Level set topology optimization of structural problems with interface cohesion
Abstract
Summary This paper presents a finite element topology optimization framework for the design of two‐phase structural systems considering contact and cohesion phenomena along the interface. The geometry of the material interface is described by an explicit level set method, and the structural response is predicted by the extended finite element method. In this work, the interface condition is described by a bilinear cohesive zone model on the basis of the traction‐separation constitutive relation. The non‐penetration condition in the presence of compressive interface forces is enforced by a stabilized Lagrange multiplier method. The mechanical model assumes a linear elastic isotropic material, infinitesimal strain theory, and a quasi‐static response. The optimization problem is solved by a nonlinear programming method, and the design sensitivities are computed by the adjoint method. The performance of the presented method is evaluated by 2D and 3D numerical examples. The results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered. In addition, 3D examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality. The optimization framework presented is limited to two‐phase structural systems where the material interface is coincident in the undeformed configuration, and to structural responses that remain valid consideringmore »
- Authors:
-
- Department of Civil, Environmental and Architectural Engineering University of Colorado Boulder Boulder 80309‐0428 CO USA
- Department of Aerospace Engineering University of Colorado Boulder Boulder 80309‐0429 CO USA
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1401074
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Additional Journal Information:
- Journal Name: International Journal for Numerical Methods in Engineering Journal Volume: 112 Journal Issue: 8; Journal ID: ISSN 0029-5981
- Publisher:
- Wiley Blackwell (John Wiley & Sons)
- Country of Publication:
- United Kingdom
- Language:
- English
Citation Formats
Behrou, Reza, Lawry, Matthew, and Maute, Kurt. Level set topology optimization of structural problems with interface cohesion. United Kingdom: N. p., 2017.
Web. doi:10.1002/nme.5540.
Behrou, Reza, Lawry, Matthew, & Maute, Kurt. Level set topology optimization of structural problems with interface cohesion. United Kingdom. https://doi.org/10.1002/nme.5540
Behrou, Reza, Lawry, Matthew, and Maute, Kurt. Fri .
"Level set topology optimization of structural problems with interface cohesion". United Kingdom. https://doi.org/10.1002/nme.5540.
@article{osti_1401074,
title = {Level set topology optimization of structural problems with interface cohesion},
author = {Behrou, Reza and Lawry, Matthew and Maute, Kurt},
abstractNote = {Summary This paper presents a finite element topology optimization framework for the design of two‐phase structural systems considering contact and cohesion phenomena along the interface. The geometry of the material interface is described by an explicit level set method, and the structural response is predicted by the extended finite element method. In this work, the interface condition is described by a bilinear cohesive zone model on the basis of the traction‐separation constitutive relation. The non‐penetration condition in the presence of compressive interface forces is enforced by a stabilized Lagrange multiplier method. The mechanical model assumes a linear elastic isotropic material, infinitesimal strain theory, and a quasi‐static response. The optimization problem is solved by a nonlinear programming method, and the design sensitivities are computed by the adjoint method. The performance of the presented method is evaluated by 2D and 3D numerical examples. The results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered. In addition, 3D examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality. The optimization framework presented is limited to two‐phase structural systems where the material interface is coincident in the undeformed configuration, and to structural responses that remain valid considering small strain kinematics. Copyright © 2017 John Wiley & Sons, Ltd.},
doi = {10.1002/nme.5540},
journal = {International Journal for Numerical Methods in Engineering},
number = 8,
volume = 112,
place = {United Kingdom},
year = {Fri Mar 17 00:00:00 EDT 2017},
month = {Fri Mar 17 00:00:00 EDT 2017}
}
https://doi.org/10.1002/nme.5540
Web of Science
Works referenced in this record:
A Continuum Model for Void Nucleation by Inclusion Debonding
journal, September 1987
- Needleman, A.
- Journal of Applied Mechanics, Vol. 54, Issue 3
Shape and topology optimization of compliant mechanisms using a parameterization level set method
journal, November 2007
- Luo, Zhen; Tong, Liyong; Wang, Michael Yu
- Journal of Computational Physics, Vol. 227, Issue 1
Topology optimization using a mixed formulation: An alternative way to solve pressure load problems
journal, March 2007
- Sigmund, O.; Clausen, P. M.
- Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 13-16
A single-domain dual-boundary-element formulation incorporating a cohesive zone model for elastostatic cracks
journal, January 1998
- Yang, B.; Ravi-Chandar, K.
- International Journal of Fracture, Vol. 93, Issue 1/4, p. 115-144
Topology optimization approaches: A comparative review
journal, August 2013
- Sigmund, Ole; Maute, Kurt
- Structural and Multidisciplinary Optimization, Vol. 48, Issue 6
Computational modelling of impact damage in brittle materials
journal, August 1996
- Camacho, G. T.; Ortiz, M.
