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

by   Arnaud Mazier, et al.

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.


page 7

page 23

page 24

page 26

page 28


Efficient formulation of a geometrically nonlinear beam element

The paper presents a two-dimensional geometrically nonlinear formulation...

SOniCS: Develop intuition on biomechanical systems through interactive error controlled simulations

This new approach allows the user to experiment with model choices easil...

On the finite element analysis of functionally graded sandwich curved beams via a new refined higher shear deformation theory

In the present paper, a new parabolic shear deformation beam theory is d...

Automatic surface mesh generation for discrete models: A complete and automatic pipeline based on reparameterization

Triangulations are an ubiquitous input for the finite element community....

Conforming and Nonconforming Finite Element Methods for Biharmonic Inverse Source Problem

This paper deals with the numerical approximation of the biharmonic inve...

Finite Element Modeling of Pneumatic Bending Actuators for Inflated-Beam Robots

Inflated-beam soft robots, such as tip-everting vine robots, can control...

Please sign up or login with your details

Forgot password? Click here to reset