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

• DOI: 10.1007/s00366-021-01597-z
• Publication Date: 2022-02-18T09:04:58Z
• Authors: Arnaud Mazier; Alexandre Bilger; Antonio E. Forte; Igor Peterlik; Jack S. Hale; Stéphane P. A. Bo...
• Keywords: Finite element method; : Materials science & engineering [C09] [Engineering, computing & technology]; Finite Element Analysis; Biomedical Engineering; Structural engineering; Geometry; Ocean Engineering; Hyperelastic material; FOS: Medical engineering; Oceanography; FEniCS Project; Mathematical analysis; 01 natural sciences; : Ingénierie mécanique [C10] [Ingénierie, informatique & technologie]; Engineering; Inverse deformation; Digital Image Correlation Techniques; FOS: Mathematics; SOFA; Hyperelastic Modeling; 0101 mathematics; Rest position; rest position; Jacobian matrix and determinant; Elasticity (physics); Biomechanical Modeling of Arterial Tissues; Inverse Modeling; Deformation (meteorology); Physics; Mathematical optimization; : Mechanical engineering [C10] [Engineering, computing & technology]; undeformed configuration; Geology; FOS: Earth and related environmental sciences; Applied mathematics; Computer science; : Science des matériaux & ingénierie [C09] [Ingénierie, informatique & technologie]; Drilling Fluid Technology and Well Integrity; Physical Sciences; Computer Science; Inverse problem; Thermodynamics; Computer Vision and Pattern Recognition; Deformation Analysis; Inverse; Undeformed configuration; Mathematics

AbstractIn 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.