Inverse deformation analysis: an experimental and numerical assessment using the FEniCS Project

Arnaud Mazier, Alexandre Bilger, Antonio E. Forte, Igor Peterlik, Jack S. Hale, Stéphane P.A. Bordas*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


In this paper we develop a framework for solving inverse deformation problems using the FEniCS Project finite-element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In contrast with inverse iterative algorithms that require multiple solutions of a standard elasticity problem, the proposed method can compute the undeformed configuration by solving only one modified elasticity problem. This modified problem has a complexity comparable to the standard one. The framework is implemented within an open-source pipeline enabling the direct and inverse deformation simulation directly from imaging data. We use the high-level unified form language (UFL) of the FEniCS Project to express the finite-element model in variational form and to automatically derive the consistent Jacobian. Consequently, the design of the pipeline is flexible: for example, it allows the modification of the constitutive models by changing a single line of code. We include a complete working example showing the inverse deformation of a beam deformed by gravity as supplementary material.

Original languageEnglish
Pages (from-to)4099-4113
Number of pages15
Issue number5
Early online date18 Feb 2022
Publication statusPublished - Oct 2022


  • FEniCS Project
  • Inverse deformation
  • Rest position
  • SOFA
  • Undeformed configuration


Dive into the research topics of 'Inverse deformation analysis: an experimental and numerical assessment using the FEniCS Project'. Together they form a unique fingerprint.

Cite this