Continuum dynamics on manifolds: application to elasticity of residually-stressed bodies

DOI10.1007/s10659-016-9617-yzbMath1373.74008arXiv1612.04180OpenAlexW2567515621MaRDI QIDQ1679580

Elihu Olami, Reuven Segev, Raz Kupferman

Publication date: 9 November 2017

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.04180

zbMATH Keywords

Riemannian metricdifferentiable manifoldskinetic energyresidual stresscontinuum dynamics

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Applications of differential geometry to physics (53Z05) Stress (74A10) Dynamical problems in solid mechanics (74H99)

Related Items (8)

An intrinsic geometric formulation of hyper-elasticity, pressure potential and non-holonomic constraints ⋮ Geometric hydrodynamics in open problems ⋮ Hyper-elastic Ricci flow ⋮ Notes on Global Stress and Hyper-Stress Theories ⋮ Contorsion of material connection in growing solids ⋮ Viscoelastic flows of Maxwell fluids with conservation laws ⋮ Non-Euclidean model for description of residual stresses in planar deformations ⋮ Reshetnyak rigidity for Riemannian manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear elasticity in a deforming ambient space
• Elastic theory of unconstrained non-Euclidean plates
• A frame-independent description of the principles of classical mechanics
• Non-metricity in the continuum limit of randomly-distributed point defects
• Covariantization of nonlinear elasticity
• A Riemannian approach to reduced plate, shell, and rod theories
• The emergence of torsion in the continuum limit of distributed edge-dislocations
• Geometry of manifolds of maps
• On Cauchy's equations of motion
• Tomography of small residual stresses
• A Riemannian approach to the membrane limit in non-Euclidean elasticity
• The shape of a long leaf
• Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics
• Scaling laws for non-Euclidean plates and theW^2,2isometric immersions of Riemannian metrics
• On spatial and material covariant balance laws in elasticity
• Forces and the existence of stresses in invariant continuum mechanics
• Differentiable manifolds and the principle of virtual work in continuum mechanics
• Global solutions of the equations of elastodynamics of incompressible neo-Hookean materials.
• Tension-field theory
• Metric-independent analysis of the stress-energy tensor
• Notes on Metric Independent Analysis of Classical Fields
• Dispersion of Rayleigh waves in vertically-inhomogeneous prestressed elastic media
• Quasijets in anisotropic media, Finsler geometry, and Fermi coordinates
• Riemannian surfaces with torsion as homogenization limits of locally Euclidean surfaces with dislocation-type singularities
• Differentiable Structures on Function Spaces

This page was built for publication: Continuum dynamics on manifolds: application to elasticity of residually-stressed bodies