On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations

DOI10.1007/BF00276434zbMath0187.48802OpenAlexW2049727165MaRDI QIDQ2537071

Publication date: 1967

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

Full work available at URL: https://doi.org/10.1007/bf00276434

zbMATH Keywords

mechanics of solids

Related Items (93)

Toward a Complete Second-Order Evolution Law ⋮ Limits of elastic models of converging Riemannian manifolds ⋮ Finsler differential geometry in continuum mechanics: Fundamental concepts, history, and renewed application to ferromagnetic solids ⋮ On tangent geometry and generalised continuum with defects ⋮ Reductions due to material constraint and material symmetry on equilibrium problems of laminated and fibrillar bodies ⋮ Gradient plasticity in isotropic solids ⋮ Characteristic foliations of material evolution: from remodeling to aging ⋮ On the integrability of second-order \(G\)-structures with applications to continuous theorems of dislocations ⋮ On the Geometry and Kinematics of Smoothly Distributed and Singular Defects ⋮ A proposal for defining continuous distribution of dislocations for objective structures ⋮ Defects in nonlinear elastic crystals: differential geometry, finite kinematics, and second‐order analytical solutions ⋮ From Saturated Elasticity to Finite Evolution, Plasticity and Growth ⋮ Homogeneity conditions for generalized Cosserat media ⋮ A Riemannian approach to the membrane limit in non-Euclidean elasticity ⋮ Non-metric connection and metric anomalies in materially uniform elastic solids ⋮ Lie groupoids and algebroids applied to the study of uniformity and homogeneity of Cosserat media ⋮ Elasto-plastic evolution of single crystals driven by dislocation flow ⋮ The kinematics of continua and the concept of connection on classical space-time ⋮ Nonlinear continuum theory of dislocations ⋮ Mechanics of materially uniform thin films ⋮ Incompatible deformations in relativistic elasticity ⋮ Scientific life and works of Walter Noll ⋮ Material geometry ⋮ A note on material symmetry ⋮ Mechanics of dislocations and metadislocations in quasicrystals and their approximants: power invariance and balance ⋮ FUNCTIONALLY GRADED MEDIA ⋮ A mathematical analysis of the simplest direct models for rods and shells ⋮ Non-metricity in the continuum limit of randomly-distributed point defects ⋮ G-structures and material homogeneity ⋮ Material distributions ⋮ Stress theory for classical fields ⋮ On anholonomic deformation, geometry, and differentiation ⋮ The role of the symmetry group in the non-uniqueness of a uniform reference. Case study: An isotropic solid body ⋮ Dualistic theory of non-Riemannian material manifolds ⋮ The Incompatibility Operator: from Riemann’s Intrinsic View of Geometry to a New Model of Elasto-Plasticity ⋮ A Primer on Plasticity ⋮ Material forces in finite elasto-plasticity with continuously distributed dislocations ⋮ Regular and Singular Dislocations ⋮ Limits of Distributed Dislocations in Geometric and Constitutive Paradigms ⋮ On the Homogeneity of Non-uniform Material Bodies ⋮ Material groupoids and algebroids ⋮ Finsler geometry of nonlinear elastic solids with internal structure ⋮ Modeling continuous distributions of dislocations in multi-walled nanotube composites ⋮ Equilibrium equations for transversely accreted shells ⋮ Variational convergence of discrete geometrically-incompatible elastic models ⋮ Some equilibrium problems for compressible, anisotropic, laminated nonlinearly elastic bodies ⋮ A Riemannian approach to reduced plate, shell, and rod theories ⋮ Canonical forms of constitutive equations of mixtures ⋮ Incompatible elasticity and the immersion of non-flat Riemannian manifolds in Euclidean space ⋮ Growth and decay of one-dimensional acceleration waves in non-linear materials with anelastic response ⋮ Geometrical theory of dislocations in bodies with microstructure ⋮ Material uniformity and inhomogeneity in anelastic bodies ⋮ On the flow rules of anelastic bodies ⋮ Thermodynamic influences on acceleration waves in inhomogeneous isotropic elastic bodies with internal state variables ⋮ Global equations of motion for anelastic bodies and bodies with elastic range ⋮ Inhomogeneous materially uniform higher order gross bodies ⋮ Acceleration waves in anelastic material bodies ⋮ Riemann-Cartan geometry of nonlinear dislocation mechanics ⋮ Line and point defects in nonlinear anisotropic solids ⋮ Generalized Continuum Mechanics: What Do We Mean by That? ⋮ Universal solutions for isotropic elastic membranes ⋮ On the field equations of motion for a smooth, materially uniform, elastic shell ⋮ The mathematical theory of growing bodies. Finite deformations ⋮ On the homogenization of a new class of locally periodic microstructures in linear elasticity with residual stress ⋮ Some stability theorems for an abstract equation in Hilbert space with applications to linear elastodynamics ⋮ Models of Continuum with Microcrack Distribution ⋮ The emergence of torsion in the continuum limit of distributed edge-dislocations ⋮ Quasi-static controllable processes of incompressible isotropic homogeneous anelastic material bodies ⋮ Uniform materials and the multiplicative decomposition of the deformation gradient in finite elasto-plasticity ⋮ An extension of the concept of material symmetry ⋮ Universal solutions for incompressible laminated bodies ⋮ Nonlinear evolutionary problem for a laminated inhomogeneous spherical shell ⋮ Materially uniform simple bodies with inhomogeneities ⋮ On the geometrical material structure of anelasticity ⋮ The geometry of uniformity in second-grade elasticity ⋮ A new mathematical theory of simple materials ⋮ Acceleration waves in inhomogeneous isotropic elastic bodies ⋮ A question of constant strain ⋮ Material uniformity and homogeneity in shells ⋮ A geometric perspective on irreversible thermodynamics with internal variables ⋮ Geometrical theory of uniform Cosserat media ⋮ A kinematic model for continuous distributions of dislocations ⋮ Acceleration waves in isotropic elastic membranes ⋮ Homogeneity conditions for elastic membranes ⋮ Unnamed Item ⋮ Finite incompatible deformations in elastic solids: relativistic approach ⋮ Locally homogeneous configurations of uniform elastic bodies ⋮ Some equilibrium problems for fibrillar bodies ⋮ Geometric characterization of hyperelastic uniformity ⋮ Metric description of singular defects in isotropic materials ⋮ Autoparallel curves and Riemannian geodesics for materially uniform but inhomogeneous bodies ⋮ Geometric aspects of singular dislocations ⋮ A finite element formulation for stressed bodies with continuous distribution of edge dislocations

Cites Work

This page was built for publication: On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations