Truncated nonsmooth Newton multigrid for phase-field brittle-fracture problems, with analysis

DOI10.1007/s00466-023-02330-xzbMath1528.74101arXiv2007.12290MaRDI QIDQ6062949

Carsten Gräser, Daniel Kienle, Oliver Sander

Publication date: 2 December 2023

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.12290

zbMATH Keywords

global convergenceconvex analysisnotched barfirst-order Lagrangian finite elementnotched specimen testspectral strain decomposition

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Brittle fracture (74R10) Finite element methods applied to problems in solid mechanics (74S05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An augmented-Lagrangian method for the phase-field approach for pressurized fractures
• A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits
• Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras
• Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments
• The variational approach to fracture mechanics. A practical application to the French Panthéon in Paris
• Numerical experiments in revisited brittle fracture
• An overview of the modelling of fracture by gradient damage models
• A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach
• Robust numerical implementation of non-standard phase-field damage models for failure in solids
• On penalization in variational phase-field models of brittle fracture
• A review on phase-field models of brittle fracture and a new fast hybrid formulation
• Matrix-free multigrid solvers for phase-field fracture problems
• Interior-point methods for the phase-field approach to brittle and ductile fracture
• On the BFGS monolithic algorithm for the unified phase field damage theory
• A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture
• An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters
• The \textsc{Dune} framework: basic concepts and recent developments
• A line search assisted monolithic approach for phase-field computing of brittle fracture
• Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation
• Rate-independent systems. Theory and application
• A nonsmooth version of Newton's method
• A phase-field crack model based on directional stress decomposition
• Numerical implementation of the variational formulation for quasi-static brittle fracture
• A phase-field model for fractures in nearly incompressible solids
• Solving primal plasticity increment problems in the time of a single predictor-corrector iteration
• Nonlinear field-split preconditioners for solving monolithic phase-field models of brittle fracture
• Twice Differentiable Spectral Functions
• Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
• Approximation of functional depending on jumps by elliptic functional via t-convergence
• Truncated Nonsmooth Newton Multigrid Methods for Convex Minimization Problems
• Semismoothness of Spectral Functions
• Projected Newton Methods for Optimization Problems with Simple Constraints
• Convex Analysis on the Hermitian Matrices
• An Optimal Control Problem Governed by a Regularized Phase-Field Fracture Propagation Model
• Truncated nonsmooth Newton multigrid methods for block-separable minimization problems
• DUNE — The Distributed and Unified Numerics Environment
• An Error-Oriented Newton/Inexact Augmented Lagrangian Approach for Fully Monolithic Phase-Field Fracture Propagation
• AN ADAPTIVE FINITE ELEMENT APPROXIMATION OF A GENERALIZED AMBROSIO–TORTORELLI FUNCTIONAL
• An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture
• Algorithm 832
• Direct methods in the calculus of variations

This page was built for publication: Truncated nonsmooth Newton multigrid for phase-field brittle-fracture problems, with analysis