skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Topology optimization for designing periodic microstructures based on finite strain viscoplasticity

Abstract

This paper presents a topology optimization framework for designing periodic viscoplastic microstructures under finite deformation. To demonstrate the framework, microstructures with tailored macroscopic mechanical properties, e.g., maximum viscoplastic energy absorption and prescribed zero contraction, are designed. The simulated macroscopic properties are obtained via homogenization wherein the unit cell constitutive model is based on finite strain isotropic hardening viscoplasticity. To solve the coupled equilibrium and constitutive equations, a nested Newton method is used together with an adaptive time-stepping scheme. A well-posed topology optimization problem is formulated by restriction using filtration which is implemented via a periodic version of the Helmholtz partial differential equation filter. The optimization problem is iteratively solved with the method of moving asymptotes, where the path-dependent sensitivities are derived using the adjoint method. The applicability of the framework is demonstrated by optimizing several two-dimensional continuum composites exposed to a wide range of macroscopic strains.

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); Swedish Research Council (SRC); Swedish Energy Agency
OSTI Identifier:
1631072
Alternate Identifier(s):
OSTI ID: 1738897
Report Number(s):
LLNL-JRNL-815163
Journal ID: ISSN 1615-147X; PII: 2555
Grant/Contract Number:  
AC52-07NA27344; 2015-05134; 48344-1
Resource Type:
Published Article
Journal Name:
Structural and Multidisciplinary Optimization
Additional Journal Information:
Journal Name: Structural and Multidisciplinary Optimization Journal Volume: 61 Journal Issue: 6; Journal ID: ISSN 1615-147X
Publisher:
Springer
Country of Publication:
Germany
Language:
English
Subject:
42 ENGINEERING; topology optimization; material design; finite strain; rate-dependent plasticity; discrete adjoint sensitivity analysis

Citation Formats

Ivarsson, Niklas, Wallin, Mathias, and Tortorelli, Daniel A. Topology optimization for designing periodic microstructures based on finite strain viscoplasticity. Germany: N. p., 2020. Web. doi:10.1007/s00158-020-02555-x.
Ivarsson, Niklas, Wallin, Mathias, & Tortorelli, Daniel A. Topology optimization for designing periodic microstructures based on finite strain viscoplasticity. Germany. doi:https://doi.org/10.1007/s00158-020-02555-x
Ivarsson, Niklas, Wallin, Mathias, and Tortorelli, Daniel A. Thu . "Topology optimization for designing periodic microstructures based on finite strain viscoplasticity". Germany. doi:https://doi.org/10.1007/s00158-020-02555-x.
@article{osti_1631072,
title = {Topology optimization for designing periodic microstructures based on finite strain viscoplasticity},
author = {Ivarsson, Niklas and Wallin, Mathias and Tortorelli, Daniel A.},
abstractNote = {This paper presents a topology optimization framework for designing periodic viscoplastic microstructures under finite deformation. To demonstrate the framework, microstructures with tailored macroscopic mechanical properties, e.g., maximum viscoplastic energy absorption and prescribed zero contraction, are designed. The simulated macroscopic properties are obtained via homogenization wherein the unit cell constitutive model is based on finite strain isotropic hardening viscoplasticity. To solve the coupled equilibrium and constitutive equations, a nested Newton method is used together with an adaptive time-stepping scheme. A well-posed topology optimization problem is formulated by restriction using filtration which is implemented via a periodic version of the Helmholtz partial differential equation filter. The optimization problem is iteratively solved with the method of moving asymptotes, where the path-dependent sensitivities are derived using the adjoint method. The applicability of the framework is demonstrated by optimizing several two-dimensional continuum composites exposed to a wide range of macroscopic strains.},
doi = {10.1007/s00158-020-02555-x},
journal = {Structural and Multidisciplinary Optimization},
number = 6,
volume = 61,
place = {Germany},
year = {2020},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1007/s00158-020-02555-x

Save / Share:

Works referenced in this record:

Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling: CONCEPTUAL DESIGN OF REINFORCED CONCRETE
journal, April 2012

  • Bogomolny, Michael; Amir, Oded
  • International Journal for Numerical Methods in Engineering, Vol. 90, Issue 13
  • DOI: 10.1002/nme.4253

Topology optimization of multiscale elastoviscoplastic structures: TOPOLOGY OPTIMIZATION OF MULTISCALE ELASTOVISCOPLASTIC STRUCTURES
journal, October 2015

  • Fritzen, Felix; Xia, Liang; Leuschner, Matthias
  • International Journal for Numerical Methods in Engineering, Vol. 106, Issue 6
  • DOI: 10.1002/nme.5122

Topology optimization of structures with anisotropic plastic materials using enhanced assumed strain elements
journal, December 2016

  • Zhang, Guodong; Li, Lei; Khandelwal, Kapil
  • Structural and Multidisciplinary Optimization, Vol. 55, Issue 6
  • DOI: 10.1007/s00158-016-1612-1

Achieving minimum length scale in topology optimization using nodal design variables and projection functions
journal, August 2004

  • Guest, J. K.; Prévost, J. H.; Belytschko, T.
  • International Journal for Numerical Methods in Engineering, Vol. 61, Issue 2
  • DOI: 10.1002/nme.1064

Simple single-scale microstructures based on optimal rank-3 laminates
journal, January 2019

