A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework

By Michael J. Borden, Thomas J. R. Hughes, Chad M. Landis, Clemens V. Verhoosel. 2014

589 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6ea06abbb3932b5ccbe71b73954c4a83051ad82d

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Phase Field Modeling of Fracture in Multi-Physics Problems. Part II. Coupled Brittle-to-Ductile Failure Criteria and Crack Propagation in Thermo-Elastic-Plastic Solids (2015, unknown): “[27].”
On penalization in variational phase-field models of brittle fracture (2018, methodology): “The staggered (also termed partitioned, or alternate minimization) solution approach based on decoupling of the strongly non-linear weak formulation into a system and then iterating between the equations is commonly used [2, 3, 4, 5, 9, 13, 14, 15, 17, 19, 21].”
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity (2016, background): “, [39,16,36,51,3]) and likewise theoretical advancements based on energy minimization concepts treated with calculus of variations techniques [25,20]; systematic studies towards goal functional evaluations and a posteriori error estimation with local mesh adaptivity are rarely to find.”
The phase field method for geometric moving interfaces and their numerical approximations (2019, methodology): “Subsequent studies include applications to phase field models for topology optimization [136], phase field models of brittle fracture [62], high order equations on surfaces [47], Darcy flows [137], chemotaxis [330] and electrochemical reactions [462].”
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture (2019, methodology): “In the energy method, the solution is obtained by minimization of the total variational energy of the system, E [7, 16, 17].”
Phase-field description of brittle fracture in plates and shells (2016, methodology): “[46] exploited the higher continuity of isogeometric basis functions for proposing a higher-order phasefield model, which was combined by Hesch et al.”
A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach (2015, background): “[41] provide some useful hints on the calculation of the strain energy decomposition in three dimensions.”