Thermomechanical topology optimization of shape-memory alloy structures using a transient bilevel adjoint method

Ziliang Kang, Kai A. James

Research output: Contribution to journalArticlepeer-review


We present a novel method for computational design of adaptive shape-memory alloy (SMA) structures via topology optimization. By optimally distributing a SMA within the prescribed design domain, the proposed algorithm seeks to tailor the two-way shape-memory effect (TWSME) and pseudoelasticity response of the SMA materials. Using a phenomenological material model, the thermomechanical response of the SMA structure is solved through inelastic finite element analysis, while assuming a transient but spatially uniform temperature distribution. The material distribution is parameterized via a SIMP formulation, with gradient-based optimization used to perform the optimization search. We derive a transient, bilevel adjoint formulation for analytically computing the design sensitivities. We demonstrate the proposed design framework using a series of two-dimensional thermomechanical benchmark problems. These examples include design for optimal displacement due to the TWSME, and design for maximum mechanical advantage while accounting for pseudoelasticity.

Original languageEnglish (US)
Pages (from-to)2558-2580
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Issue number11
StatePublished - Jun 15 2020


  • computational inelasticity
  • pseudoelasticity
  • shape-memory alloys
  • topology optimization
  • transient adjoint sensitivity analysis
  • two-way shape-memory effects

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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