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

Riboflavin alleviates cardiac failure in Type I diabetic cardiomyopathy

Heart failure (HF) is a common and serious comorbidity of diabetes. Oxidative stress has been associated with the pathogenesis of chronic diabetic complications including cardiomyopathy. The ability of antioxidants to inhibit injury has raised the possibility of new therapeutic treatment for diabetic heart diseases. Riboflavin constitutes an essential nutrient for humans and animals and it is an important food additive. Riboflavin, a precursor of flavin mononucleotide (FMN) and flavin adenine dinucleotide (FAD), enhances the oxidative folding and subsequent secretion of proteins. The objective of this study was to investigate the cardioprotective effect of riboflavin in diabetic rats. Diabetes was induced in 30 rats by a single injection of streptozotocin (STZ) (70 mg /kg). Riboflavin (20 mg/kg) was orally administered to animals immediately after induction of diabetes and was continued for eight weeks. Rats were examined for diabetic cardiomyopathy by left ventricular (LV) remadynamic function. Myocardial oxidative stress was assessed by measuring the activity of superoxide dismutase (SOD), the level of malondialdehyde (MDA) as well as heme oxygenase-1 (HO-1) protein level. Myocardial connective tissue growth factor (CTGF) level was measured by Western blot in all rats at the end of the study. In the untreated diabetic rats, left ventricular systolic pressure (LVSP) rate of pressure rose (+dp/dt), and rate of pressure decay (−dp/dt) were depressed while left ventricular end-diastolic pressure (LVEDP) was increased, which indicated the reduced left ventricular contractility and slowing of left ventricular relaxation. The level of SOD decreased, CTGF and HO-1 protein expression and MDA content rose. Riboflavin treatment significantly improved left ventricular systolic and diastolic function in diabetic rats, there were persistent increases in significant activation of SOD and the level of HO-1 protein, and a decrease in the level of CTGF. These results suggest that riboflavin treatment ameliorates myocardial function and improves heart oxidant status, whereas raising myocardial HO-1 and decreasing myocardial CTGF levels have beneficial effects on diabetic cardiomyopathy

On worm-like chain models within the three-dimensional continuum mechanics framework

In this paper, we review critically some basic models derived from the statistics of long chain molecules and then discuss the status of such models within the three-dimensional nonlinear theory of elasticity. We draw attention to some deficiencies of certain wormlike chain (WLC) models when viewed within the three-dimensional continuum mechanics framework. Modifications of the WLC models motivated by such considerations and avoiding these deficiencies are then discussed and shown to correspond well with data generated by the exact WLC model