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Title: Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity]

Abstract

In this paper, 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. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.

Authors:
ORCiD logo [1];  [1];  [2]
  1. Lund Univ. (Sweden). Division of Solid Mechanics
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Design and Optimization
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE; Swedish Research Council (SRC)
OSTI Identifier:
1432978
Report Number(s):
LLNL-JRNL-739019
Journal ID: ISSN 0029-5981
Grant/Contract Number:  
AC52-07NA27344; 2015-05134
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 114; Journal Issue: 13; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Topology optimization; Finite strain; Rate-dependent plasticity; Discrete adjoint sensitivity analysis; Crashworthiness

Citation Formats

Ivarsson, Niklas, Wallin, Mathias, and Tortorelli, Daniel. Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity]. United States: N. p., 2018. Web. doi:10.1002/nme.5789.
Ivarsson, Niklas, Wallin, Mathias, & Tortorelli, Daniel. Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity]. United States. doi:10.1002/nme.5789.
Ivarsson, Niklas, Wallin, Mathias, and Tortorelli, Daniel. Thu . "Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity]". United States. doi:10.1002/nme.5789. https://www.osti.gov/servlets/purl/1432978.
@article{osti_1432978,
title = {Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity]},
author = {Ivarsson, Niklas and Wallin, Mathias and Tortorelli, Daniel},
abstractNote = {In this paper, 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. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.},
doi = {10.1002/nme.5789},
journal = {International Journal for Numerical Methods in Engineering},
number = 13,
volume = 114,
place = {United States},
year = {2018},
month = {2}
}

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Table-1 Table-1: Material parameters.

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