Four‐node tetrahedral elements for gradient‐elasticity analysis
Sign Up to like & getrecommendations! Published in 2020 at "International Journal for Numerical Methods in Engineering"
DOI: 10.1002/nme.6375
Abstract: Computational analyses of gradient‐elasticity often require the trial solution to be C1 yet constructing simple C1 finite elements is not trivial. This article develops two 48‐dof 4‐node tetrahedral elements for 3D gradient‐elasticity analyses by generalizing… read more here.
Keywords: elasticity; node tetrahedral; gradient elasticity; displacement ... See more keywords
Mixed meshless local Petrov–Galerkin (MLPG) collocation methods for gradient elasticity theories of Helmholtz type
Sign Up to like & getrecommendations! Published in 2020 at "Computational Mechanics"
DOI: 10.1007/s00466-020-01866-6
Abstract: Two mixed meshless collocation methods for solving problems by considering a linear gradient elasticity theory of the Helmholtz type are proposed. The solution process is facilitated by employing operator-split procedures, splitting the original 4th-order problem… read more here.
Keywords: elasticity; helmholtz type; gradient elasticity; collocation methods ... See more keywords
Asymptotic solution for interface crack between two materials governed by dipolar gradient elasticity
Sign Up to like & getrecommendations! Published in 2018 at "Engineering Fracture Mechanics"
DOI: 10.1016/j.engfracmech.2018.05.002
Abstract: Abstract An asymptotic solution for interface crack between mismatched materials that obey a special form of linear isotropic strain gradient elasticity under conditions of plane strain is developed. It is shown that the asymptotic solution… read more here.
Keywords: asymptotic solution; gradient elasticity; interface crack; interface ... See more keywords
Strain-gradient elasticity and gradient-dependent plasticity with hierarchical refinement of NURBS
Sign Up to like & getrecommendations! Published in 2019 at "Finite Elements in Analysis and Design"
DOI: 10.1016/j.finel.2019.06.001
Abstract: Abstract Higher-order strain-gradient models are relevant for engineering materials which exhibit size-dependent behaviour as observed from experiments. Typically, this class of models incorporate a length scale - related to micro-mechanical material properties - to capture… read more here.
Keywords: refinement; gradient elasticity; plasticity; strain gradient ... See more keywords
A von Karman plate analogue for solving anti-plane problems in couple stress and dipolar gradient elasticity
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Solids and Structures"
DOI: 10.1016/j.ijsolstr.2017.07.026
Abstract: Abstract The purpose of the present work is to present a direct analogy regarding the formulation and solution of anti-plane problems in the context of couple stress and dipolar gradient elasticity and the von Karman… read more here.
Keywords: karman plate; anti plane; von karman; gradient elasticity ... See more keywords
Gradient elasticity and dispersive wave propagation: Model motivation and length scale identification procedures in concrete and composite laminates
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Solids and Structures"
DOI: 10.1016/j.ijsolstr.2018.09.007
Abstract: Abstract Nano-scale experimental findings reveal that wave propagation in heterogeneous materials is dispersive. In order to capture such dispersive behavior, in this paper gradient elasticity theory is resorted to. A popular gradient elasticity model arising… read more here.
Keywords: gradient elasticity; length scale; model; length ... See more keywords
Non-singular dislocation continuum theories: strain gradient elasticity vs. Peierls–Nabarro model
Sign Up to like & getrecommendations! Published in 2017 at "Philosophical Magazine"
DOI: 10.1080/14786435.2017.1375608
Abstract: Abstract Non-singular dislocation continuum theories are studied. A comparison between Peierls–Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analysed… read more here.
Keywords: strain gradient; dislocation; gradient elasticity; peierls nabarro ... See more keywords
A non-singular continuum theory of point defects using gradient elasticity of bi-Helmholtz type
Sign Up to like & getrecommendations! Published in 2019 at "Philosophical Magazine"
DOI: 10.1080/14786435.2019.1584684
Abstract: ABSTRACT In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a generalised continuum theory possesses a… read more here.
Keywords: point defects; gradient elasticity; point; non singular ... See more keywords
Symmetry conditions in strain gradient elasticity
Sign Up to like & getrecommendations! Published in 2017 at "Mathematics and Mechanics of Solids"
DOI: 10.1177/1081286515606960
Abstract: We study the variational significance of the “order-of-differentiation” symmetry condition of strain gradient elasticity. This symmetry condition stems from the fact that in strain gradient elasticity, one can interchange the order of differentiation in the… read more here.
Keywords: strain gradient; symmetry condition; gradient elasticity;
On variational principles in coupled strain-gradient elasticity
Sign Up to like & getrecommendations! Published in 2022 at "Mathematics and Mechanics of Solids"
DOI: 10.1177/10812865221081854
Abstract: Strain-gradient elasticity is a special case of high-gradient theories in which the potential energy density depends on the first and second gradient of the displacement field. The presence of a coupling term in the material… read more here.
Keywords: coupled strain; elasticity; strain gradient; energy ... See more keywords
Axisymmetric problem within strain-gradient elasticity and mixed FEM solution for cylinders with cracks under tension
Sign Up to like & getrecommendations! Published in 2025 at "Mathematics and Mechanics of Solids"
DOI: 10.1177/10812865251321800
Abstract: The two-dimensional axisymmetric boundary value problem was formulated in cylindrical coordinates within simplified strain-gradient elasticity. A mixed variation formulation of the finite element method (FEM) was applied to solve the set of modeling axisymmetric boundary… read more here.
Keywords: within strain; problem; strain gradient; gradient elasticity ... See more keywords