An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional

By Siobhan Burke, Christoph Ortner, Endre Süli. 2013

86 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/1704f9195ff3b2e9aa426c5a40a6368788520f02

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model (2016, methodology): “In particular, mesh refinement allows us to perform systematic studies with respect to the spatial discretization parameter.”
Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation (2017, background): “directions as attested in papers on various solution techniques [39, 50, 53, 1, 3, 48, 27, 74, 24], isogeometric analysis [12, 11, 34, 4, 33], discontinuous/enriched Galerkin [23, 58], adaptive (spatial) discretizations [18, 19, 8, 72], dynamic fracture [40, 41, 12, 16, 35, 62], ductile/cohesive fra”
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity (2016, methodology): “An analysis of adaptive finite element approximations for fracture evolutions based on Ambrosio-Tortorelli approximations [4,5] has been carried out in [23,24].”
Crack nucleation in variational phase-field models of brittle fracture (2018, unknown): “…a broad class of energies, including the ones above was achieved with various degrees of reﬁnement going from static scalar elasticity to time discrete and time continuous quasi-static evolution linearized elasticity, and their ﬁnite element discretization [12, 16, 23, 46, 27, 28, 45, 25, 26, 56].”
A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects (2016, background): “[15] and also a higher-order functional by Borden et al.”
A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach (2015, methodology): “Additionally, the numerical techniques based on the alternate minimization algorithm with backtracking (fixing one variable while solving for the other in an iteration process) does not guarantee convergence to the global minimum [3, 8, 27, 28].”
The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “Other examples include image classification and restoration [370], edge detection [15], motion estimation [351], image segmentation [76, 280, 308], curve smoothing [465], active contour [362], clustering of vector fields [227], and so on.”