0215 Locking, Stability and Robustness of Non-linear Finite Elements for Large Deformation Problems

  • Simon Bieber, University of Stuttgart
  • Manfred Bischoff, University of Stuttgart
  • Robin Pfefferkorn, Karlsruhe Institute of Technology
  • Peter Betsch, Karlsruhe Institute of Technology
  • Alessandro Reali, University of Pavia
  • Ferdinando Auricchio, University of Pavia

Although the topic of finite element technology is well understood in many respects, there still exist several open questions, especially for geometrically and physically nonlinear problems, where mathematical tools are limited. Moreover, an increasing number of alternative discretization schemes have (re-) entered the stage, demanding new answers to old questions.

The main motive within this research field is the locking-free response of finite elements. This comes along with optimal convergence rates already in the pre-asymptotic range of coarse meshes, independent of critical parameters like slenderness or Poisson's ratio. However, in the course of large deformation problems as well as severely distorted meshes it may become difficult to (fully) avoid locking. Promising recent approaches, which reduce sensitivity to mesh distortion, are based on a Petrov-Galerkin approach instead of the usual Bubnov-Galerkin method.

Another typical issue that comes up with locking-free element formulations are artificial, non-physical instabilities ("hourglassing"). The latter is particularly critical in the large strain regime and typical problems involve hourglassing of hyperelastic specimens under compression and spurious modes due to material induced instabilities, which can e.g. be observed in elasto-plastic necking simulations.

In this context, a particular difficulty lies in the analysis itself, which is inevitably connected to deformation states which are also potentially prone to physical instabilities. Thus, getting a clear view on whether or not artificial instabilities are present, one always has to cope with the physical instability problem.

With a general focus on nonlinear problems, the proposed mini-symposium invites all contributions from the field of locking, efficiency, stability and robustness of finite elements and other, non-standard discretization schemes, both from method development and application. Typical topics are expected to be, but not restricted to:

・locking-free formulations for geometrically and materially non-linear simulations
・Petrov-Galerkin displacement based and mixed finite elements
・element performance for non-structured and distorted meshes
・benchmarks for the analysis of finite elements w.r.t. physical and artificial instabilities
・finite elements and non-standard discretization methods, such as spline-based, meshless or discontinuous Galerkin methods
・efficiency, convergence, stability and approximation properties

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