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Topology optimization of finite strain viscoplastic systems under transient loads

Ivarsson, Niklas LU ; Wallin, Mathias LU and Tortorelli, Daniel (2018) In International Journal for Numerical Methods in Engineering 114(13). p.1351-1367
Abstract

A transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several... (More)

A transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Crashworthiness, Discrete adjoint sensitivity analysis, Finite strain, Rate-dependent plasticity, Topology optimization
in
International Journal for Numerical Methods in Engineering
volume
114
issue
13
pages
1351 - 1367
publisher
John Wiley & Sons
external identifiers
  • scopus:85044210967
ISSN
0029-5981
DOI
10.1002/nme.5789
language
English
LU publication?
yes
id
9334528a-7b94-4ac1-a723-7054d6a565ff
date added to LUP
2018-04-09 15:18:16
date last changed
2019-03-12 04:08:07
@article{9334528a-7b94-4ac1-a723-7054d6a565ff,
  abstract     = {<p>A transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.</p>},
  author       = {Ivarsson, Niklas and Wallin, Mathias and Tortorelli, Daniel},
  issn         = {0029-5981},
  keyword      = {Crashworthiness,Discrete adjoint sensitivity analysis,Finite strain,Rate-dependent plasticity,Topology optimization},
  language     = {eng},
  month        = {03},
  number       = {13},
  pages        = {1351--1367},
  publisher    = {John Wiley & Sons},
  series       = {International Journal for Numerical Methods in Engineering},
  title        = {Topology optimization of finite strain viscoplastic systems under transient loads},
  url          = {http://dx.doi.org/10.1002/nme.5789},
  volume       = {114},
  year         = {2018},
}