A gradient approach to localization of deformation. I. Hyperelastic materials
From MaRDI portal
Publication:1077215
DOI10.1007/BF00040814zbMath0594.73044MaRDI QIDQ1077215
Elias C. Aifantis, Nicholas Triantafyllidis
Publication date: 1986
Published in: Journal of Elasticity (Search for Journal in Brave)
strain energy densityfinite strainshyperelastic materialsequilibrium equationslocalization of deformationBlatz-Ko materialsremain always ellipticsecond deformation gradient-dependent termstrain-induced localized deformation
Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).
Related Items (only showing first 100 items - show all)
Explicit and implicit gradient series in damage mechanics ⋮ Geophysical models of heat and fluid flow in damageable poro-elastic continua ⋮ On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models ⋮ Axisymmetric necking versus Treloar–Kearsley instability in a hyperelastic sheet under equibiaxial stretching ⋮ A probabilistic nonlocal model for crack initiation and propagation in heterogeneous brittle materials ⋮ On constructing the analytical solutions for localizations in a slender cylinder composed of an incompressible hyperelastic material ⋮ A discontinuous Galerkin method for strain gradient-dependent damage: study of interpolations and convergence ⋮ Effects of structural and material length scales on stress-induced martensite macro-domain patterns in tube configurations ⋮ A variational approach for a nonlinear 1-dimensional second gradient continuum damage model ⋮ Finite gradient elasticity and plasticity: a constitutive mechanical framework ⋮ Robust and Efficient Finite Element Discretizations for Higher-Order Gradient Formulations ⋮ GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS ⋮ Nonlocal continuum effects on bifurcation in the plane strain tension-compression test ⋮ Dynamic strain localization in elasto-(visco-)plastic solids. I: General formulation and one-dimensional examples ⋮ A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model ⋮ On the capability of generalized continuum theories to capture dispersion characteristics at the atomic scale ⋮ Single crystal plasticity with bend-twist modes ⋮ Homogenization of periodic graph-based elastic structures ⋮ Thermodynamic coupling between gradient elasticity and a Cahn-Hilliard type of diffusion: size-dependent spinodal gaps ⋮ Automated band identification procedure for dynamic strain localization ⋮ Adaptive meshing for dynamic strain localization ⋮ Local bifurcation analysis of a second-gradient model for deformations of a rectangular slab ⋮ Reduction of mesh sensitivity in continuum damage mechanics ⋮ Strain-gradient elastic-plastic material models and assessment of the higher-order boundary conditions ⋮ Unconstrained and Cauchy-Born-constrained atomistic systems: deformational and configurational mechanics ⋮ Three-dimensional isogeometric solutions to general boundary value problems of Toupin's gradient elasticity theory at finite strains ⋮ Formulation of Toupin-Mindlin strain gradient theory in prolate and oblate spheroidal coordinates ⋮ A large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identification ⋮ Influence of soil non-homogeneity on shear band evolution investigated by the numerical manifold method combined with the assumed enhanced strain method ⋮ Stress channelling in extreme couple-stress materials. I: Strong ellipticity, wave propagation, ellipticity, and discontinuity relations ⋮ A nonlocal rate-type viscoplastic approach to patterning of deformation ⋮ Theory of gradient-elastic membranes and its application in the wrinkling analysis of stretched thin sheets ⋮ How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert ⋮ Pattern formation in plasticity ⋮ Buckling analysis of orthotropic nanoplates based on nonlocal strain gradient theory using the higher-order finite strip method (H-FSM) ⋮ A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis ⋮ Nonlocal strain gradient model for thermal buckling analysis of functionally graded nanobeams ⋮ Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture ⋮ Three‐field mixed finite element formulations for gradient elasticity at finite strains ⋮ Integrated finite element neural network (I-FENN) for non-local continuum damage mechanics ⋮ A large strain anisotropic ductile damage model -- effective driving forces and gradient-enhancement of damage vs. plasticity ⋮ Mixed meshless local Petrov-Galerkin (MLPG) collocation methods for gradient elasticity theories of Helmholtz type ⋮ Strong tangential discontinuity modeling of shear bands using the extended finite element method ⋮ Homogenization of a nonlinear elastic fibre-reinforced composite: a second gradient nonlinear elastic material ⋮ A strain gradient generalized continuum approach for modelling elastic scale effects ⋮ A boundary element technique for incremental, nonlinear elasticity. II: Bifurcation and shear bands. ⋮ Archetype-blending continuum theory ⋮ Gradient damage models: toward full-scale computations ⋮ A diffuse interface model for the analysis of propagating bulges in cylindrical balloons ⋮ A Variational Approach to Single Crystals with Dislocations ⋮ Quasistatic viscoelasticity with self-contact at large strains ⋮ Finite element implementation of gradient plasticity models. I: Gradient-dependent yield functions. II: Gradient-dependent evolution equations ⋮ Continuum Damage Mechanics—Modelling and Simulation ⋮ A gradient flow theory of plasticity for granular materials ⋮ Finite thermoelastoplasticity and creep under small elastic strains ⋮ A note on ill-posedness for rate-dependent problems and its relation to the rate-independent case ⋮ On the gradient-dependent theory of plasticity and shear banding ⋮ The influence of microstructure-induced gradients on the localization of deformation in viscoplastic materials ⋮ Necking of a hyperelastic solid cylinder under axial stretching: evaluation of the infinite-length approximation ⋮ Elasticity with gradient-disarrangements: a multiscale perspective for strain-gradient theories of elasticity and of plasticity ⋮ On the role of gradients in the localization of deformation and fracture ⋮ Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field ⋮ Thermoviscoplastic shear instability and higher order strain gradients ⋮ Instability and ill-posedness in some friction problems ⋮ Strain localization in frictional materials exhibiting displacement jumps ⋮ A renormalization approach to model interaction in microstructured solids: application to porous elastomer ⋮ Damage growth modeling using the thick level set (TLS) approach: efficient discretization for quasi-static loadings ⋮ On scale invariance in anisotropic plasticity, gradient plasticity and gradient elasticity ⋮ A generalisation of \(J_ 2\)-flow theory for polar continua ⋮ One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. I: Generic formulation ⋮ Numerical determination of representative volumes for granular materials ⋮ Convergence of a gradient damage model toward a cohesive zone model ⋮ \(h\)-adaptive mesh refinement for shear band localization in elasto-plasticity Cosserat continuum ⋮ Multiscale aggregating discontinuities: A method for circumventing loss of material stability ⋮ Gradient constitutive relations: numerical aspects and application to gradient damage ⋮ Micro-mechanical modelling of granular material. I: Derivation of a second-gradient micro-polar constitutive theory. II: Plane wave propagation in infinite media ⋮ A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis ⋮ Thermodynamics of Elastoplastic Porous Rocks at Large Strains Towards Earthquake Modeling ⋮ On the Uniqueness of the Lagrangian of Gradient Elastic Continua ⋮ Gradient and size effects on spinodal and miscibility gaps ⋮ Cauchy tetrahedron argument applied to higher contact interactions ⋮ A crystal plasticity model that incorporates stresses and strains due to slip gradients ⋮ Modeling the onset of shear boundary layers in fibrous composite reinforcements by second-gradient theory ⋮ Spatial patterns and size effects in shear zones: A hyperelastic model with higher-order gradients ⋮ Magnetorheological Elastomer’s Material Modeling and Parameter Determination by Using the Energy-based Method ⋮ Computational shape optimisation for a gradient-enhanced continuum damage model ⋮ Concurrent development of local and non-local damage with the thick level set approach: implementation aspects and application to quasi-brittle failure ⋮ Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua ⋮ Localization in anisotropic elastoplastic micropolar media: application to fiber reinforced composites ⋮ Macrohomogeneity condition for strain gradient homogenization of periodic heterogeneous media with interfacial strong discontinuities ⋮ Thermoviscoelasticity in Kelvin-Voigt rheology at large strains ⋮ A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation ⋮ Strain-based transient-gradient damage model for failure analyses ⋮ The influence of scale size on the stability of periodic solids and the role of associated higher-order gradient continuum models. ⋮ Bearing capacity of shallow foundations in transversely isotropic granular media ⋮ Free-discontinuity problems generated by singular perturbation ⋮ A simple approach to solve boundary-value problems in gradient elasticity ⋮ Derivation of higher order gradient continuum theories in 2,3-D nonlinear elasticity from periodic lattice models ⋮ A level set based model for damage growth: The thick level set approach ⋮ Internal inertia gradient effect on two mode magneto‐elastic wave propagation
Cites Work
- Unnamed Item
- Unnamed Item
- On the thermomechanics of interstitial working
- Acceleration waves in solids
- Elastic materials with couple-stresses
- On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics
- Flow localization in the plane strain tensile test
- On the ellipticity of the equations of nonlinear elastostatics for a special material
- Bifurcation phenomena in the plane tension test
- On the failure of ellipticity of the equations for finite elastostatic plane strain
- Theories of elasticity with couple-stress
- Multipolar continuum mechanics
- Micro-structure in linear elasticity
This page was built for publication: A gradient approach to localization of deformation. I. Hyperelastic materials