- International Journal of Solids and Structures, Vol. 33, Issue 20-22
Explicit level-set-based topology optimization using an exact Heaviside function and consistent sensitivity analysis: LEVEL-SET-BASED TOP. OPT. USING AN EXACT HEAVISIDE
journal, May 2012
- Dijk, N. P.; Langelaar, M.; Keulen, F.
- International Journal for Numerical Methods in Engineering, Vol. 91, Issue 1
A survey of structural and multidisciplinary continuum topology optimization: post 2000
journal, July 2013
- Deaton, Joshua D.; Grandhi, Ramana V.
- Structural and Multidisciplinary Optimization, Vol. 49, Issue 1
Level-set methods for structural topology optimization: a review
journal, March 2013
- van Dijk, N. P.; Maute, K.; Langelaar, M.
- Structural and Multidisciplinary Optimization, Vol. 48, Issue 3
A stable 3D contact formulation using X-FEM
journal, January 2007
- Geniaut, Samuel; Massin, Patrick; Moës, Nicolas
- European Journal of Computational Mechanics, Vol. 16, Issue 2
Levelset based fluid topology optimization using the extended finite element method
journal, March 2012
- Kreissl, Sebastian; Maute, Kurt
- Structural and Multidisciplinary Optimization, Vol. 46, Issue 3
Radial basis functions and level set method for structural topology optimization
journal, January 2006
- Wang, Shengyin; Wang, Michael Yu
- International Journal for Numerical Methods in Engineering, Vol. 65, Issue 12
An extended finite element/level set method to study surface effects on the mechanical behavior and properties of nanomaterials
journal, November 2010
- Farsad, Mehdi; Vernerey, Franck J.; Park, Harold S.
- International Journal for Numerical Methods in Engineering, Vol. 84, Issue 12
Cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials
journal, June 2005
- Zhang, Zhengyu (Jenny); Paulino, Glaucio H.
- International Journal of Plasticity, Vol. 21, Issue 6
Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces
journal, September 2000
- Tijssens, Martin G. A.; Sluys, Bert L. J.; van der Giessen, Erik
- European Journal of Mechanics - A/Solids, Vol. 19, Issue 5
Element-free galerkin methods for dynamic fracture in concrete
journal, July 2000
- Belytschko, T.; Organ, D.; Gerlach, C.
- Computer Methods in Applied Mechanics and Engineering, Vol. 187, Issue 3-4
Topology optimization of continuum structures subjected to pressure loading
journal, April 2000
- Hammer, V. B.; Olhoff, N.
- Structural and Multidisciplinary Optimization, Vol. 19, Issue 2
The relation between crack growth resistance and fracture process parameters in elastic-plastic solids
journal, August 1992
- Tvergaard, Viggo; Hutchinson, John W.
- Journal of the Mechanics and Physics of Solids, Vol. 40, Issue 6
Modified adaptive Dynamic Relaxation method and its application to elastic-plastic bending and wrinkling of circular plates
journal, January 1989
- Zhang, L. G.; Yu, T. X.
- Computers & Structures, Vol. 33, Issue 2
Topology optimization for unsteady flow: TOPOLOGY OPTIMIZATION FOR UNSTEADY FLOW
journal, March 2011
- Kreissl, Sebastian; Pingen, Georg; Maute, Kurt
- International Journal for Numerical Methods in Engineering, Vol. 87, Issue 13
The Levenberg-Marquardt algorithm: Implementation and theory
book, January 1978
- Moré, Jorge J.; Watson, G. A.
- Numerical Analysis, Vol. 630, p. 105-116
Effect of fibre debonding in a whisker-reinforced metal
journal, June 1990
- Tvergaard, Viggo
- Materials Science and Engineering: A, Vol. 125, Issue 2
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
journal, June 2004
- Davis, Timothy A.
- ACM Transactions on Mathematical Software, Vol. 30, Issue 2
A parametric level-set approach for topology optimization of flow domains
journal, June 2009
- Pingen, Georg; Waidmann, Matthias; Evgrafov, Anton
- Structural and Multidisciplinary Optimization, Vol. 41, Issue 1
Level set topology optimization of problems with sliding contact interfaces
journal, July 2015
- Lawry, Matthew; Maute, Kurt
- Structural and Multidisciplinary Optimization, Vol. 52, Issue 6
Extended finite element method for cohesive crack growth
journal, May 2002
- Moës, Nicolas; Belytschko, Ted
- Engineering Fracture Mechanics, Vol. 69, Issue 7
Crack face contact in X-FEM using a segment-to-segment approach: CRACK FACE CONTACT IN X-FEM
journal, December 2009
- Giner, E.; Tur, M.; Tarancón, J. E.
