacific Institute for Mathematics Sciences (PIMS) and the NSERC Discovery Grant for the funding of the research described in this pape

30-day mortality after systemic anticancer treatment for breast and lung cancer in England: a population-based, observational study

Background: 30-day mortality might be a useful indicator of avoidable harm to patients from systemic anticancer treatments, but data for this indicator are limited. The Systemic Anti-Cancer Therapy (SACT) dataset collated by Public Health England allows the assessment of factors affecting 30-day mortality in a national patient population. The aim of this first study based on the SACT dataset was to establish national 30-day mortality benchmarks for breast and lung cancer patients receiving SACT in England, and to start to identify where patient care could be improved. Methods: In this population-based study, we included all women with breast cancer and all men and women with lung cancer residing in England, who were 24 years or older and who started a cycle of SACT in 2014 irrespective of the number of previous treatment cycles or programmes, and irrespective of their position within the disease trajectory. We calculated 30-day mortality after the most recent cycle of SACT for those patients. We did logistic regression analyses, adjusting for relevant factors, to examine whether patient, tumour, or treatment-related factors were associated with the risk of 30-day mortality. For each cancer type and intent, we calculated 30-day mortality rates and patient volume at the hospital trust level, and contrasted these in a funnel plot. Findings: Between Jan 1, and Dec, 31, 2014, we included 23 228 patients with breast cancer and 9634 patients with non-small cell lung cancer (NSCLC) in our regression and trust-level analyses. 30-day mortality increased with age for both patients with breast cancer and patients with NSCLC treated with curative intent, and decreased with age for patients receiving palliative SACT (breast curative: odds ratio [OR] 1·085, 99% CI 1·040–1·132; p<0·0001; NSCLC curative: 1·045, 1·013–1·079; p=0·00033; breast palliative: 0·987, 0·977–0·996; p=0·00034; NSCLC palliative: 0·987, 0·976–0·998; p=0·0015). 30-day mortality was also significantly higher for patients receiving their first reported curative or palliative SACT versus those who received SACT previously (breast palliative: OR 2·326 99% CI 1·634–3·312; p<0·0001; NSCLC curative: 3·371, 1·554–7·316; p<0·0001; NSCLC palliative: 2·667, 2·109–3·373; p<0·0001), and for patients with worse general wellbeing (performance status 2–4) versus those who were generally well (breast curative: 6·057, 1·333–27·513; p=0·0021; breast palliative: 6·241, 4·180–9·319; p<0·0001; NSCLC palliative: 3·384, 2·276–5·032; p<0·0001). We identified trusts with mortality rates in excess of the 95% control limits; this included seven for curative breast cancer, four for palliative breast cancer, five for curative NSCLC, and seven for palliative NSCLC. Interpretation: Our findings show that several factors affect the risk of early mortality of breast and lung cancer patients in England and that some groups are at a substantially increased risk of 30-day mortality. The identification of hospitals with significantly higher 30-day mortality rates should promote review of clinical decision making in these hospitals. Furthermore, our results highlight the importance of collecting routine data beyond clinical trials to better understand the factors placing patients at higher risk of 30-day mortality, and ultimately improve clinical decision making. Our insights into the factors affecting risk of 30-day mortality will help treating clinicians and their patients predict the balance of harms and benefits associated with SACT. Funding: Public Health England