Elastic materials with couple-stresses
1962/01/01 by R. A. Toupin · 2,962 citations
Engineering · #Composite Material Mechanics #Composite material #Elasticity and Material Modeling #Elasticity and Wave Propagation #Engineering #Materials science #Structural engineering
paper · open access · doi:10.1007/bf00253945
published in Archive for Rational Mechanics and Analysis 11(1), 385-414 (Springer Science+Business Media)
openalex publication_date 1962/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Cited by
- On the thermodynamics of systems with nonlocality
- Derivation of von Kármán plate theory in the framework of three-dimensional viscoelasticity
- Thermoviscoelasticity in Kelvin-Voigt rheology at large strains
- Nonlinear and Linearized Models in Thermoviscoelasticity
- On the thermomechanics of interstitial working
- Bernoulli–Euler Dielectric Beam Model Based on Strain-Gradient Effect
- Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme
- Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis
- A Lowest-Order Robust Mixed Finite Element Method with a Third-Order Tensor Variable for Strain Gradient Elasticity
- Approximation of planar Sobolev W2,1 homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms
- Torsional and SH surface waves in an isotropic and homogenous elastic half-space characterized by the Toupin-Mindlin gradient theory
- Commentary about the paper "Continuum Mech. Thermodyn. (2010) 22:163-176" by Podio Guidugli and Vianello and some related papers on higher gradient theories
- Symmetry classes for even-order tensors
- Size-dependent deflection of cross-ply composite laminated plate induced by piezoelectric actuators based on a re-modified couple stress theory
- Existence of minimizers for a finite-strain micromorphic elastic solid
- Well-posed homogenized strain-gradient models for linear elastodynamics and elastostatics in arbitrary periodic media
- Size Effects on Mechanical Properties of Micro/Nano Structures
- Numerical approximation of von Kármán viscoelastic plates
- Analytical continuum mechanics à la Hamilton-Piola: least action principle for second gradient continua and capillary fluids
- Staggered time discretization in finitely-strained heterogeneous visco-elastodynamics with damage or diffusion in the Eulerian frame
- Dynamic micromagnetism a la Ericksen-Leslie, allowing the Einstein-de Haas and Barnett effects
- On the size‐dependent vibrations of doubly curved porous shear deformable FGM microshells
- Recovering elastic subdomains with strain-gradient elastic interfaces from force measurements: the antiplane shear setting
- Perfect plasticity with damage and healing at small strains, its modelling, analysis, and computer implementation
- At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola
- Construction of micropolar continua from the asymptotic homogenization of beam lattices
- Shell energies derived from three-dimensional isotropic strain-gradient elasticity
- The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity
- Hyper-Stresses in k-Jet Field Theories
- Unified nonlocal rational continuum models developed from discrete atomistic equations
- A New Framework for Unidimensional Structures Based on Generalised Continua
- Reduced order models from computed states of physical systems using non-local calculus on finite weighted graphs
- Relativistic second gradient theory of continuous media
- Non-classical solutions of a continuum model for rock descriptions
- Geometric Analysis of Hyper-Stresses
- Relativistic electrodynamics with a universal length scale
- A variant of the linear isotropic indeterminate couple stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and complete traction boundary conditions
- Infeasibility of the nonlocal strain gradient theory for applied Physics
- Macroscopic physics of the silicon inversion layer
- Elastic Boundary Conditions in the Theory with Second Gradients in the Thermodynamic Potential
- Quasistatic adhesive contact delaminating in mixed mode and its\n numerical treatment
- Geometric theory of generalised continua using moving frames
- Second-gradient models for incompressible viscous fluids and associated cylindrical flows
- Size effect in micro-scale cantilever beam bending
- Investigation of static buckling and bending of nanoplates made of new functionally graded materials considering surface effects on an elastic foundation
