Locking-Proof Tetrahedra

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young\u27s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For , we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis

Data accompanying: Ásgeirsson, Á.G. & Nieuwenhuis, S. (2017). No arousal-biased competition in focused visuospatial attention. Cognition, 168, 191-204.

The zipped folder DATA.zip contains behavioral and eye tracking data from Experiments 1A, 2, 3A and 3B from the article "No arousal-biased competition in focused visuospatial attention", currently (3rd July, 2017) in press in <i>Cognition</i>. <br><br><div>The zipped folder EEG_DATA.zip contains data from an ERP experiment (Experiment 1B), presented in the same article.<br><br>Article doi:<br><a href="https://doi.org/10.1016/j.cognition.2017.07.001" target="doilink">10.1016/j.cognition.2017.07.001</a><br></div