A three-dimensionalC1finite element for gradient elasticity
From MaRDI portal
Publication:3617497
DOI10.1002/nme.2449zbMath1156.74382OpenAlexW1973202187WikidataQ107465420 ScholiaQ107465420MaRDI QIDQ3617497
Stefanos-Aldo Papanicolopulos, A. Zervos, I. G. Vardoulakis
Publication date: 24 March 2009
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/nme.2449
finite element methodssolidsgradient elasticityhigher-order continuum\(C^{1}\) elementelasticity with microstructure
Related Items (56)
Numerical simulations of classical problems in two-dimensional (non) linear second gradient elasticity ⋮ A method for creating a class of triangular C1 finite elements ⋮ A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method ⋮ Lamé's strain potential method for plane gradient elasticity problems ⋮ Large strain, two-scale computational approach using \(C^1\) continuity finite element employing a second gradient theory ⋮ Isogeometric topology optimization of strain gradient materials ⋮ A unified reproducing kernel gradient smoothing Galerkin meshfree approach to strain gradient elasticity ⋮ Three-dimensional finite element analysis of finite deformation micromorphic linear isotropic elasticity ⋮ Three-dimensional isogeometric solutions to general boundary value problems of Toupin's gradient elasticity theory at finite strains ⋮ A non-classical Mindlin plate finite element based on a modified couple stress theory ⋮ Non-singular stresses in gradient elasticity at bi-material interface with transverse crack ⋮ A Nitsche-type variational formulation for the shape deformation of a single component vesicle ⋮ Consistent integration schemes for meshfree analysis of strain gradient elasticity ⋮ Two robust nonconforming \(H^2\)-elements for linear strain gradient elasticity ⋮ Laplace-domain, high-order homogenization for transient dynamic response of viscoelastic composites ⋮ On the mapping procedure based on higher‐order Hermite polynomials for laminated thin plates with arbitrary domains in gradient elasticity ⋮ Three‐field mixed finite element formulations for gradient elasticity at finite strains ⋮ A Robust Lower-Order Mixed Finite Element Method for a Strain Gradient Elastic Model ⋮ Eight‐node hexahedral elements for gradient elasticity analysis ⋮ An efficient 4‐node facet shell element for the modified couple stress elasticity ⋮ The scaled boundary finite element method for dispersive wave propagation in higher‐order continua ⋮ A fully second‐order homogenization formulation for the multi‐scale modeling of heterogeneous materials ⋮ Mixed finite elements based on superconvergent patch recovery for strain gradient theory ⋮ Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems ⋮ Chirality in isotropic linear gradient elasticity ⋮ Verification of strain gradient elasticity computation by analytical solutions ⋮ Isogeometric analysis of 2D gradient elasticity ⋮ Mixed meshless local Petrov-Galerkin (MLPG) collocation methods for gradient elasticity theories of Helmholtz type ⋮ A finite element based on the strain approach using Airy's function ⋮ A high order homogenization model for transient dynamics of heterogeneous media including micro-inertia effects ⋮ Large elastic deformation of micromorphic shells. Part II. Isogeometric analysis ⋮ Multiscale computational homogenization methods with a gradient enhanced scheme based on the discontinuous Galerkin formulation ⋮ Second-grade elasticity revisited ⋮ Boundary element analysis of static plane problems in size-dependent consistent couple stress elasticity ⋮ Finite element analysis of plane strain solids in strain-gradient elasticity ⋮ Application of a non-conforming tetrahedral element in the context of the three-dimensional strain gradient elasticity ⋮ A Family of Nonconforming Rectangular Elements for Strain Gradient Elasticity ⋮ Three dimensional elements with Lagrange multipliers for the modified couple stress theory ⋮ Mixed meshless local Petrov-Galerkin collocation method for modeling of material discontinuity ⋮ A mixed element based on Lagrange multiplier method for modified couple stress theory ⋮ On the C 1 continuous discretization of non-linear gradient elasticity: A comparison of NEM and FEM based on Bernstein-Bézier patches ⋮ A refined nonconforming quadrilateral element for couple stress/strain gradient elasticity ⋮ Refined 18-DOF triangular hybrid stress element for couple stress theory ⋮ Discretization of Gradient Elasticity Problems Using C 1 Finite Elements ⋮ C 1 Discretizations for the Application to Gradient Elasticity ⋮ An advanced boundary element method for solving 2D and 3D static problems in Mindlin's strain-gradient theory of elasticity ⋮ Nonlinear finite element analysis within strain gradient elasticity: Reissner-Mindlin plate theory versus three-dimensional theory ⋮ 24-DOF quadrilateral hybrid stress element for couple stress theory ⋮ A second-order two-scale homogenization procedure using \(C^1\) macrolevel discretization ⋮ On rotation deformation zones for finite-strain Cosserat plasticity ⋮ \(H^2\)-Korn's inequality and the nonconforming elements for the strain gradient elastic model ⋮ Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems ⋮ Local and nonlocal continuum modeling of inelastic periodic networks applied to stretching-dominated trusses ⋮ A multi-field finite element approach for the modelling of fibre-reinforced composites with fibre-bending stiffness ⋮ 3D strain gradient elasticity: variational formulations, isogeometric analysis and model peculiarities ⋮ A four-node \(C^0\) tetrahedral element based on the node-based smoothing technique for the modified couple stress theory
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Elastic materials with couple-stresses
- One-dimensional localisation studied with a second grade model
- Mixed finite element formulations of strain-gradient elasticity problems
- On first strain-gradient theories in linear elasticity
- A higher-order triangular plate bending element revisited
- Implicit gradient elasticity
- Finite elements for elasticity with microstructure and gradient elasticity
- LAPACK Users' Guide
- Isoparametric Hermite elements
- On Natural Boundary Conditions in Linear 2nd-Grade Elasticity
- Large strain finite element analysis of a local second gradient model: application to localization
- Modelling of localisation and scale effect in thick-walled cylinders with gradient elastoplasticity
This page was built for publication: A three-dimensionalC1finite element for gradient elasticity