A mixed method for 3D nonlinear elasticity using finite element exterior calculus

DOI10.1002/nme.7089arXiv2109.01491OpenAlexW3197947090WikidataQ114018606 ScholiaQ114018606MaRDI QIDQ6092221

Bensingh Dhas, Debasish Roy, J. N. Reddy, Unnamed Author

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://arxiv.org/abs/2109.01491

zbMATH Keywords

finite element method cotangent bundle critical point Newton method Hu-Washizu principle differential form

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Exterior differential systems (Cartan theory) (58A15)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
A new mixed finite element based on different approximations of the minors of deformation tensors
A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
Geometric decompositions and local bases for spaces of finite element differential forms
A nonlinear hu-washizu variational formulation and related finite-element implementation for spatial beams with arbitrary moderate thick cross-sections
Mimetic scalar products of discrete differential forms
Mixed finite elements in \(\mathbb{R}^3\)
Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms
Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids
A computational framework for polyconvex large strain elasticity
On the mathematical foundations of electrical circuit theory
Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems
A mixed variational principle in nonlinear elasticity using Cartan's moving frames and implementation with finite element exterior calculus
Compatible-strain mixed finite element methods for 3D compressible and incompressible nonlinear elasticity
Compatible-strain mixed finite element methods for 2D compressible nonlinear elasticity
Approximation of incompressible large deformation elastic problems: some unresolved issues
A geometric structure-preserving discretization scheme for incompressible linearized elasticity
On the geometric character of stress in continuum mechanics
On geometric discretization of elasticity
Finite element exterior calculus: from Hodge theory to numerical stability
A class of mixed assumed strain methods and the method of incompatible modes

This page was built for publication: A mixed method for 3D nonlinear elasticity using finite element exterior calculus