skip to main content


This content will become publicly available on February 8, 2019

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

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.
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:
Report Number(s):
Journal ID: ISSN 0029-5981
Grant/Contract Number:
AC52-07NA27344; 2015-05134
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Name: International Journal for Numerical Methods in Engineering; Journal ID: ISSN 0029-5981
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE; Swedish Research Council (SRC)
Country of Publication:
United States
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Topology optimization; Finite strain; Rate-dependent plasticity; Discrete adjoint sensitivity analysis; Crashworthiness
OSTI Identifier: