On the characterization of geometrically necessary dislocations in finite plasticity

DOI10.1016/S0022-5096(00)00084-3zbMath0989.74013OpenAlexW1983264166MaRDI QIDQ5939367

Paolo Cermelli, Morton E. Gurtin

Publication date: 28 July 2002

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

Full work available at URL: https://doi.org/10.1016/s0022-5096(00)00084-3

zbMATH Keywords

finite straincrystal plasticityanti-plane sheardecompositionplane strainEuler anglesBurgers vectorgeometrically necessary dislocationsmicrostructural intermediate configurationmicrostructural planesreferential curlrigid-plastic materialspatial curl

Mathematics Subject Classification ID

Crystalline structure (74E15) Micromechanical theories (74A60) Plastic materials, materials of stress-rate and internal-variable type (74C99)

Related Items

Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations, Unnamed Item, A model for elastic-viscoplastic deformations of crystalline solids based on material symmetry: theory and plane-strain simulations, Modeling size effects in microwire torsion: a comparison between a Lagrange multiplier-based and a \(CurlF^p\) gradient crystal plasticity model, Gradient plasticity in isotropic solids, Dislocations and disclinations: continuously distributed defects in elasto-plastic crystalline materials, A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS, Inspection of free energy functions in gradient crystal plasticity, Variational Modeling of Slip: From Crystal Plasticity to Geological Strata, Variational Gradient Plasticity: Local-Global Updates, Regularization and Laminate Microstructures in Single Crystals, Energy Estimates, Relaxation, and Existence for Strain-Gradient Plasticity with Cross-Hardening, Microstructure in Plasticity, a Comparison between Theory and Experiment, The structure of uniform discrete defective crystals, Single crystal plasticity with bend-twist modes, Obituary: Morton Edward Gurtin (1934--2022), A study of gradient strengthening based on a finite-deformation gradient crystal-plasticity model, On the microscopic definitions of the dislocation density tensor, A gradient theory of small-deformation, single-crystal plasticity that accounts for GND-induced interactions between slip systems, Microstructural pattern formation in finite-deformation single-slip crystal plasticity under cyclic loading: relaxation vs. gradient plasticity, A novel continuum approach to gradient plasticity based on the complementing concepts of dislocation and disequilibrium densities, A minimum principle for microstructuring in rigid-viscoplastic crystalline solids, Finite element approximation of finite deformation dislocation mechanics, Particle-based approach to the Eulerian distortion field and its dynamics, On the existence of minimisers for strain‐gradient single‐crystal plasticity, Linearization for finite plasticity under dislocation-density tensor regularization, Line-tension limits for line singularities and application to the mixed-growth case, A duality‐based coupling of Cosserat crystal plasticity and phase field theories for modeling grain refinement, Aspects of the phenomenological theory of elastic-plastic deformation, Existence for dislocation-free finite plasticity, An extended crystal plasticity model for latent hardening in polycrystals, A gradient crystal plasticity theory for large deformations with a discontinuous accumulated plastic slip, A geometric field theory of dislocation mechanics, Estimating geometric dislocation densities in polycrystalline materials from orientation imaging microscopy, A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on the accumulation of geometrically necessary dislocations, Experimental lower bounds on geometrically necessary dislocation density, A note on material forces in finite inelasticity, An explicit finite element approach with patch projection technique for strain gradient plasticity formulations, Size effects in generalised continuum crystal plasticity for two-phase laminates, Deformation patterning driven by rate-dependent non-convex strain gradient plasticity, A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner’s incompatibility tensor, Multiscale modeling of dislocation patterns and simulation of nanoscale plasticity in body-centered cubic (BCC) single crystals, Predicting the Hall-Petch effect in fcc metals using non-local crystal plasticity, A distributional approach to the geometry of \(2D\) dislocations at the continuum scale, Instability origin of subgrain formation in plastically deformed materials, A Primer on Plasticity, A Counterpoint to Cermelli and Gurtin’s Criteria for Choosing the ‘Correct’ Geometric Dislocation Tensor in Finite Plasticity, Mechanism-based strain gradient crystal plasticity. I: Theory, Mechanism-based strain gradient crystal plasticity. II: Analysis, A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. I: small deformations, The Burgers vector and the flow of screw and edge dislocations in finite-deformation single-crystal plasticity, Distribution-based model for the grain boundaries in polycrystalline plasticity, Plastic flow in solids with interfaces, A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations, Globally stable quasistatic evolution for strain gradient plasticity coupled with damage, Some theoretical and computational aspects of single‐crystal strain‐gradient plasticity, Optimal energy scaling for a shear experiment in single-crystal plasticity with cross-hardening, A note on residual stress, lattice orientation and dislocation density in crystalline solids, Theory and numerics of geometrically non-linear gradient plasticity, A multiscale gradient theory for single crystalline elastoviscoplasticity, On spatial and material settings of hyperelastostatic crystal defects, On the characterization of geometrically necessary dislocations in finite plasticity, On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals, Dislocation patterns and work-hardening in crystalline plasticity, Characterizing geometrically necessary dislocations using an elastic-plastic decomposition of Laplace stretch, On finite strain micromorphic elastoplasticity, A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations, Curl bounds Grad on SO(3), Scaling relation for low energy states in a single-slip model in finite crystal plasticity, On the completeness of root functions of Sturm-Liouville problems for the Lamé system in weighted spaces, A finite deformation theory of higher-order gradient crystal plasticity, Intermittency in crystal plasticity informed by lattice symmetry, A review of higher order strain gradient theories of plasticity: origins, thermodynamics and connections with dislocation mechanics, On the Evolution of Plasticity and Incompatibility, A large-deformation strain-gradient theory for isotropic viscoplastic materials, Variational gradient plasticity at finite strains. I: Mixed potentials for the evolution and update problems of gradient-extended dissipative solids, Variational gradient plasticity at finite strains. III: Local-global updates and regularization techniques in multiplicative plasticity for single crystals, Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation, A finite element formulation to solve a non-local constitutive model with stresses and strains due to slip gradients, Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of \(\mathbf F=\mathbf F^e\mathbf F^p\), A continuum mechanical theory for turbulence: a generalized Navier-Stokes-\(\alpha\) equation with boundary conditions, Computational homogenization of mesoscale gradient viscoplasticity, Computational systems mechanobiology of wound healing, A nonlocal strain gradient plasticity theory for finite deformations, Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis, On configurational compatibility and multiscale energy momentum tensors, Gradient single-crystal plasticity with free energy dependent on dislocation densities, Theoretical development of continuum dislocation dynamics for finite-deformation crystal plasticity at the mesoscale, Relaxation of the single-slip condition in strain-gradient plasticity, On standard and vector finite element analysis of a strict anti-plane shear plasticity model with elastic curvature, Derivation of \(\mathbf{F} = \mathbf{F}^{\operatorname{e}} \mathbf{F}^{\operatorname{p}}\) as the continuum limit of crystalline slip, Kinematics of elasto-plasticity: validity and limits of applicability of \(\mathbf{F}=\mathbf{F}^{\mathrm{e}}\mathbf{F}^{\mathrm{p}}\) for general three-dimensional deformations, Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals, Dislocation walls in crystals under single slip, On the comparison of two approaches to compute material forces for inelastic materials. Application to single-slip crystal-plasticity, A variational multiscale method to incorporate strain gradients in a phenomenological plasticity model, Moving dislocations in finite plasticity: a topological approach, Micromorphic modelling of grain size effects in metal polycrystals, On generalized crystal-plasticity based on defect-densities in a second-order continuum, A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An analysis of texture and plastic spin for planar polycrystals
• Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
• On defect-preserving deformations in crystals
• A proposal for a continuum theory of defective crystals
• Multi-phase equilibrium of crystalline solids
• Lattice incompatibility and a gradient theory of crystal plasticity
• Materially uniform simple bodies with inhomogeneities
• Variational principles in the linear theory of viscoelasticity
• A dynamical theory of structures solids. I Basic developments
• Elastic scalar invariants in the theory of defective crystals
• Elastic-Plastic Deformation at Finite Strains
• On the characterization of geometrically necessary dislocations in finite plasticity