A NURBS-based inverse analysis of thermal expansion induced morphing of thin shells

N. Vu-Bac, T. X. Duong, T. Lahmer, P. Areias, R. A. Sauer, H. S. Park, T. Rabczuk

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


Soft, active materials have been widely studied due to their ability to undergo large, complex shape changes in response to both mechanical and non-mechanical external stimuli. However, the vast majority of such studies has focused on investigating the forward problem, i.e. determining the shape changes that result from the applied stimuli. In contrast, very little work has been done to solve the inverse problem, i.e. that of identifying the external loads and stimuli that are needed to generate desired shapes and morphological changes. In this work, we present a new inverse methodology to study residual thermal expansion induced morphological changes in geometric composites made of soft, thin shells. In particular, the method presented in this work aims to determine the prescribed external stimuli needed to reconstruct a specific target shape, with a specific focus and interest in morphological changes from two-dimensional (2D) to three-dimensional (3D) shapes by considering the external stimuli within a thermohyperelastic framework. To do so, we utilize a geometrically exact, rotation-free Kirchhoff–Love shell formulation discretized by NURBS-based shape functions. We show that the proposed method is capable of identifying the stimuli, including cases where thermal expansion induced shape changes involving elastic softening occur in morphing from the initially flat 2D to non-planar 3D shapes. Validation indicates that the reconstructed shapes are in good agreement with the target shape.

Original languageEnglish
Pages (from-to)480-510
Number of pages31
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2019 Jun 15

Bibliographical note

Funding Information:
We gratefully acknowledge the support of European Research Council through Consolidator Grant 615132 - COMBAT . R.A. Sauer and T.X. Duong are grateful to the German Research Foundation (DFG) for funding this work through projects GSC 111 and SA1822/8-1 . We are also grateful to Professor Krister Svanberg from Royal Institute of Technology for providing his MMA code.

Publisher Copyright:
© 2019 Elsevier B.V.


  • Coupled thermohyperelastic model
  • Inverse analysis
  • Isogeometric analysis
  • Large shape changes
  • Nonlinear mechanics
  • Soft materials

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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