scholarly journals Phase-field approximation for a class of cohesive fracture energies with an activation threshold

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonin Chambolle ◽  
Vito Crismale
Keyword(s):  
Brittle Fracture ◽  
Asymptotic Analysis ◽  
Phase Field ◽  
Symmetric Operator ◽  
Field Approximation ◽  
Field Variable ◽  
Activation Threshold ◽  
Linearized Elasticity ◽  
The One ◽  
Limit Energy

AbstractWe study the Γ-limit of Ambrosio–Tortorelli-type functionals {D_{\varepsilon}(u,v)}, whose dependence on the symmetrised gradient {e(u)} is different in {\mathbb{A}u} and in {e(u)-\mathbb{A}u}, for a {\mathbb{C}}-elliptic symmetric operator {\mathbb{A}}, in terms of the prefactor depending on the phase-field variable v. The limit energy depends both on the opening and on the surface of the crack, and is intermediate between the Griffith brittle fracture energy and the one considered by Focardi and Iurlano [Asymptotic analysis of Ambrosio–Tortorelli energies in linearized elasticity, SIAM J. Math. Anal. 46 2014, 4, 2936–2955]. In particular, we prove that G(S)BD functions with bounded {\mathbb{A}}-variation are (S)BD.

Phase field approximation of dynamic brittle fracture

2014 ◽  
Vol 54 (5) ◽  
pp. 1141-1161 ◽  
Author(s):  
Alexander Schlüter ◽  
Adrian Willenbücher ◽  
Charlotte Kuhn ◽  
Ralf Müller
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Field Approximation ◽  
Dynamic Brittle Fracture

Phase Field Approximation of Dynamic Brittle Fracture

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 143-144 ◽  
Author(s):  
Alexander Schlüter ◽  
Charlotte Kuhn ◽  
Ralf Müller
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Field Approximation ◽  
Dynamic Brittle Fracture

scholarly journals Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Marco Cicalese ◽  
Matteo Focardi ◽  
Caterina Ida Zeppieri
Keyword(s):  
Brittle Fracture ◽  
Nonlinear Elasticity ◽  
Phase Field ◽  
Field Approximation ◽  
Variational Approximation ◽  
Geometrically Nonlinear

AbstractWe provide a variational approximation of Ambrosio–Tortorelli type for brittle fracture energies of piecewise-rigid solids. Our result covers both the case of geometrically nonlinear elasticity and that of linearised elasticity.

scholarly journals Quasi-Brittle Fracture Modeling of Preflawed Bitumen Using a Diffuse Interface Model

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yue Hou ◽  
Fengyan Sun ◽  
Wenjuan Sun ◽  
Meng Guo ◽  
Chao Xing ◽  
...  
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Field Method ◽  
Field Variable ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Bituminous Materials ◽  
Fracture Modeling

Fundamental understandings on the bitumen fracture mechanism are vital to improve the mixture design of asphalt concrete. In this paper, a diffuse interface model, namely, phase-field method is used for modeling the quasi-brittle fracture in bitumen. This method describes the microstructure using a phase-field variable which assumes one in the intact solid and negative one in the crack region. Only the elastic energy will directly contribute to cracking. To account for the growth of cracks, a nonconserved Allen-Cahn equation is adopted to evolve the phase-field variable. Numerical simulations of fracture are performed in bituminous materials with the consideration of quasi-brittle properties. It is found that the simulation results agree well with classic fracture mechanics.

scholarly journals Approximation of the Mumford–Shah functional by phase fields of bounded variation

2020 ◽  
pp. 1-35
Author(s):  
Sandro Belz ◽  
Kristian Bredies
Keyword(s):  
Image Processing ◽  
Image Segmentation ◽  
Bounded Variation ◽  
Phase Field ◽  
Field Approximation ◽  
Field Variable ◽  
Function Of Bounded Variation ◽  
Total Variation Minimization ◽  
Phase Fields ◽  
New Phase

In this paper, we introduce a new phase field approximation of the Mumford–Shah functional similar to the well-known one from Ambrosio and Tortorelli. However, in our setting the phase field is allowed to be a function of bounded variation, instead of an [Formula: see text]-function. In the context of image segmentation, we also show how this new approximation can be used for numerical computations, which contains a total variation minimization of the phase field variable, as it appears in many problems of image processing. A comparison to the classical Ambrosio–Tortorelli approximation, where the phase field is an [Formula: see text]-function, shows that the new model leads to sharper phase fields.

Convergence of discrete and continuous unilateral flows for Ambrosio–Tortorelli energies and application to mechanics

2019 ◽  
Vol 53 (2) ◽  
pp. 659-699 ◽  
Author(s):  
S. Almi ◽  
S. Belz ◽  
M. Negri
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Gradient Flow ◽  
Time Discretization ◽  
Field Variable ◽  
Small Time ◽  
One Step ◽  
The One ◽  
Discrete Finite Element ◽  
Minimization Scheme

We study the convergence of an alternate minimization scheme for a Ginzburg–Landau phase-field model of fracture. This algorithm is characterized by the lack of irreversibility constraints in the minimization of the phase-field variable; the advantage of this choice, from a computational stand point, is in the efficiency of the numerical implementation. Irreversibility is then recovered a posteriori by a simple pointwise truncation. We exploit a time discretization procedure, with either a one-step or a multi (or infinite)-step alternate minimization algorithm. We prove that the time-discrete solutions converge to a unilateral L2-gradient flow with respect to the phase-field variable, satisfying equilibrium of forces and energy identity. Convergence is proved in the continuous (Sobolev space) setting and in a discrete (finite element) setting, with any stopping criterion for the alternate minimization scheme. Numerical results show that the multi-step scheme is both more accurate and faster. It provides indeed good simulations for a large range of time increments, while the one-step scheme gives comparable results only for very small time increments.

scholarly journals Phase-field model of precipitation processes with coherency loss

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Tian-Le Cheng ◽  
You-Hai Wen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Ostwald Ripening ◽  
Phase Field Model ◽  
Energy Criterion ◽  
Field Variable ◽  
Ginzburg Landau ◽  
Underlying Mechanisms ◽  
Flood Fill ◽  
Coherency Loss

AbstractA phase-field model is proposed to simulate coherency loss coupled with microstructure evolution. A special field variable is employed to describe the degree of coherency loss of each particle and its evolution is governed by a Ginzburg-Landau type kinetic equation. For the sake of computational efficiency, a flood-fill algorithm is introduced that can drastically reduce the required number of field variables, which allows the model to efficiently simulate a large number of particles sufficient for characterizing their statistical features during Ostwald ripening. The model can incorporate size dependence of coherency loss, metastability of coherent particles, and effectively incorporate the underlying mechanisms of coherency loss by introducing a so-called differential energy criterion. The model is applied to simulate coarsening of Al3Sc precipitates in aluminum alloy and comprehensively compared with experiments. Our results clearly show how the particle size distribution is changed during coherency loss and affects the coarsening rate.

A residual control staggered solution scheme for the phase-field modeling of brittle fracture

2019 ◽  
Vol 205 ◽  
pp. 370-386 ◽  
Author(s):  
Karlo Seleš ◽  
Tomislav Lesičar ◽  
Zdenko Tonković ◽  
Jurica Sorić
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Phase Field Modeling ◽  
Field Modeling ◽  
Solution Scheme ◽  
Residual Control
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