A fast and robust numerical treatment of a gradient-enhanced model for brittle damage

authored by: Philipp Junker, Stephan Schwarz, Dustin Roman Jantos, Klaus Hackl
Abstract: Damage processes are modeled by a softening behavior in a stress/strain diagram. This reveals that the stiffness loses its ellipticity and the energy is thus not coercive. A numerical implementation of such ill-posed problems yields results that are strongly dependent on the chosen spatial discretization. Consequently, regularization strategies have to be employed that render the problem well-posed. A prominent method for regularization is a gradient enhancement of the free energy. This, however, results in field equations that have to be solved in parallel to the Euler-Lagrange equation for the displacement field. An usual finite element treatment thus deals with an increased number of nodal unknowns, which remarkably increases numerical costs. We present a gradient-enhanced material model for brittle damage using Hamilton’s principle for nonconservative continua. We propose an improved algorithm, which is based on a combination of the finite element and strategies from meshless methods, for a fast update of the field function. This treatment keeps the numerical effort limited and close to purely elastic problems. Several boundary value problems prove the mesh-independence of the results.
External Organisation(s): Ruhr-Universität Bochum
Type: Article
Journal: International Journal for Multiscale Computational Engineering
Volume: 17
Pages: 151-180
No. of pages: 30
ISSN: 1543-1649
Publication date: 2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Systems Engineering, Computational Mechanics, Computer Networks and Communications
Electronic version(s): https://doi.org/10.1615/intjmultcompeng.2018027813 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{a1a9d11c0c2549708cec12b2d0dbc3d8,
title = "A fast and robust numerical treatment of a gradient-enhanced model for brittle damage",
abstract = "Damage processes are modeled by a softening behavior in a stress/strain diagram. This reveals that the stiffness loses its ellipticity and the energy is thus not coercive. A numerical implementation of such ill-posed problems yields results that are strongly dependent on the chosen spatial discretization. Consequently, regularization strategies have to be employed that render the problem well-posed. A prominent method for regularization is a gradient enhancement of the free energy. This, however, results in field equations that have to be solved in parallel to the Euler-Lagrange equation for the displacement field. An usual finite element treatment thus deals with an increased number of nodal unknowns, which remarkably increases numerical costs. We present a gradient-enhanced material model for brittle damage using Hamilton{\textquoteright}s principle for nonconservative continua. We propose an improved algorithm, which is based on a combination of the finite element and strategies from meshless methods, for a fast update of the field function. This treatment keeps the numerical effort limited and close to purely elastic problems. Several boundary value problems prove the mesh-independence of the results.",
keywords = "Brittle damage, Finite element method, Gradient-enhanced regularization, Meshless method, Operator split",
author = "Philipp Junker and Stephan Schwarz and Jantos, {Dustin Roman} and Klaus Hackl",
note = "Publisher Copyright: {\textcopyright} 2019 by Begell House, Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",
year = "2019",
doi = "10.1615/intjmultcompeng.2018027813",
language = "English",
volume = "17",
pages = "151--180",
journal = "International Journal for Multiscale Computational Engineering",
issn = "1543-1649",
publisher = "Begell House Inc.",
number = "2",
}