Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications

Keywords

Simple (philosophy), Stability (learning theory), Tetrahedron, Compressibility, Jacobian matrix and determinant

References

• Recent developments in large-scale finite-element Lagrangian hydrocode technology. [Dyna 20/dyna 30 computer code]G.L. Goudreau, J.O. Hallquist — 1981
• Triangles and tetrahedra in explicit dynamic codes for solidsO. C. Zienkiewicz, Jerzy Rojek, R.L. Taylor — 1998
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• A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applicationsJavier Bonet, Alice Burton — 1998
• A numerical method for solving incompressible viscous flow problemsAlexandre J. Chorin — 1967

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• Effects of Ankle Arthrodesis on Biomechanical Performance of the Entire FootYan Wang, Zengyong Li, Duo Wai‐Chi Wong — 2015
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• Inf-suf stable bES-FEM method for nearly incompressible elasticityThanh Hai Ong, Guiqin Liu, T. Nguyen‐Thoi — 2013
• Two‐phase dynamic analysis by material point methodIssam Jassim, Dieter Stolle, P Vermeer — 2013
• Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendumJaroslav Mackerle — 2002
• Variationally consistent methods for Lagrangian dynamics in continuum mechanicsSudeep K. Lahiri — 2006
• Gradient Smoothing in Finite Elasticity: near-incompressibilityChangkye Lee — 2016
• A variationally consistent fractional time‐step integration method for incompressible and nearly incompressible Lagrangian dynamicsSudeep K. Lahiri, Javier Bonet, J. Peraire — 2005
• A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamicsAntonio J. Gil, Chun Hean Lee, Javier Bonet — 2014
• Combination of discrete element and finite element methods for dynamic analysis of geomechanics problemsEugenio Oñate, Jerzy Rojek — 2004
• From the Hu–Washizu formulation to the average nodal strain formulationP. Lamichhane — 2009
• Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticityMiguel Cervera, Michele Chiumenti, C. Agelet de Saracibar — 2004
• A new efficient explicit formulation for linear tetrahedral elements non‐sensitive to volumetric locking for infinitesimal elasticity and inelasticityP. O. De Micheli, Katia Mocellin — 2009
• Mixed linear/linear simplicial elements for incompressible elasticity and plasticityMiguel Cervera, Michele Chiumenti, Quino Valverde — 2003
• A unified fractional step method for compressible and incompressible flows, heat transfer and incompressible solid mechanicsPerumal Nithiarasu — 2008
• A vertex centred Finite Volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamicsMiquel Aguirre, Antonio J. Gil, Javier Bonet — 2014

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