On the characterizations of matrix fields as linearized strain tensor fields

DOI10.1016/j.matpur.2006.04.004zbMath1115.35131OpenAlexW2005391789MaRDI QIDQ869109

Chérif Amrouche, Srinivasan Kesavan, Liliana Gratie, Philippe G. Ciarlet

Publication date: 26 February 2007

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2006.04.004

zbMATH Keywords

linearized elasticityDonati's theoremKorn's inequalityPoincaré's lemmaSaint Venant compatibility conditions

Mathematics Subject Classification ID

Related Items (45)

Stress gradient elasticity theory: existence and uniqueness of solution ⋮ A NEW DUALITY APPROACH TO ELASTICITY ⋮ A Cesàro-Volterra formula with little regularity ⋮ Nonlinear Donati compatibility conditions for the nonlinear Kirchhoff-von Kármán-Love plate theory ⋮ Characterization of the kernel of the operator CURL CURL ⋮ Green's formulas with little regularity on a surface -- application to Donati-like compatibility conditions on a surface ⋮ Donati compatibility conditions for membrane and flexural shells ⋮ New boundary conditions for the computation of the apparent stiffness of statistical volume elements ⋮ Civil engineering applications of the asymptotic expansion load decomposition beam model: an overview ⋮ Beltrami’s completeness for 𝕃p symmetric matrix fields ⋮ Higher‐order beam model with eigenstrains: theory and illustrations ⋮ On a vector version of a fundamental lemma of J. L. Lions ⋮ Trace Operator's range characterization for Sobolev spaces on Lipschitz domains of \(\mathbb{R}^2\) ⋮ Existence and asymptotic results for an intrinsic model of small-strain incompatible elasticity ⋮ Intrinsic formulations of the nonlinear Kirchhoff-Love-von Kármán plate theory ⋮ A new approach to the fundamental theorem of surface theory ⋮ Donati compatibility conditions on a surface -- application to shell theory ⋮ Nonlinear donati compatibility conditions and the intrinsic approach for nonlinearly elastic plates ⋮ Korn's inequality and Donati's theorem for the conformal Killing operator on pseudo-Euclidean space ⋮ On the curl operator and some characterizations of matrix fields in Lipschitz domains ⋮ On Korn's inequality ⋮ Direct computation of stresses in linear elasticity ⋮ LAGRANGE MULTIPLIERS IN INTRINSIC ELASTICITY ⋮ Vector and scalar potentials, Poincaré's theorem and Korn's inequality ⋮ A hybrid high-order discretization method for nonlinear poroelasticity ⋮ The kinematics of plate models: a geometrical deduction ⋮ Topological defects and metric anomalies as sources of incompatibility for piecewise smooth strain fields ⋮ On the equation \(A \nabla u + \left( \nabla u\right)^t A = G\) ⋮ Turbulent flows as generalized Kelvin-Voigt materials: modeling and analysis ⋮ An intrinsic approach to a nonlinear model in shell theory ⋮ Generalized compatibility equations for tensors of high ranks in multidimensional continuum mechanics ⋮ A new approach for approximating linear elasticity problems ⋮ Intrinsic formulation of the displacement-traction problem in linearized elasticity ⋮ Legendre-Fenchel duality in elasticity ⋮ A Lagrangian approach to intrinsic linearized elasticity ⋮ New formulations of linearized elasticity problems, based on extensions of Donati's theorem ⋮ On Saint Venant's compatibility conditions and Poincaré's lemma ⋮ Unnamed Item ⋮ New variational principles for solving extended Dirichlet-Neumann problems ⋮ CESÀRO–VOLTERRA PATH INTEGRAL FORMULA ON A SURFACE ⋮ A generalization of the classical Cesàro-Volterra path integral formula ⋮ DIRECT COMPUTATION OF STRESSES IN PLANAR LINEARIZED ELASTICITY ⋮ Compensated integrability. Applications to the Vlasov-Poisson equation and other models in mathematical physics ⋮ WEAK VECTOR AND SCALAR POTENTIALS: APPLICATIONS TO POINCARÉ'S THEOREM AND KORN'S INEQUALITY IN SOBOLEV SPACES WITH NEGATIVE EXPONENTS ⋮ On a lemma of Jacques-Louis Lions and its relation to other fundamental results

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Intrinsic equations for non-linear deformation and stability of thin elastic shells
• Beltrami's solutions of general equilibrium equations in continuum mechanics
• Duality characterization of strain tensor distributions in an arbitrary open set
• An analysis of a mixed finite element method for the Navier-Stokes equations
• On Poincaré's and J. L. Lions' lemmas
• New formulations of linearized elasticity problems, based on extensions of Donati's theorem
• On Saint Venant's compatibility conditions and Poincaré's lemma
• Hodge decomposition for symmetric matrix fields and the elasticity complex in Lipschitz domains
• Espaces d'interpolation et théorème de Soboleff
• Error-bounds for finite element method
• On the equations rot\ v\(=g\) and div\ u\(=f\) with zero boundary conditions
• Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
• ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY
• Functional spaces for norton‐hoff materials
• Equivalent Norms for Sobolev Spaces

This page was built for publication: On the characterizations of matrix fields as linearized strain tensor fields