Contact problems of hyperelastic membranes: Existence theory

In this paper we describe the pressure-driven inflation of an incompressible isotropic hyperelastic mem brane into a rigid mould by a variational inequality and consider the existence of a solution in the case of various, suitably modified, strain energy functions of the Ogden form. The variational inequality description is applicable to the case of perfect sliding contact of the membrane with the mould and the modification to the strain energy function is according to tension field theory which rules out compressive stresses. The modified or relaxed strain energy functions obtained are shown, in our examples, to be polyconvex and in some cases convex. Using such properties, the main result of the paper is an existence theorem for a solution of the variational inequality

Numerical Techniques for the Treatment of Quasistatic Solid Viscoelastic Stress Problems

For quasistatic stress problems two alternative constitutive relationships expressing the stress in a linear viscoelastic solid body as a linear functional of the strain are derived. In conjunction with the equations of equilibrium these form the mathematical models for the stress problems. These models are first discretized in the space domain using a finite element method and semi-discrete error estimates are presented corresponding to each constitutive relationship. Through the use respectively of quadrature rules and finite difference replacements each semi-discrete scheme is fully discretized into the time domain so that two practical algorithms suitable for the numerical stress analysis of linear viscoelastic solids are produced. The semi-discretes estimates are then also extended into the time domain to give spatially H1 error estimates for each alogrithm. The numerical schemes are predicated on exact analytical solutions for a simple model problem, and finally on design data for a real polymerical material

‘I am not someone who gets skin cancer’: Risk, time and malignant melanoma

‘Delay’ is a term used in the cancer literature since the 1930s to describe the period between self-detection of a concerning sign of possible disease and presentation to a health professional. This linguistic choice carries an implication of blame for apparent failure to manage a risk appropriately, drawing attention away from the contemporaneous perspectives of those who respond to suspicious indicators more or less quickly. We present findings from a grounded theory study of accounts given by 45 patients about their slower or quicker journeys to a diagnosis of cutaneous malignant melanoma, a cancer which can ‘hide in plain sight’. There has been little research exploring in qualitative detail patients’ perspectives on their decision-making about what subsequently turn out to have been signs of this most risky of skin cancers. The findings frame referral time-lapses in terms of normalisation of symptoms, sometimes buttressed by reassurance derived from health promotion messages, disconfirmation of patients’ concerns by their general practitioners and prioritisation of other life concerns. We argue that a shared sense of urgency surrounding melanoma self-referral derives from a clinical representation of current knowledge which conceals numerous evidential uncertainties