Efficient simulation of heterogeneous materials with the finite cell method

First published in
Proceedings in applied mathematics and mechanics 
Number in series
21,1
Article Number
e202100139
Citation
PAMM 21 (1): e202100139 (2021)
Contribution to Conference
92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2022 
Publisher DOI
10.1002/pamm.202100139
Publisher
Wiley-VCH
The finite cell method (FCM) represents a combination of high-order finite elements with the fictitious domain approach. Due to it's simple mesh generation the FCM reduces the pre-processing effort. For heterogeneous problems of solid mechanics however, discontinuities occur at the material interfaces, which cannot be captured by the smooth shape functions of the FCM anymore, whereby the convergence deteriorates. Thus, to recover the optimal convergence rate, we extend the FCM ansatz by specially designed shape functions, which are able to capture discontinuities at the material interfaces. To get more insight into the problem, we study the performance of the proposed method by means of a two-dimensional example.
DDC Class
510: Mathematik
530: Physik
600: Technik
620: Ingenieurwissenschaften