Contact modeling from images using cut finite element solvers

S Claus,C Wong,F Moshfeghifar,P Kerfriden,K Erleben,S Darkner

doi:10.1186/s40323-021-00197-2

Abstract

This paper presents a robust digital pipeline from CT images to the simulation of contact between multiple bodies. The proposed strategy relies on a recently developed immersed finite element algorithm that is capable of simulating unilateral contact between solids without meshing (Claus and Kerfriden in Int J Numer Methods Eng 113(6):938–966, 2018). It was shown that such an approach reduces the difficulties associated with the digital flow of information from analytically defined geometries to mechanical simulations. We now propose to extend our approach to include geometries, which are not defined mathematically but instead are obtained from images, and encoded in 3D arrays of voxels. This paper introduces two novel elements. Firstly, we reformulate our contact algorithm into an extension of an augmented Lagrangian CutFEM algorithm. Secondly, we develop an efficient algorithm to convert the surface data generated by standard segmentation tools used in medical imaging into level-set functions. These two elements give rise to a robust digital pipeline with minimum user intervention. We demonstrate the capabilities of our algorithm on a hip joint geometry with contact between the femur and the hip bone.

Highlights

In this article, we present a modern digital pipeline for the simulation of the mechanical interaction between solid bodies from computed tomography (CT) images
We formally show that the CutFEM-LaTIn algorithm is an extension of the augmented Lagrangian CutFEM algorithm presented in [7,8]
In [12], we have shown that our LaTIn/CutFEM algorithm was stable and converged optimally for a range of carefully selected benchmark problems

Summary

Introduction

We present a modern digital pipeline for the simulation of the mechanical interaction between solid bodies from CT images. Boundaries are often of key importance to analysts This is the case in the present contribution, which focusses on the simulation of contact between two elastic bodies. As per usual with level-set-based methods, the surfaces of the bodies will be represented by the zero contour line of these functions. Zero contour lines may intersect the background mesh in an arbitrary manner This allows for a sharp and smooth (continuous and elements-wise linear in this paper) surface representation which are used simulate contact and compute contact forces between the elastic bodies. The boundary of the elastic bodies will be represented by the zero contour lines of level set functions, which will be allowed to intersect the background mesh cells in an arbitrary manner. CutFEM/level-set approximation of the geometry Let us introduce a triangulation Th of the background domain b.

Overlapping domain decomposition

Domain decomposition formulation

Lagrange multiplier

Average Distance Average Distance

Conclusions