A linear second-order in time unconditionally energy stable finite element scheme for a Cahn–Hilliard phase-field model for two-phase incompressible flow of variable densities

2021 ◽  
Vol 387 ◽  
pp. 114186
Author(s):  
Guosheng Fu ◽  
Daozhi Han
Keyword(s):  
Finite Element ◽  
Incompressible Flow ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Finite Element Scheme ◽  
Two Phase ◽  
Element Scheme ◽  
Second Order In Time ◽  
Energy Stable

Simulation of Laser-Induced Controlled Fracturing Utilizing a Phase Field Model

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
Alexander Schlüter ◽  
Charlotte Kuhn ◽  
Ralf Müller
Keyword(s):  
Finite Element ◽  
Phase Field ◽  
Laser Power ◽  
Laser Cutting ◽  
Field Model ◽  
Phase Field Model ◽  
Work Piece ◽  
Finite Element Scheme ◽  
Ceramic Substrates ◽  
Element Scheme

This work presents an approach to simulate laser cutting of ceramic substrates utilizing a phase field model for brittle fracture. To start with, the necessary thermoelastic extension of the original phase field model is introduced. Here, the Beer–Lambert law is used in order to model the effect of the laser on the substrate. The arising system of partial differential equations—which comprises the balance of linear momentum, the energy balance, and the evolution equation that governs crack propagation—is solved by a monolithic finite-element scheme. Finally, the influences of the laser power and the initial groove size on the manufactured work piece are analyzed numerically in simulations of a laser-cutting process.

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