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

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 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.

To characterize the material properties, we used the Mach-1™ mechanical testing system (Biomomentum, Canada) as a testing rig for the unconfined compression tests.

Keywords: Inverse deformation, rest position, undeformed configuration, SOFA, FEniCS Project.