scholarly journals Phase field approximation of cohesive fracture models

2016 ◽  
Vol 33 (4) ◽  
pp. 1033-1067 ◽  
Author(s):  
S. Conti ◽  
M. Focardi ◽  
F. Iurlano
Author(s):  
Meng Fan ◽  
Yan Jin ◽  
Thomas Wick

AbstractIn this work, we develop a mixed-mode phase-field fracture model employing a parallel-adaptive quasi-monolithic framework. In nature, failure of rocks and rock-like materials is usually accompanied by the propagation of mixed-mode fractures. To address this aspect, some recent studies have incorporated mixed-mode fracture propagation criteria to classical phase-field fracture models, and new energy splitting methods were proposed to split the total crack driving energy into mode-I and mode-II parts. As extension in this work, a splitting method for masonry-like materials is modified and incorporated into the mixed-mode phase-field fracture model. A robust, accurate and efficient parallel-adaptive quasi-monolithic framework serves as basis for the implementation of our new model. Three numerical tests are carried out, and the results of the new model are compared to those of existing models, demonstrating the numerical robustness and physical soundness of the new model. In total, six models are computationally analyzed and compared.


2012 ◽  
Vol 44 (6) ◽  
pp. 3734-3754 ◽  
Author(s):  
Pierluigi Colli ◽  
Philippe Laurençot

2019 ◽  
Vol 51 (5) ◽  
pp. 3902-3920
Author(s):  
Patrick W. Dondl ◽  
Matteo Novaga ◽  
Benedikt Wirth ◽  
Stephan Wojtowytsch

2019 ◽  
Vol 12 (2) ◽  
pp. 157-179 ◽  
Author(s):  
Antonin Chambolle ◽  
Luca Alberto Davide Ferrari ◽  
Benoit Merlet

AbstractIn this paper we consider the branched transportation problem in two dimensions associated with a cost per unit length of the form {1+\beta\,\theta}, where θ denotes the amount of transported mass and {\beta>0} is a fixed parameter (notice that the limit case {\beta=0} corresponds to the classical Steiner problem). Motivated by the numerical approximation of this problem, we introduce a family of functionals ({\{\mathcal{F}_{\varepsilon}\}_{\varepsilon>0}}) which approximate the above branched transport energy. We justify rigorously the approximation by establishing the equicoercivity and the Γ-convergence of {\{\mathcal{F}_{\varepsilon}\}} as {\varepsilon\downarrow 0}. Our functionals are modeled on the Ambrosio–Tortorelli functional and are easy to optimize in practice. We present numerical evidences of the efficiency of the method.


2015 ◽  
Vol 108 ◽  
pp. 374-384 ◽  
Author(s):  
Charlotte Kuhn ◽  
Alexander Schlüter ◽  
Ralf Müller
Keyword(s):  

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