An efficient mixed finite element formulation for 3D strain gradient elasticity

DOI10.1016/j.cma.2024.117422MaRDI QIDQ6643586

Johannes Riesselmann, Nasrin Rezaei, Daniel Balzani, Luca Placidi

Publication date: 26 November 2024

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

mixed finite elementsstrain gradient elasticitymeta-materialslength-scale dependence

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Elastic materials (74Bxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• A family of 3D continuously differentiable finite elements on tetrahedral grids
• A trivariate Clough-Tocher scheme for tetrahedral data
• Elastic materials with couple-stresses
• Full-explicit interpolation formulas for the Argyris triangle
• Three-dimensional isogeometric solutions to general boundary value problems of Toupin's gradient elasticity theory at finite strains
• Polynomial approximation on tetrahedrons in the finite element method
• A C0 interior penalty finite element method for flexoelectricity
• Theories of elasticity with couple-stress
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
• Micro-structure in linear elasticity
• A robust nonconforming \(H^2\)-element
• Finite element method. Vol. 2: Solid mechanics.
• Generalized Hooke's law for isotropic second gradient materials
• Spline Functions on Triangulations
• C0 finite element discretization of Kirchhoff's equations of thin plate bending
• Mixed Finite Element Methods and Applications
• A general approach to transforming finite elements
• The Hellan--Herrmann--Johnson Method with Curved Elements
• Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation
• Stable splitting of polyharmonic operators by generalized Stokes systems
• Finite Elemente
• A $C^1$ Tetrahedral Finite Element without Edge Degrees of Freedom
• Micromechanics-based elasto-plastic-damage energy formulation for strain gradient solids with granular microstructure
• A procedure for the experimental identification of the strain gradient characteristic length
• Rot-free mixed finite elements for gradient elasticity at finite strains

This page was built for publication: An efficient mixed finite element formulation for 3D strain gradient elasticity