- A study of gradient strengthening based on a finite-deformation gradient crystal-plasticity model
- On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush
- Anti-plane analysis of an infinite plane with multiple cracks based on strain gradient theory
- Interaction of cracks with dislocations in couple-stress elasticity. Part I: Opening mode
- Defects in unidimensional structures
- Hypertractions and hyperstresses convey the same mechanical information
- Equilibrium of elastic lattice shells
- Dual gauge field theory of quantum liquid crystals in two dimensions
- Free Vibration of Edge Cracked Functionally Graded Microscale Beams Based on the Modified Couple Stress Theory
- Geometrically nonlinear Cosserat elasticity in the plane: applications to chirality
- Time discretization in convected linearized thermo-visco-elastodynamics at large displacements
- A size-dependent isogeometric analysis of laminated composite plates based on the nonlocal strain gradient theory
- Dynamic stability of smart sandwich nanotubes based on modified couple stress theory using differential quadrature method (DQM)
- Computational homogenization of higher-order continua
- Static, stability and dynamic analyses of second strain gradient elastic Euler–Bernoulli beams
- A new view on boundary conditions in the Grioli–Koiter–Mindlin–Toupin indeterminate couple stress model
- Mechanochemical spinodal decomposition: a phenomenological theory of phase transformations in multi-component, crystalline solids
- Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformations
- On admissible external loadings within the first and second strain gradient elasticity
- Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures. [europepmc]
- The postulations á la D'Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results. [europepmc]
- Folding and faulting of an elastic continuum. [europepmc]
- Mixed finite-element formulations in piezoelectricity and flexoelectricity. [europepmc]
- Snap-through buckling of initially curved microbeam subject to an electrostatic force. [europepmc]
- Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review. [europepmc]
- Energy approach to brittle fracture in strain-gradient modelling. [europepmc]
- Scale Effects in Orthotropic Composite Assemblies as Micropolar Continua: A Comparison between Weak- and Strong-Form Finite Element Solutions. [europepmc]
- Reduced micromorphic model in orthogonal curvilinear coordinates and its application to a metamaterial hemisphere. [europepmc]
- A new Rayleigh-like wave in guided propagation of antiplane waves in couple stress materials. [europepmc]
- Non-Conventional Thermodynamics and Models of Gradient Elasticity. [europepmc]
- Phenomenological Thermodynamics of Irreversible Processes. [europepmc]
- New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method. [europepmc]
- Nonlinear viscoelasticity of strain rate type: an overview. [europepmc]
- Bio-Inspired Design of a Porous Resorbable Scaffold for Bone Reconstruction: A Preliminary Study. [europepmc]
- Dynamics of Space-Fractional Euler-Bernoulli and Timoshenko Beams. [europepmc]
- Thermodynamics and Analysis of Predicted Responses of a Phase Field Model for Ductile Fracture. [europepmc]
- Size-Dependent Buckling and Post-Buckling Analysis of the Functionally Graded Thin Plate Al-Cu Material Based on a Modified Couple Stress Theory. [europepmc]
- Nonlinear Finite Element Model for Bending Analysis of Functionally-Graded Porous Circular/Annular Micro-Plates under Thermomechanical Loads Using Quasi-3D Reddy Third-Order Plate Theory. [europepmc]
- 3D Size-Dependent Dynamic Instability Analysis of FG Cylindrical Microshells Subjected to Combinations of Periodic Axial Compression and External Pressure Using a Hermitian C 2 Finite Layer Method Based on the Consistent Couple Stress Theory. [europepmc]
- Band gaps of elastic waves in 1-D dielectric phononic crystal with the flexoelectric and strain gradient effects consideration. [europepmc]
- Penalty 4-Node Quadrilateral Element Formulation for Axisymmetric Couple Stress Problems. [europepmc]
- Surrogate model for statics of fractional thin bar element and its equivalence with mass-spring metamaterial. [europepmc]
- Thermo-elastodynamics of nonlinearly viscous solids. [europepmc]
- A Moment-of-Inertia-Dependent Surface Homogenization Method for Porous Polymer Beams. [europepmc]