Mixed Kirchhoff stress-displacement-pressure formulations for incompressible hyperelasticity
type: Item
instance of: scholarly article
title: Mixed Kirchhoff stress-displacement-pressure formulations for incompressible hyperelasticity
zbMATH Open document ID: 1506.74050
author: Yanyan Li
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2021-04-26T00:00:00Z
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 65F99
zbMATH DE Number: 7338012
zbMATH Keywords: Kirchhoff stress formulation
zbMATH Keywords: incompressible hyperelasticity
zbMATH Keywords: augmented Lagrangian preconditioning
zbMATH Keywords: mixed finite element methods
describes a project that uses: Firedrake
describes a project that uses: FEniCS
MaRDI profile type: Publication
full work available at URL: j.cma.2020.113562
OpenAlex ID: W3109625129
cites work: Q3514988
cites work: Mixed Finite Element Methods and Applications
cites work: A First-Order System Least Squares Method for Hyperelasticity
cites work: An alternative version of the Pian-Sumihara element with a simple extension to nonlinear problems
cites work: A hybridizable discontinuous Galerkin formulation for non-linear elasticity
cites work: A mixed three-field FE formulation for stress accurate analysis including the incompressible limit
cites work: Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics
cites work: Mathematical and computational models of incompressible materials subject to shear
cites work: On volumetric locking‐free behaviour of p‐version finite elements under finite deformations
cites work: A stabilization technique to avoid hourglassing in finite elasticity
cites work: A non-conforming piecewise quadratic finite element on triangles
cites work: Generalized finite element method for modeling nearly incompressible bimaterial hyperelastic solids
cites work: Variational and projection methods for the volume constraint in finite deformation elasto-plasticity
cites work: Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes
cites work: Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms
cites work: A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems
cites work: Mixed finite element methods for elliptic problems
cites work: A dual-mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions
cites work: Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D
cites work: Modelling Thermo-Electro-Mechanical Effects in Orthotropic Cardiac Tissue
cites work: Mixed finite element methods for linear elasticity with weakly imposed symmetry
cites work: Primal-mixed formulations for reaction-diffusion systems on deforming domains
cites work: Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics
cites work: A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach
cites work: Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity
cites work: The importance of mechano-electrical feedback and inertia in cardiac electromechanics
cites work: Computational modeling of passive myocardium
cites work: A displacement-based finite element formulation for incompressible and nearly-incompressible cardiac mechanics
cites work: Finite element implementation of incompressible, transversely isotropic hyperelasticity
cites work: A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning
cites work: A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations
cites work: Preconditioning
cites work: A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
cites work: A Note on Preconditioning for Indefinite Linear Systems
cites work: Numerical solution of saddle point problems
cites work: A note on preconditioning nonsymmetric matrices
cites work: Finite elements and fast iterative solvers. With applications in incompressible fluid dynamics
cites work: An Augmented Lagrangian‐Based Approach to the Oseen Problem
cites work: Constitutive modelling of passive myocardium: a structurally based framework for material characterization
cites work: A nonlinear Korn inequality with boundary conditions and its relation to the existence of minimizers in nonlinear elasticity
cites work: Q4039741
cites work: Q4039724
cites work: Singularities and computation of minimizers for variational problems
cites work: \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
cites work: Convexity conditions and existence theorems in nonlinear elasticity
cites work: Energy minimizers in nonlinear elastostatics and the implicit function theorem
cites work: Existence and approximation results for nonlinear mixed problems: Application to incompressible finite elasticity
cites work: A Simple Introduction to the Mixed Finite Element Method
cites work: Finite Element Methods for Navier-Stokes Equations
cites work: The Mathematical Theory of Finite Element Methods
cites work: An Augmented Lagrangian Preconditioner for the 3D Stationary Incompressible Navier--Stokes Equations at High Reynolds Number
cites work: A Unified Approach for Uzawa Algorithms
cites work: An Augmented Lagrangian Preconditioner for Implicitly Constituted Non-Newtonian Incompressible Flow
cites work: The method of penalty estimates for conditional extremum problems
cites work: A Flexible Inner-Outer Preconditioned GMRES Algorithm
cites work: Multigrid methods for a parameter-dependent problem in primal variables
cites work: Firedrake
cites work: On the Equivalent of Mixed Element Formulations and the Concept of Reduced Integration in Large Deformation Problems
cites work: Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics
cites work: Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation

Mixed Kirchhoff stress-displacement-pressure formulations for incompressible hyperelasticity (DOI)
DOI: 10.1016/J.CMA.2020.113562