Gonzalo Gonzalez de Diego (Universität Duisburg-Essen)
Wednesday, April 18, 2018 - 09:15
Humboldt-Universität, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin, Raum 3.007, Haus 3
Forschungsseminar "Numerische Mathematik"
Prof. C. Carstensen
In this presentation, a least squares finite element method (LSFEM) is presented for the first order system of hyperelasticity defined over the deformed configuration in order to approximate the Cauchy stress tensor. Unlike the first Piola-Kirchhoff stress tensor, the Cauchy stress tensor is symmetric, a property intimately related to the conservation of angular momentum. With this work, we wish to explore the possibility of imposing the symmetry of the stress tensor, strongly or weakly, in non-linear elasticity. Firstly, an overview of a LSFEM for hyperelasticity (over the reference configuration) by (Müller et al., 2014) is presented. Secondly, we address the question of under which conditions can a first order system over the deformed configuration be considered. Then, the former LSFEM is extended to the deformed configuration; we introduce a Gauss-Newton method for solving the non-linear minimization problem and show that, under small strains and stresses, the least-squares functional represents an a posteriori error estimator. Finally, we display numerical results for two test cases. These results indicate that this LSFEM is capable of giving reliable results even when the regularity assumptions from the analysis are not satisfied.
submitted by S. Schmidt (sschmidt@math.hu-berlin.de, 2093 1820)