Anisotropic strain gradient thermoelasticity for cellular structures: plate models, homogenization and isogeometric analysis

DOI10.1016/j.jmps.2019.103728zbMath1481.74108OpenAlexW2972412557WikidataQ127235651 ScholiaQ127235651MaRDI QIDQ2670028

Jarkko Niiranen, Sergei Khakalo

Publication date: 10 March 2022

Published in: Journal of the Mechanics and Physics of Solids (Search for Journal in Brave)

Full work available at URL: https://aaltodoc.aalto.fi/handle/123456789/40446

zbMATH Keywords

Kirchhoff platesize effectsReissner-Mindlin platestrain gradient thermoelasticityisogeometric analysiscellular plateslattice microarchitecture

Mathematics Subject Classification ID

Anisotropy in solid mechanics (74E10) Thermal effects in solid mechanics (74F05) Homogenization, determination of effective properties in solid mechanics (74Q99)

Related Items (21)

Isogeometric analysis for non-classical Bernoulli-Euler beam model incorporating microstructure and surface energy effects ⋮ Direct \(\mathrm{FE}^2\) modeling of heterogeneous materials with a micromorphic computational homogenization framework ⋮ Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory ⋮ Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the relaxed micromorphic model ⋮ A Robust Lower-Order Mixed Finite Element Method for a Strain Gradient Elastic Model ⋮ Anisotropic structure of two-dimensional linear Cosserat elasticity ⋮ Granular micromechanics‐based identification of isotropic strain gradient parameters for elastic geometrically nonlinear deformations ⋮ Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems ⋮ Verification of strain gradient elasticity computation by analytical solutions ⋮ Higher order finite element models for transient analysis of strain gradient functionally graded microplates ⋮ A hierarchical wavelet method for nonlinear bending of materially and geometrically anisotropic thin plate ⋮ RI-IGABEM in inhomogeneous heat conduction problems ⋮ Surface energy-enriched gradient elastic Kirchhoff plate model and a novel weak-form solution scheme ⋮ A geometrically nonlinear Euler-Bernoulli beam model within strain gradient elasticity with isogeometric analysis and lattice structure applications ⋮ Nonlinear finite element analysis within strain gradient elasticity: Reissner-Mindlin plate theory versus three-dimensional theory ⋮ Three-point bending test of pantographic blocks: numerical and experimental investigation ⋮ Strain gradient elasto-plasticity model: 3D isogeometric implementation and applications to cellular structures ⋮ 3D strain gradient elasticity: variational formulations, isogeometric analysis and model peculiarities ⋮ Computation of brittle fracture propagation in strain gradient materials by the FEniCS library ⋮ Strain-gradient modeling and computation of 3-D printed metamaterials for verifying constitutive parameters determined by asymptotic homogenization ⋮ Do we really need pantographic structures?

Cites Work

• Unnamed Item
• Unnamed Item
• Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum
• Minimal loading conditions for higher-order numerical homogenisation schemes. Cauchy, second gradient and micromorphic substitute media.
• Geometrically nonlinear higher-gradient elasticity with energetic boundaries
• Analysis of anisotropic gradient elastic shear deformable plates
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics
• Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients
• Multi-scale computational homogenization: trends and challenges
• On the role of gradients in the localization of deformation and fracture
• A simple approach to solve boundary-value problems in gradient elasticity
• Dynamic problems for metamaterials: review of existing models and ideas for further research
• Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices
• Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: applications to sandwich beams and auxetics
• Variational formulations and general boundary conditions for sixth-order boundary value problems of gradient-elastic Kirchhoff plates
• Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model
• Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams
• Anisotropy in strain gradient elasticity: simplified models with different forms of internal length and moduli tensors
• Form II of Mindlin's second strain gradient theory of elasticity with a simplification: for materials and structures from nano- to macro-scales
• Matrix representations for 3D strain-gradient elasticity
• Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity
• Kirchhoff-Love shells within strain gradient elasticity: weak and strong formulations and an \(H^3\)-conforming isogeometric implementation
• Granular micromechanics based continuum model for grain rotations and grain rotation waves
• A predictive micropolar continuum model for a novel three-dimensional chiral lattice with size effect and tension-twist coupling behavior
• Anisotropic and dispersive wave propagation within strain-gradient framework
• On generalized Cosserat-type theories of plates and shells: a short review and bibliography
• 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
• Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates
• Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization
• Continuum modelling of frequency dependent acoustic beam focussing and steering in hexagonal lattices
• The non-singular Green tensor of Mindlin's anisotropic gradient elasticity with separable weak non-locality
• Micro-structure in linear elasticity
• Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps
• Micromorphic computational homogenization for mechanical metamaterials with patterning fluctuation fields
• 2D lattice material architectures for actuation
• A quasicontinuum theory for the nonlinear mechanical response of general periodic truss lattices
• On asymptotic elastodynamic homogenization approaches for periodic media
• Energy approach to brittle fracture in strain-gradient modelling
• Homogenization methods and mechanics of generalized continua - part 2
• On the Direct Approach in the Theory of Second Gradient Plates
• Variational asymptotic homogenization of beam-like square lattice structures
• Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models
• A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS
• The Shear Coefficient in Timoshenko’s Beam Theory

This page was built for publication: Anisotropic strain gradient thermoelasticity for cellular structures: plate models, homogenization and isogeometric analysis