Hourglassing‐ and locking‐free mesh distortion insensitive Petrov–Galerkin EAS element for large deformation solid mechanics

DOI10.1002/nme.7166OpenAlexW4308908058MaRDI QIDQ6092130

Publication date: 23 November 2023

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.7166

zbMATH Keywords

hyperelastic material mixed finite element unsymmetric finite element method mixed integration point elasto-plastic bar necking elasto-plastic plate necking large mesh stability analysis metric shape function

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) (74C15)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
A technique to develop mesh-distortion immune finite elements
Variational and projection methods for the volume constraint in finite deformation elasto-plasticity
An improved EAS brick element for finite deformation
Hourglass control in linear and nonlinear problems
A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. II: Computational aspects
Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory
Computational inelasticity
An efficient 3D enhanced strain element with Taylor expansion of the shape functions
On enhanced strain methods for small and finite deformations of solids
A note on enhanced strain methods for large deformations
Using assumed enhanced strain elements for large compressive deformation
On the stability of mixed finite elements in large strain analysis of incompressible solids
Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility.
A new 3-D finite element for nonlinear elasticity using the theory of a Cosserat point.
A deformation-dependent stabilization technique, exemplified by EAS elements at large strains
Mixed formulation and locking in path-following nonlinear analysis
Enhanced lower-order element formulations for large strains
Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems
Compatible-strain mixed finite element methods for 2D compressible nonlinear elasticity
How to improve efficiency and robustness of the Newton method in geometrically non-linear structural problem discretized via displacement-based finite elements
Post-bifurcation equilibria in the plane-strain test of a hyperelastic rectangular block
Conditions for equivalence between the Hu-Washizu and related formulations, and computational behavior in the incompressible limit
An enhanced strain 3D element for large deformation elastoplastic thin-shell applications
On a physically stabilized one point finite element formulation for three-dimensional finite elasto-plasticity
A robust nonlinear solid shell element based on a mixed variational formulation
Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation
A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains
New finite elements with embedded strong discontinuities in the finite deformation range
On the formulation of enhanced strain finite elements in finite deformations
Stabilization of mixed tetrahedral elements at large deformations
An unsymmetric 4-node, 8-DOF plane membrane element perfectly breaking through MacNeal's theorem
A theorem regarding the locking of tapered four-noded membrane elements
Rational approach for assumed stress finite elements
A general procedure for the direct computation of turning and bifurcation points
A finite deformation brick element with inhomogeneous mode enhancement
Finite elements with embedded strong discontinuities for the modeling of failure in solids
Improved four-node Hellinger-Reissner elements based on skew coordinates
Relations between incompatible displacement model and hybrid stress model
On invariance of isoparametric hybrid/mixed elements
On the limits of finite element perfectability
Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes
A non-conforming element for stress analysis
Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept
A CO-ROTATIONAL FORMULATION FOR 2-D CONTINUA INCLUDING INCOMPATIBLE MODES
A geometrical non-linear brick element based on the EAS-method
Analysis of 3D problems using a new enhanced strain hexahedral element
A novel unsymmetric 8-node plane element immune to mesh distortion under a quadratic displacement field
A stabilization technique to avoid hourglassing in finite elasticity
A highly efficient enhanced assumed strain physically stabilized hexahedral element
A quadrilateral mixed finite element with two enhanced strain modes
Remarks on the stability of enhanced strain elements in finite elasticity and elastoplasticity
Stability and Convergence of a Class of Enhanced Strain Methods
Mixed Finite Element Methods and Applications
Locking-Free Mixed Finite Element Methods and Their Spurious Hourglassing Patterns
Lineare Algebra
A class of mixed assumed strain methods and the method of incompatible modes
EAS‐elements for two‐dimensional, three‐dimensional, plate and shell structures and their equivalence to HR‐elements
New strategy for assumed stresses for 4‐node hybrid stress membrane element
Remedies to rotational frame dependence and interpolation failure of US‐QUAD8 element
Nonlinear Continuum Mechanics for Finite Element Analysis
On the enhancement of low-order mixed finite element methods for the large deformation analysis of diffusion in solids
Unsymmetric extensions of Wilson's incompatible four‐node quadrilateral and eight‐node hexahedral elements

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