Journal
ENGINEERING WITH COMPUTERS
Volume 38, Issue 5, Pages 4099-4113Publisher
SPRINGER
DOI: 10.1007/s00366-021-01597-z
Keywords
Inverse deformation; Rest position; Undeformed configuration; SOFA; FEniCS Project
Funding
- European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant [764644, 798244]
- European Research Council Starting Independent Research Grant (ERC) [279578]
- National Research Fund, Luxembourg
- Marie Curie Actions of the European Commission (FP7-COFUND) [6693582]
- programme Projects of Large Research, Development, and Innovations Infrastructures (CERIT Scientific Cloud) [LM2015085]
- Marie Curie Actions (MSCA) [798244] Funding Source: Marie Curie Actions (MSCA)
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This paper presents a framework for solving inverse deformation problems using the FEniCS Project finite-element software. The proposed method can compute the undeformed configuration by solving only one modified elasticity problem, with complexity comparable to the standard one. The use of the high-level unified form language (UFL) allows for flexible design and easy modification of constitutive models.
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.
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