In this paper a phase-field model for cohesive fracture is developed. After casting the cohesive zone approach in an energetic framework, which is suitable for incorporation in phase-field approaches, the phase-field approach to brittle fracture is recapitulated. The approximation to the Dirac function is discussed with particular emphasis on the Dirichlet boundary conditions that arise in the ...

Abstract We have developed a 2-D numerical meshless adaptive approach for phase-field modelling of dendritic solidification. The quadtree-based decomposes the computational domain into quadtree sub-domains different sizes. algorithm generates uniformly-distributed nodes in each sub-domain. apply radial basis function generated finite difference method and forward Euler scheme to discretise gove...

Electrode particle cracking is one of the main phenomena driving battery capacity degradation. Recent phase field fracture studies have investigated behaviour. However, only beginning life has been considered and effects such as damage accumulation neglected. Here, a multi-physics fatigue model developed to study crack propagation in electrode particles undergoing hundreds cycles. In addition, ...

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with ...

the aim of present paper is to provide mathematical modelling for the two-dimensional mhd flow with induced magnetic field. the flaws in the already existing equations have been pointed out. the results of low magnetic reynolds number approximation are recovered as a special case from the developed equations. as an example, the peristaltic flow for a couple stress fluid in a channel is consider...

Abstract There is a growing demand for magnetic materials straight forward in wind turbines and electric motors. Their functional properties depend critically on their microstructure thus the evolution during sintering or heat treatment. Field-assisted selective grain growth allows to optimize microstructure. However, simultaneous modeling of structural degrees freedom micrometer scale not poss...