On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations

DOI10.1007/s00466-017-1415-2zbMath1386.74141OpenAlexW2611112104WikidataQ64017267 ScholiaQ64017267MaRDI QIDQ1697130

Nils Viebahn, Karl Steeger, Peter Wriggers, Jörg Schröder, Ferdinando Auricchio

Publication date: 15 February 2018

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-017-1415-2

zbMATH Keywords

stability analysiscondensed formulationssignature of a matrixthree-field and two-field mixed FEM

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Stability of dynamical problems in solid mechanics (74H55)

Related Items (9)

A stabilized one-point integrated mixed formulation for finite element and meshfree methods in modeling nearly incompressible materials ⋮ Novel Finite Elements - Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Applications ⋮ Variational schemes and mixed finite elements for large strain isotropic elasticity in principal stretches: Closed‐form tangent eigensystems, convexity conditions, and stabilised elasticity ⋮ Artificial instabilities of finite elements for nonlinear elasticity: Analysis and remedies ⋮ A structure-preserving integrator for incompressible finite elastodynamics based on a Grad-div stabilized mixed formulation with particular emphasis on stretch-based material models ⋮ Simultaneous shape and topology optimization of inflatable soft robots ⋮ Swelling-induced interface crease instabilities at hydrogel bilayers ⋮ A Taylor-Hood type virtual element formulations for large incompressible strains ⋮ Computational stability analysis of periodic electroactive polymer composites across scales

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new mixed finite element based on different approximations of the minors of deformation tensors
• The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations
• Variational and projection methods for the volume constraint in finite deformation elasto-plasticity
• Une méthode numérique pour les problèmes d'équilibre de corps hyperélastiques compressibles en grandes déformations
• An improved EAS brick element for finite deformation
• Hourglass control in linear and nonlinear problems
• Locking effects in the finite element approximation of elasticity problems
• On some mixed finite element methods for incompressible and nearly incompressible finite elasticity
• A note on enhanced strain methods for large deformations
• Design of simple low order finite elements for large strain analysis of nearly incompressible solids
• Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility.
• Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions.
• On numerically accurate finite element solutions in the fully plastic range
• Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems
• Approximation of incompressible large deformation elastic problems: some unresolved issues
• A stability study of some mixed finite elements for large deformation elasticity problems
• The finite element method with Lagrangian multipliers
• A First-Order System Least Squares Method for Hyperelasticity
• Least-Squares Mixed Finite Element Formulations for Isotropic and Anisotropic Elasticity at Small and Large Strains
• The inf-sup test
• Rational approach for assumed stress finite elements
• On the Variational Foundations of Assumed Strain Methods
• Generalization of selective integration procedures to anisotropic and nonlinear media
• [https://portal.mardi4nfdi.de/wiki/Publication:3940969 Nichtlineare Stabilit�tsuntersuchungen mit der Methode der Finiten Elemente]
• Mixed and Hybrid Finite Element Methods
• Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes
• A new stabilization technique for finite elements in non-linear elasticity
• A stabilization technique to avoid hourglassing in finite elasticity
• An assessment of the average nodal volume formulation for the analysis of nearly incompressible solids under finite strains
• Finite Elements

This page was built for publication: On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations