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.

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 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.

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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