45 citations · 139 across the 12 of their papers we have counts for
12 papers
Mixed Finite Elements for Geometrically Exact Beams using Discontinuous Rotations and Discrete Curvature
Alexander Humer, Ivo Steinbrecher, Astrid Pechstein
We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific m…
Direct coupling of continuum and shell elements in large deformation problems
Astrid Pechstein, Michael Neunteufel
In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight…
New mixed finite elements for the discretization of piezoelectric structures or macro-fibre composites
Astrid Pechstein, Martin Meindlhumer, Alexander Humer
We propose a new three-dimensional formulation based on the mixed Tangential-Displacement Normal-Normal-Stress (TDNNS) method for elasticity. In elastic TDNNS elements, the tangent…
Three-field mixed finite element methods for nonlinear elasticity
Michael Neunteufel, Astrid Pechstein, Joachim Schöberl
In this paper, we extend the tangential-displacement normal-normal-stress continuous (TDNNS) method from [26] to nonlinear elasticity. By means of the Hu-Washizu principle, the dis…
High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials
Astrid S. Pechstein, Martin Meindlhumer, Alexander Humer
An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displac…
Variational inequalities for ferroelectric constitutive modeling
Martin Meindlhumer, Astrid Pechstein, Alexander Humer
This paper is concerned with modeling the polarization process in ferroelectric media. We develop a thermodynamically consistent model, based on phenomenological descriptions of fr…
The polarization process of ferroelectric materials analyzed in the framework of variational inequalities
Astrid S. Pechstein, Martin Meindlhumer, Alexander Humer
We are concerned with the mathematical modeling of the polarization process in ferroelectric media. We assume that this dissipative process is governed by two constitutive function…
3D mixed finite elements for curved, flat piezoelectric structures
Martin Meindlhumer, Astrid Pechstein
The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric mat…
Large deformation mixed finite elements for smart structures
Astrid S. Pechstein
Recently, "Tangential Displacement Normal Normal Stress" (TDNNS) elements were introduced for small-deformation piezoelectric structures. Benefits of these ele- ments are that they…
An Equilibration Based A Posteriori Error Estimate for the Biharmonic Equation and Two Finite Element Methods
Dietrich Braess, Astrid S. Pechstein, J. Schöberl
We develop an a posteriori error estimator for the Interior Penalty Discontinuous Galerkin approximation of the biharmonic equation with continuous finite elements. The error bound…
The TDNNS method for Reissner-Mindlin plates
Astrid Pechstein, Joachim Schöberl
A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress"…
An analysis of the TDNNS method using natural norms
Astrid S. Pechstein, Joachim Schöberl
The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method for mixed elasticity. As the name suggests, the tangential component of the displacement…