A phase-field description of dynamic brittle fracture

By Michael J. Borden, Clemens V. Verhoosel, Michael A. Scott, Thomas J. R. Hughes, Chad M. Landis. 2012

1,857 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e8645f50da635b816dcadcf242a8d31eb9d0d425

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Phase-field description of brittle fracture in plates and shells (2016, result): “The resulting crack paths coincide with those obtained in previous investigations [10,11,13,25].”
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”
Isogeometric collocation using analysis-suitable T-splines of arbitrary degree (2016, methodology): “Relevant advances have been carried out since then: mathematical background of T-splines has been studied [52, 53, 54, 55], several procedures to create volumetric T-splines have been designed [56, 57, 58, 59, 60], the conversion of a trimmed NURBS surface to an untrimmed T-spline surface was tackle”
Phase-field models for brittle and cohesive fracture (2014, neutral): “As in [4] we consider the approximated Dirac function with ‘ [ 0 a length scale parameter.”
A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects (2016, methodology): “The temporal discretization of the governing equations is achieved through an adaptation of the generalized-α method using a staggered scheme to solve for displacement and phase-field increments independently (see [8] for details).”
A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations (2015, methodology): “Pham et al.(2011); Borden et al.(2012) andPham and Marigo (2013) also state that the length scale parameterℓ in the model byBourdin et al. (2000) can be interpreted as a material parameter since it influences the critical stress.”
Isogeometric analysis: An overview and computer implementation aspects (2012, methodology): “, [18, 83], and the thick level set method [85].”
Why do cracks branch? A peridynamic investigation of dynamic brittle fracture (2015, background): “The regularization parameter that defines the width of the failure zone in phase-field models permits (see Borden et al. 2012) obtaining the “crack thickening” before branching that may be a representation of roughening of the crack surface before branching observed in experiments.”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, background): “More recently, phase field approaches have been successfully considered to provide mathematical models for problems in different disciplines; for example, there are models for crack propagation [18, 66], also with Cahn–Hilliard equation [97], image segmentation [104] and cancer and tumor growth [41,”