  • Träff, E.; Sigmund, O.; Groen, J. P.
  • Structural and Multidisciplinary Optimization, Vol. 59, Issue 4
  • DOI: 10.1007/s00158-018-2180-3

Topology optimization of finite strain viscoplastic systems under transient loads: Transient finite strain viscoplastic effects in topology optimization
journal, March 2018

  • Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel
  • International Journal for Numerical Methods in Engineering, Vol. 114, Issue 13
  • DOI: 10.1002/nme.5789

Optimal microstructures of elastoplastic cellular materials under various macroscopic strains
journal, March 2018


Topological design of microstructures of cellular materials for maximum bulk or shear modulus
journal, April 2011


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
  • DOI: 10.1007/s00158-013-0956-z

Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity
journal, July 1994

  • Michaleris, Panagiotis; Tortorelli, Daniel A.; Vidal, Creto A.
  • International Journal for Numerical Methods in Engineering, Vol. 37, Issue 14
  • DOI: 10.1002/nme.1620371408

Design of materials with extreme thermal expansion using a three-phase topology optimization method
journal, June 1997


Stress-constrained continuum topology optimization: a new approach based on elasto-plasticity
journal, November 2016


Consequences of dynamic yield surface in viscoplasticity
journal, August 2000


Analytical sensitivity in topology optimization for elastoplastic composites
journal, May 2015

  • Kato, Junji; Hoshiba, Hiroya; Takase, Shinsuke
  • Structural and Multidisciplinary Optimization, Vol. 52, Issue 3
  • DOI: 10.1007/s00158-015-1246-8

Nonlinear homogenization for topology optimization
journal, June 2020


Filters in topology optimization based on Helmholtz-type differential equations
journal, December 2010

  • Lazarov, B. S.; Sigmund, O.
  • International Journal for Numerical Methods in Engineering, Vol. 86, Issue 6
  • DOI: 10.1002/nme.3072

Adaptive topology optimization of elastoplastic structures
journal, April 1998

  • Maute, K.; Schwarz, S.; Ramm, E.
  • Structural Optimization, Vol. 15, Issue 2
  • DOI: 10.1007/BF01278493

Tailoring materials with prescribed elastic properties
journal, June 1995


Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials
journal, July 2009

  • Yvonnet, J.; Gonzalez, D.; He, Q. -C.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 33-36
  • DOI: 10.1016/j.cma.2009.03.017

On the realization of the bulk modulus bounds for two-phase viscoelastic composites
journal, February 2014

  • Andreasen, Casper Schousboe; Andreassen, Erik; Jensen, Jakob Søndergaard
  • Journal of the Mechanics and Physics of Solids, Vol. 63
  • DOI: 10.1016/j.jmps.2013.09.007

An alternative interpolation scheme for minimum compliance topology optimization
journal, September 2001

  • Stolpe, M.; Svanberg, K.
  • Structural and Multidisciplinary Optimization, Vol. 22, Issue 2
  • DOI: 10.1007/s001580100129

Topology optimization based on finite strain plasticity
journal, April 2016

  • Wallin, Mathias; Jönsson, Viktor; Wingren, Eric
  • Structural and Multidisciplinary Optimization, Vol. 54, Issue 4
  • DOI: 10.1007/s00158-016-1435-0

Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge–Kutta integration scheme
journal, January 2012

  • Borgqvist, Eric; Wallin, Mathias
  • International Journal of Damage Mechanics, Vol. 22, Issue 1
  • DOI: 10.1177/1056789511433341

Design of materials with prescribed nonlinear properties
journal, September 2014


Design of periodic elastoplastic energy dissipating microstructures
journal, September 2018

  • Alberdi, Ryan; Khandelwal, Kapil
  • Structural and Multidisciplinary Optimization, Vol. 59, Issue 2
  • DOI: 10.1007/s00158-018-2076-2

Nonlinear structural design using multiscale topology optimization. Part I: Static formulation
journal, July 2013

  • Nakshatrala, P. B.; Tortorelli, D. A.; Nakshatrala, K. B.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 261-262
  • DOI: 10.1016/j.cma.2012.12.018

Stiffness optimization of non-linear elastic structures
journal, March 2018

  • Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel
  • Computer Methods in Applied Mechanics and Engineering, Vol. 330
  • DOI: 10.1016/j.cma.2017.11.004

Topology optimization for effective energy propagation in rate-independent elastoplastic material systems
journal, October 2015

  • Nakshatrala, P. B.; Tortorelli, D. A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 295
  • DOI: 10.1016/j.cma.2015.05.004

A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations
journal, January 2002


The method of moving asymptotes—a new method for structural optimization
journal, February 1987

  • Svanberg, Krister
  • International Journal for Numerical Methods in Engineering, Vol. 24, Issue 2
  • DOI: 10.1002/nme.1620240207

Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization
journal, May 2019

  • Zhang, Guodong; Khandelwal, Kapil
  • International Journal for Numerical Methods in Engineering, Vol. 119, Issue 11
  • DOI: 10.1002/nme.6083

Crashworthiness design of transient frame structures using topology optimization
journal, February 2004

  • Pedersen, Claus B. W.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 6-8
  • DOI: 10.1016/j.cma.2003.11.001

Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation
journal, July 1992