Details
| Original language | English |
|---|---|
| Pages (from-to) | 151-180 |
| Number of pages | 30 |
| Journal | International Journal for Multiscale Computational Engineering |
| Volume | 17 |
| Issue number | 2 |
| Publication status | Published - 2019 |
| Externally published | Yes |
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.
Keywords
- Brittle damage, Finite element method, Gradient-enhanced regularization, Meshless method, Operator split
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Engineering(all)
- Computational Mechanics
- Computer Science(all)
- Computer Networks and Communications
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In: International Journal for Multiscale Computational Engineering, Vol. 17, No. 2, 2019, p. 151-180.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A fast and robust numerical treatment of a gradient-enhanced model for brittle damage
AU - Junker, Philipp
AU - Schwarz, Stephan
AU - Jantos, Dustin Roman
AU - Hackl, Klaus
N1 - Publisher Copyright: © 2019 by Begell House, Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Brittle damage
KW - Finite element method
KW - Gradient-enhanced regularization
KW - Meshless method
KW - Operator split
UR - http://www.scopus.com/inward/record.url?scp=85061659689&partnerID=8YFLogxK
U2 - 10.1615/intjmultcompeng.2018027813
DO - 10.1615/intjmultcompeng.2018027813
M3 - Article
VL - 17
SP - 151
EP - 180
JO - International Journal for Multiscale Computational Engineering
JF - International Journal for Multiscale Computational Engineering
SN - 1543-1649
IS - 2
ER -