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We begin with a short introduction of the phase-field model for brittle fractures based on the variational approach in Section 2. Subsequently, we present the numerical implementation of the phase-field model in COMSOL in Section 3. In Section 4, we examine some 2D and 3D numerical examples ...
which themselves correspond to the two minima of the functionf(φ). The constants,Kandh0, have, respectively, dimensions of energy per unit length and energy per unit volume. The interface width is then given byW=K/h0. The phase field model can then be obtained from the following variation...
The principal idea of the variational (phase-field) approach to fracture (here explained for quasi-static fracture in brittle materials) is based on energy minimization in which potential and fracture energies interact. To this end, let\(\varOmega \subset \mathbb {R}^n\)be the intact domain ...
Many functional and quantum materials derive their functionality from the responses of both their electronic and lattice subsystems to thermal, electric, and mechanical stimuli or light. Here we propose a dynamical phase-field model for predicting and mo
The complex degradation of metallic materials in aggressive environments can result in morphological and microstructural changes. The phase-field (PF) method is an effective computational approach to understanding and predicting the morphology, phase cha
We present a phase-field model (PFM) for solidification in binary alloys, which is found from the phase-field model for a pure material by direct comparison of the variables for a pure material solidification and alloy solidification. The model appears to be equivalent with the Wheeler-Boettinge...
Phase-Field Modeling of Ductile Fracture at Finite Strains. A Robust Variational-Based Numerical Implementation of a Gradient-Extended Theory by Micromorph... This work provides a robust variational-based numerical implementation of a phase field model of ductile fracture in elastic-plastic solids under...
Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn–Hilliard approach. In this paper we study a macroscopic mechanical model for tumour growth in which cell–cell adhesion effects are taken into account with the help of a Ginzburg–Landau...
Existing grand-potential based multicomponent phase-field model is extended to handle systems with interstitial sublattice. This is achieved by treating the concentration of alloying elements in site-fraction. Correspondingly, the chemical species are distinguished based on their lattice positions, and thei...