Topology optimization of finite strain viscoplastic systems under transient loads

Niklas Ivarsson, Mathias Wallin, Daniel Tortorelli

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1351-1367
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Issue number13
StatePublished - Jun 29 2018
Externally publishedYes


  • crashworthiness
  • discrete adjoint sensitivity analysis
  • finite strain
  • rate-dependent plasticity
  • topology optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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