Mixed Kirchhoff stress-displacement-pressure formulations for incompressible hyperelasticity
From MaRDI portal
Publication:2021235
DOI10.1016/j.cma.2020.113562zbMath1506.74050OpenAlexW3109625129MaRDI QIDQ2021235
Publication date: 26 April 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2020.113562
mixed finite element methodsincompressible hyperelasticityaugmented Lagrangian preconditioningKirchhoff stress formulation
Nonlinear elasticity (74B20) Numerical linear algebra (65F99) PDEs in connection with mechanics of deformable solids (35Q74)
Related Items
An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity ⋮ Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema ⋮ A stabilized mixed three‐field formulation for stress accurate analysis including the incompressible limit in finite strain solid dynamics ⋮ Transformations for Piola-mapped elements ⋮ Velocity-vorticity-pressure formulation for the Oseen problem with variable viscosity
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity
- A displacement-based finite element formulation for incompressible and nearly-incompressible cardiac mechanics
- A nonlinear Korn inequality with boundary conditions and its relation to the existence of minimizers in nonlinear elasticity
- Primal-mixed formulations for reaction-diffusion systems on deforming domains
- Variational and projection methods for the volume constraint in finite deformation elasto-plasticity
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- Mixed finite element methods for elliptic problems
- Energy minimizers in nonlinear elastostatics and the implicit function theorem
- A dual-mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions
- Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D
- Existence and approximation results for nonlinear mixed problems: Application to incompressible finite elasticity
- Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms
- Convexity conditions and existence theorems in nonlinear elasticity
- Finite element implementation of incompressible, transversely isotropic hyperelasticity
- An alternative version of the Pian-Sumihara element with a simple extension to nonlinear problems
- Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics
- A mixed three-field FE formulation for stress accurate analysis including the incompressible limit
- A hybridizable discontinuous Galerkin formulation for non-linear elasticity
- Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics
- A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations
- Multigrid methods for a parameter-dependent problem in primal variables
- A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning
- The importance of mechano-electrical feedback and inertia in cardiac electromechanics
- Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation
- Generalized finite element method for modeling nearly incompressible bimaterial hyperelastic solids
- Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics
- A Note on Preconditioning Nonsymmetric Matrices
- A Simple Introduction to the Mixed Finite Element Method
- Finite Elements and Fast Iterative Solvers
- A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems
- Mathematical and computational models of incompressible materials subject to shear
- A First-Order System Least Squares Method for Hyperelasticity
- A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach
- Computational modeling of passive myocardium
- Firedrake
- Numerical solution of saddle point problems
- Constitutive modelling of passive myocardium: a structurally based framework for material characterization
- Mixed finite element methods for linear elasticity with weakly imposed symmetry
- A non-conforming piecewise quadratic finite element on triangles
- Finite Element Methods for Navier-Stokes Equations
- Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes
- A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
- A stabilization technique to avoid hourglassing in finite elasticity
- A Note on Preconditioning for Indefinite Linear Systems
- Mixed Finite Element Methods and Applications
- An Augmented Lagrangian Preconditioner for Implicitly Constituted Non-Newtonian Incompressible Flow
- Modelling Thermo-Electro-Mechanical Effects in Orthotropic Cardiac Tissue
- The method of penalty estimates for conditional extremum problems
- An Augmented Lagrangian Preconditioner for the 3D Stationary Incompressible Navier--Stokes Equations at High Reynolds Number
- Preconditioning
- A Flexible Inner-Outer Preconditioned GMRES Algorithm
- On volumetric locking‐free behaviour of p‐version finite elements under finite deformations
- An Augmented Lagrangian‐Based Approach to the Oseen Problem
- The Mathematical Theory of Finite Element Methods
- A Unified Approach for Uzawa Algorithms
- On the Equivalent of Mixed Element Formulations and the Concept of Reduced Integration in Large Deformation Problems
