scholarly journals Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions

2017 ◽  
Vol 122 (4) ◽  
pp. 2565-2589 ◽  
Author(s):  
David Santillán ◽  
Ruben Juanes ◽  
Luis Cueto-Felgueroso
Keyword(s):  
Analytical Solutions ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Elastic Media

A Γ-convergence result for fluid-filled fracture propagation

2020 ◽  
Vol 54 (3) ◽  
pp. 1003-1023
Author(s):  
Annika Bach ◽  
Liesel Sommer
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Discontinuous Galerkin ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Fracture Propagation ◽  
Convergence Result ◽  
Elastic Media ◽  
Γ Convergence

In this paper we provide a rigorous asymptotic analysis of a phase-field model used to simulate pressure-driven fracture propagation in poro-elastic media. More precisely, assuming a given pressure p ∈ W 1,∞ (Ω) we show that functionals of the form $$ E(\vec{u})={\int }_{\mathrm{\Omega }} e(\vec{u}):\mathbb{C}e(\vec{u})+p\nabla \cdot \vec{u}+\left\langle \nabla p,\vec{u}\right\rangle\enspace \mathrm{d}x+{\mathcal{H}}^{n-1}({J}_{\vec{u}}),\enspace \vec{u}\in \mathrm{G}{SBD}(\mathrm{\Omega })\cap {L}^1(\mathrm{\Omega };{\mathbb{R}}^n) $$ can be approximated in terms of Γ-convergence by a sequence of phase-field functionals, which are suitable for numerical simulations. The Γ-convergence result is complemented by a numerical example where the phase-field model is implemented using a Discontinuous Galerkin Discretization.

CO2 fracturing using the phase field approach for the brittle fracture

2021 ◽  
Author(s):  
Mostafa Mollaali ◽  
Vahid Ziaei-Rad ◽  
Yongxing Shen
Keyword(s):  
Analytical Solutions ◽  
Phase Field ◽  
Field Model ◽  
Isothermal Condition ◽  
Phase Field Model ◽  
Fracture Initiation ◽  
State Equation ◽  
Fracture Path ◽  
Field Approach ◽  
Good Agreement

<p>To simulate CO<sub>2</sub> fracturing under an isothermal condition, we propose a phase field model. We take advantage of the ability of the phase field approach to predict fracture initiation and branching, as well as to avoid tracking the fracture path. We model the CO<sub>2</sub> as a compressible fluid by modifying Darcy's law. In particular, we assume that the permeability is correlated to the value of the phase field by the exponential function. The dependence of the CO<sub>2</sub> density as a function of the pressure is captured by the Span-Wagner state equation. The computed pressure breakdown values show good agreement with analytical solutions and experimental results.</p>

MARMOT Phase-Field Model for the U-Si System

2016 ◽  
Author(s):  
Larry Kenneth Aagesen ◽  
Daniel Schwen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model

scholarly journals Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Min Yang ◽  
Lu Wang ◽  
Wentao Yan
Keyword(s):  
Additive Manufacturing ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Nucleation Theory ◽  
Experimental Result ◽  
Classical Nucleation Theory ◽  
Validation Experiment ◽  
Powder Particles

AbstractA three-dimensional phase-field model is developed to simulate grain evolutions during powder-bed-fusion (PBF) additive manufacturing, while the physically-informed temperature profile is implemented from a thermal-fluid flow model. The phase-field model incorporates a nucleation model based on classical nucleation theory, as well as the initial grain structures of powder particles and substrate. The grain evolutions during the three-layer three-track PBF process are comprehensively reproduced, including grain nucleation and growth in molten pools, epitaxial growth from powder particles, substrate and previous tracks, grain re-melting and re-growth in overlapping zones, and grain coarsening in heat-affected zones. A validation experiment has been carried out, showing that the simulation results are consistent with the experimental results in the molten pool and grain morphologies. Furthermore, the grain refinement by adding nanoparticles is preliminarily reproduced and compared against the experimental result in literature.

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