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

‘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