Analysis and simulations for a phase‐field fracture model at finite strains based on modified invariants

Phase‐field models have already been proven to predict complex fracture patterns for brittle fracture at small strains. In this paper we discuss a model for phase‐field fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in solid mechanics. Here we present a phase‐field model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split of the modified invariants of the right Cauchy‐Green strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions and we show that the time‐discrete solutions converge in a weak sense to a solution of the time‐continuous formulation of the model. Numerical examples in two and three space dimensions illustrate the range of validity of the analytical results

Women, men and coronary heart disease: a review of the qualitative literature

Aim. This paper presents a review of the qualitative literature which examines the experiences of patients with coronary heart disease. The paper also assesses whether the experiences of both female and male patients are reflected in the literature and summarizes key themes. Background. Understanding patients' experiences of their illness is important for coronary heart disease prevention and education. Qualitative methods are particularly suited to eliciting patients' detailed understandings and perceptions of illness. As much previous research has been 'gender neutral', this review pays particular attention to gender. Methods. Published papers from 60 qualitative studies were identified for the review through searches in MEDLINE, EMBASE, CINAHL, PREMEDLINE, PsychINFO, Social Sciences Citation Index and Web of Science using keywords related to coronary heart disease. Findings. Early qualitative studies of patients with coronary heart disease were conducted almost exclusively with men, and tended to generalize from 'male' experience to 'human' experience. By the late 1990s this pattern had changed, with the majority of studies including women and many being conducted with solely female samples. However, many studies that include both male and female coronary heart disease patients still do not have a specific gender focus. Key themes in the literature include interpreting symptoms and seeking help, belief about coronary 'candidates' and relationships with health professionals. The influence of social roles is important: many female patients have difficulties reconciling family responsibilities and medical advice, while male patients worry about being absent from work. Conclusions. There is a need for studies that compare the experiences of men and women. There is also an urgent need for work that takes masculinity and gender roles into account when exploring the experiences of men with coronary heart disease

Foundation, analysis, and numerical investigation of a variational network-based model for rubber

Since the pioneering work by Treloar, many models based on polymer chain statistics have been proposed to describe rubber elasticity. Recently, Alicandro, Cicalese, and the first author rigorously derived a continuum theory of rubber elasticity from a discrete model by variational convergence. The aim of this paper is twofold. First, we further physically motivate this model and complete the analysis by numerical simulations. Second, in order to compare this model to the literature, we present in a common language two other representative types of models, specify their underlying assumptions, check their mathematical properties, and compare them to Treloar's experiments. © 2012 Springer-Verlag Berlin Heidelberg.SCOPUS: ar.jinfo:eu-repo/semantics/publishe