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[en] 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.
FNR6693582 - Advanced Computational Methods For The Simulation Of Cutting In Surgery, 2013 (01/01/2014-31/12/2015) - Jack Samuel Hale
Funders :
CE - Commission Européenne [BE]
Commentary :
This study was supported by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 764644, No. 798244 and the financial support of the European Research Council Starting Independent Research Grant (ERC StG Grant Agreement No. 279578). Jack S. Hale is supported by the National Research Fund, Luxembourg, and cofunded under the Marie Curie Actions of the European Commission (FP7-COFUND) Grant No. 6693582. A.E. Forte acknowledges that this project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 798244. Access to the computing facilities provided under the programme "Projects of Large Research, Development, and Innovations Infrastructures" (CERIT Scientific Cloud LM2015085) was greatly appreciated.
