Multi-material inverse design of soft deformable bodies via functional optimization

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Controlling the deformation of a soft body has potential applications in fields requiring precise control over the shape of the body. Areas such as medical robotics can use the shape control of soft robots to repair aneurysms in humans, deliver medicines within the body, among other applications. However, given known external loading, it is usually not possible to deform a soft body into arbitrary shapes if it is fabricated using only a single material. In this work, we propose a new physics-based method for the computational design of soft hyperelastic bodies to address this problem. The method takes as input an undeformed shape of a body, a specified external load, and a user desired final shape. It then solves an inverse problem in design using nonlinear optimization subject to physics constraints. The nonlinear program is solved using a gradient-based interior-point method. Analytical gradients are computed for efficiency. The method outputs fields of material properties which can be used to fabricate a soft body. A body fabricated to match this material field is expected to deform into a user-desired shape, given the same external loading input. Two regularizers are used to ascribe a priori characteristics of smoothness and contrast, respectively, to the spatial distribution of material fields. The performance of the method is tested on three example cases in silico.

Original languageEnglish (US)
Article number035006
JournalInverse Problems
Issue number3
StatePublished - Mar 2023

Bibliographical note

Funding Information:
The authors would like to acknowledge the support of National Science Foundation’s (NSF) Emerging Frontiers in Research and Innovation (EFRI) C3 SoRo Program Grant (Grant No. 1830950).

Publisher Copyright:
© 2023 The Author(s). Published by IOP Publishing Ltd.


  • hyperelasticity
  • inverse design problem
  • nonlinear elasticity
  • nonlinear optimization


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