- International Journal for Numerical Methods in Engineering, Vol. 82, Issue 11
Numerical instabilities in level set topology optimization with the extended finite element method
journal, August 2013
- Makhija, David; Maute, Kurt
- Structural and Multidisciplinary Optimization, Vol. 49, Issue 2
Generalized shape optimization without homogenization
journal, September 1992
- Rozvany, G. I. N.; Zhou, M.; Birker, T.
- Structural Optimization, Vol. 4, Issue 3-4
Level set topology optimization of cooling and heating devices using a simplified convection model
journal, December 2015
- Coffin, Peter; Maute, Kurt
- Structural and Multidisciplinary Optimization, Vol. 53, Issue 5
Topology optimization with design-dependent loads
journal, January 2001
- Chen, Bing-Chung; Kikuchi, Noboru
- Finite Elements in Analysis and Design, Vol. 37, Issue 1
A finite element with embedded localization zones
journal, September 1988
- Belytschko, Ted; Fish, Jacob; Engelmann, Bruce E.
- Computer Methods in Applied Mechanics and Engineering, Vol. 70, Issue 1
Density and level set-XFEM schemes for topology optimization of 3-D structures
journal, April 2014
- Villanueva, Carlos H.; Maute, Kurt
- Computational Mechanics, Vol. 54, Issue 1
Parametric Shape and Topology Optimization with Radial Basis Functions
book, January 2006
- Wang, Michael Yu; Wang, Shengyin
- Solid Mechanics and Its Applications
Crack face contact for a hexahedral-based XFEM formulation
journal, March 2012
- Mueller-Hoeppe, D. S.; Wriggers, P.; Loehnert, S.
- Computational Mechanics, Vol. 49, Issue 6
Simulation of Crack Propagation in Asphalt Concrete Using an Intrinsic Cohesive Zone Model
journal, November 2006
- Song, Seong Hyeok; Paulino, Glaucio H.; Buttlar, William G.
- Journal of Engineering Mechanics, Vol. 132, Issue 11
Stabilization of geometrically nonlinear topology optimization by the Levenberg–Marquardt method
journal, February 2008
- Kawamoto, Atsushi
- Structural and Multidisciplinary Optimization, Vol. 37, Issue 4
Modeling Large Sliding Frictional Contact Along Non-Smooth Discontinuities in X-FEM [Modeling Large Sliding Frictional Contact Along Non-Smooth Discontinuities in X-FEM]
journal, January 2011
- Mousavi, Seyed Mohammad Jafar Taheri; Mousavi, Seyedeh Mohadeseh Taheri
- International Journal of Modeling and Optimization
An enriched finite element algorithm for numerical computation of contact friction problems
journal, February 2007
- Khoei, A. R.; Nikbakht, M.
- International Journal of Mechanical Sciences, Vol. 49, Issue 2
A finite element method for crack growth without remeshing
journal, September 1999
- Mo�s, Nicolas; Dolbow, John; Belytschko, Ted
- International Journal for Numerical Methods in Engineering, Vol. 46, Issue 1
Structural optimization using sensitivity analysis and a level-set method
journal, February 2004
- Allaire, Grégoire; Jouve, François; Toader, Anca-Maria
- Journal of Computational Physics, Vol. 194, Issue 1
Topology optimization for stationary fluid-structure interaction problems using a new monolithic formulation: TOPOLOGY OPTIMIZATION FOR STATIONARY FSI PROBLEMS
journal, November 2009
- Yoon, Gil Ho
- International Journal for Numerical Methods in Engineering, Vol. 82, Issue 5
An X-FEM approach for large sliding contact along discontinuities
journal, June 2009
- Nistor, I.; Guiton, M. L. E.; Massin, P.
- International Journal for Numerical Methods in Engineering, Vol. 78, Issue 12
A contact algorithm for frictional crack propagation with the extended finite element method
journal, December 2008
- Liu, Fushen; Borja, Ronaldo I.
- International Journal for Numerical Methods in Engineering, Vol. 76, Issue 10
A multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within XFEM
journal, September 2010
- Tran, A. B.; Yvonnet, J.; He, Q-C.
- International Journal for Numerical Methods in Engineering, Vol. 85, Issue 11
The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns
journal, January 2006
- Fries, Thomas-Peter; Belytschko, Ted
- International Journal for Numerical Methods in Engineering, Vol. 68, Issue 13
Finite cover method for linear and non-linear analyses of heterogeneous solids
journal, January 2003
- Terada, Kenjiro; Asai, Mitsuteru; Yamagishi, Michihiro
- International Journal for Numerical Methods in Engineering, Vol. 58, Issue 9
Multi-material topology optimization considering interface behavior via XFEM and level set method
journal, August 2016
- Liu, Pai; Luo, Yangjun; Kang, Zhan
- Computer Methods in Applied Mechanics and Engineering, Vol. 308
Void nucleation by inclusion debonding in a crystal matrix
journal, January 1993
- Xu, X. -P; Needleman, A.
- Modelling and Simulation in Materials Science and Engineering, Vol. 1, Issue 2
Stabilized low-order finite elements for frictional contact with the extended finite element method
journal, August 2010
- Liu, Fushen; Borja, Ronaldo I.
- Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 37-40
A level-set method for steady-state and transient natural convection problems
journal, December 2015
- Coffin, Peter; Maute, Kurt
- Structural and Multidisciplinary Optimization, Vol. 53, Issue 5
A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
journal, February 2012
- Amdouni, Saber; Hild, Patrick; Lleras, Vanessa
- ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 46, Issue 4
Numerical simulations of fast crack growth in brittle solids
journal, September 1994
- Xu, X. -P.; Needleman, A.
- Journal of the Mechanics and Physics of Solids, Vol. 42, Issue 9
A model of bone adaptation as a topology optimization process with contact
journal, January 2012
- Andrade-Campos, António; Ramos, António; Simões, José A.
- Journal of Biomedical Science and Engineering, Vol. 05, Issue 05
Optimal shape design as a material distribution problem
journal, December 1989
- Bendsøe, M. P.
- Structural Optimization, Vol. 1, Issue 4
ILUT: A dual threshold incomplete LU factorization
journal, July 1994
- Saad, Yousef
- Numerical Linear Algebra with Applications, Vol. 1, Issue 4
Stress concentration minimization of 2D filets using X-FEM and level set description
journal, January 2007
- Van Miegroet, Laurent; Duysinx, Pierre
- Structural and Multidisciplinary Optimization, Vol. 33, Issue 4-5
Modeling interfacial debonding and matrix cracking in fiber reinforced composites by the extended Voronoi cell FEM
journal, March 2007
- Li, S.; Ghosh, S.
- Finite Elements in Analysis and Design, Vol. 43, Issue 5
Dynamic relaxation large deflection analysis of non-axisymmetric circular viscoelastic plates
journal, September 2005
- Salehi, M.; Aghaei, H.
- Computers & Structures, Vol. 83, Issue 23-24
Robust implementation of contact under friction and large sliding with the eXtended finite element method
journal, January 2010
- Siavelis, Maximilien; Massin, Patrick; Guiton, Martin L. E.
- European Journal of Computational Mechanics, Vol. 19, Issue 1-3
A simple and efficient preconditioning scheme for heaviside enriched XFEM
journal, August 2014
- Lang, Christapher; Makhija, David; Doostan, Alireza
- Computational Mechanics, Vol. 54, Issue 5
Comparative study on finite elements with embedded discontinuities
journal, July 2000
- Jirásek, Milan
- Computer Methods in Applied Mechanics and Engineering, Vol. 188, Issue 1-3
The extended/generalized finite element method: An overview of the method and its applications
journal, January 2010
- Fries, Thomas-Peter; Belytschko, Ted
- International Journal for Numerical Methods in Engineering
Simulation of ductile crack growth using computational cells: numerical aspects
journal, May 2000
- Gullerud, Arne S.; Gao, Xiaosheng; Dodds, Robert H.
- Engineering Fracture Mechanics, Vol. 66, Issue 1
Modeling of large deformation – Large sliding contact via the penalty X-FEM technique
journal, May 2010
- Khoei, A. R.; Taheri Mousavi, S. M.
- Computational Materials Science, Vol. 48, Issue 3
Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces
journal, November 2011
- Park, Kyoungsoo; Paulino, Glaucio H.
- Applied Mechanics Reviews, Vol. 64, Issue 6
Modeling impact induced delamination of woven fiber reinforced composites with contact/cohesive laws
journal, March 2000
- Espinosa, H. D.; Dwivedi, S.; Lu, H. -C.
- Computer Methods in Applied Mechanics and Engineering, Vol. 183, Issue 3-4
The Meshless Dynamic Relaxation Techniques for Simulating Atomic Structures of Materials
conference, August 2008
- Pan, Li; Metzger, Don R.; Niewczas, Marek
- ASME 2002 Pressure Vessels and Piping Conference, Computational Mechanics: Developments and Applications
Yielding of steel sheets containing slits
journal, May 1960
- Dugdale, D. S.
- Journal of the Mechanics and Physics of Solids, Vol. 8, Issue 2
Level set topology optimization of stationary fluid-structure interaction problems
journal, March 2015
- Jenkins, Nicholas; Maute, Kurt
- Structural and Multidisciplinary Optimization, Vol. 52, Issue 1