Topology optimization for designing periodic microstructures based on finite strain visco-plasticity

Niklas Ivarsson, Mathias Wallin, Daniel Tortorelli

Research output: Contribution to conferencePaper, not in proceedingpeer-review

Abstract

In the current work, we present a topology optimization framework for designing periodic microstructures with viscoplastic constitutive behavior under finite deformation. Materials with tailored macroscopic mechanical properties, i.e. maximum viscoplastic energy absorp- tion and prescribed Poisson's ratio, are designed by performing numerical tests of a single unit cell subjected to periodic boundary conditions. The kinematic and constitutive models are based on finite strain isotropic hardening viscoplasticity, and the mechanical balance laws are formulated in a total Lagrangian finite element setting. To solve the coupled momentum balance equation and constitutive equations, a nested Newton method is used together with an adaptive time-stepping scheme. The optimization problem is iteratively solved using the method of moving asymptotes (MMA), where path-dependent sensitivities are derived using the adjoint method. The applicability of the framework is demonstrated by numerical examples of optimized continuum structures exposed to multiple load cases over a wide macroscopic strain range.

Original languageEnglish
Pages84-86
Number of pages3
Publication statusPublished - 2018
Event2018 IUTAM Symposium on When Topology Optimization Meets Additive Manufacturing - Theory and Methods - Dalian, China
Duration: 2018 Oct 72018 Oct 12

Conference

Conference2018 IUTAM Symposium on When Topology Optimization Meets Additive Manufacturing - Theory and Methods
Country/TerritoryChina
CityDalian
Period2018/10/072018/10/12

Subject classification (UKÄ)

  • Computational Mathematics
  • Applied Mechanics

Free keywords

  • Discrete adjoint sensitivity analysis
  • Finite strains
  • Material design
  • Rate-dependent plasticity
  • Topology optimization

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