Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales

DOI10.1007/s00205-006-0015-7zbMath1104.74006OpenAlexW2023495095MaRDI QIDQ859745

Publication date: 18 January 2007

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-006-0015-7

zbMATH Keywords

Navier-Stokes equations plane Poiseuille flow principle of virtual power

Mathematics Subject Classification ID

Nonsimple materials (74A30) Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena (76A99)

Related Items

Generalized Swift-Hohenberg and phase-field-crystal equations based on a second-gradient phase-field theory, Visco-elastodynamics at large strains Eulerian, Geophysical models of heat and fluid flow in damageable poro-elastic continua, On a stress-power-based characterization of second-gradient elastic fluids, Quasistatic hypoplasticity at large strains Eulerian, Free and forced vibration nonlinear analysis of a microbeam using finite strain and velocity gradients theory, A second-gradient theory of dilute suspensions of flexible rods in a Newtonian fluid, Obituary: Morton Edward Gurtin (1934--2022), On the thermodynamics of the Swift-Hohenberg theory, Analysis of a gradient-elastic beam on Winkler foundation and applications to nano-structure modelling, A hierarchy of simplified constitutive models within isotropic strain gradient elasticity, The Leray-\(\alpha\beta\)-deconvolution model: energy analysis and numerical algorithms, The multiple nature of concentrated interactions in second-gradient dissipative liquids, Nonlinearly coupled thermo-visco-elasticity, Three-dimensional nonsimple viscous liquids dragged by one-dimensional immersed bodies, Comment to ``Hypertractions and hyperstresses convey the same mechanical information`` by Prof. Podio-Guidugli and Prof. Vianello and some related papers on higher gradient theories, On the ``principle of virtual power for arbitrary parts of a body, Approximation in multiscale modelling of microstructure evolution in shape-memory alloys, Thermodynamics of nonlocal materials: extra fluxes and internal powers, A method to transform a nonlocal model into a gradient one within elasticity and plasticity, A unifying variational framework for stress gradient and strain gradient elasticity theories, A numerical method for a second-gradient theory of incompressible fluid flow, How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert, Second-gradient viscoelastic fluids: dissipation principle and free energies, Pattern competition for the sequential bifurcations approach (SBA) to turbulence in the co-rotating Taylor-Couette system: quinary states, Exegesis of Sect. II and III.A from “Fundamentals of the Mechanics of Continua” by E. Hellinger, Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Continua” by E. Hellinger, Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger, Surface phenomena of gradient materials, Weak Lower Semicontinuity of Integral Functionals and Applications, Interaction of finitely-strained viscoelastic multipolar solids and fluids by an Eulerian approach, Variational methods for fluid-structure interaction and porous media, The «materialization» of forces: Why confounding mathematical concept and physical entity makes the design of metamaterials arduous, Thermodynamics of viscoelastic solids, its Eulerian formulation, and existence of weak solutions, The crust shell and the edge beams of third-gradient continua in current and referential description, Viscoelastodynamics of Swelling Porous Solids at Large Strains by an Eulerian Approach, The Stefan problem in a thermomechanical context with fracture and fluid flow, The peridynamic stress tensors and the non‐local to local passage, Variant of strain gradient elasticity with simplified formulation of traction boundary value problems, Derivation of microstructured continua from lattice systems via principle of virtual works: the case of masonry-like materials as micropolar, second gradient and classical continua, A deconvolution enhancement of the Navier-Stokes-\({\alpha}{\beta}\) model, A consistent and stabilized continuous/discontinuous Galerkin method for fourth-order incompressible flow problems, Quasistatic viscoelasticity with self-contact at large strains, Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization, A numerical study of the Navier-Stokes-\(\alpha \beta \) model, Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids, Going to new lengths: studying the Navier-Stokes-\(\alpha\beta\) equations using the strained spiral vortex model, Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number, Second-grade elasticity revisited, Finite thermoelastoplasticity and creep under small elastic strains, Existence, uniqueness, and regularity for the second-gradient Navier-Stokes equations in exterior domains, Gradient extension of classical material models: from nuclear \& condensed matter scales to Earth \& cosmological scales, Travelling waves of density for a fourth-gradient model of fluids, Cahn-Hilliard equation with capillarity in actual deforming configurations, Nonsimple isotropic incompressible linear fluids surrounding one-dimensional structures, Covariant balance laws in continua with microstructure, Phase-field gradient theory, Gradient nanoscale polycrystalline elasticity: intergrain interactions and triple-junction conditions, Hypertractions and hyperstresses convey the same mechanical information, A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis, Perfect Plasticity with Damage and Healing at Small Strains, Its Modeling, Analysis, and Computer Implementation, Two-scale nonlocal shear rate formulation of Bingham plastic fluid, Thermodynamics of Elastoplastic Porous Rocks at Large Strains Towards Earthquake Modeling, On Natural Boundary Conditions in Linear 2nd-Grade Elasticity, Anisotropy in strain gradient elasticity: simplified models with different forms of internal length and moduli tensors, Cauchy tetrahedron argument applied to higher contact interactions, Isotropic linear constitutive relations for nonsimple fluids, A continuum mechanical theory for turbulence: a generalized Navier-Stokes-\(\alpha\) equation with boundary conditions, From quasi-incompressible to semi-compressible fluids, Thermoviscoelasticity in Kelvin-Voigt rheology at large strains, Observations concerning virtual power, A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains, A continuum framework for phase field with bulk-surface dynamics, Variational approach to dynamic analysis of third-order shear deformable plates within gradient elasticity

Cites Work