Cavitation, invertibility, and convergence of regularized minimizers in nonlinear elasticity

DOI10.1007/s10659-008-9184-yzbMath1159.74322OpenAlexW2027792923MaRDI QIDQ1013586

Duvan Henao

Publication date: 20 April 2009

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

Full work available at URL: https://doi.org/10.1007/s10659-008-9184-y

zbMATH Keywords

convergenceinvertibilitycaviationmultiple cavitiesregular minimizerssingular minimizers

Mathematics Subject Classification ID

Related Items (18)

Global invertibility of Sobolev maps ⋮ Cavitation in elastomeric solids. I: A defect-growth theory ⋮ A meshing strategy for a quadratic iso-parametric FEM in cavitation computation in nonlinear elasticity ⋮ A numerical study of void coalescence and fracture in nonlinear elasticity ⋮ A micromechanical model of distributed damage due to void growth in general materials and under general deformation histories ⋮ A locking-free FEM for cavitation computation in nearly incompressible nonlinear elasticity ⋮ Relaxation of nonlinear elastic energies involving the deformed configuration and applications to nematic elastomers ⋮ Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity ⋮ Orientation-preservation conditions on an iso-parametric FEM in cavitation computation ⋮ A characterisation of the boundary displacements which induce cavitation in an elastic body ⋮ An extension of the identity Det = det ⋮ On the symmetry of energy-minimising deformations in nonlinear elasticity. I: Incompressible materials ⋮ The closure of planar diffeomorphisms in Sobolev spaces ⋮ A remark on a stability criterion for the radial cavitating map in nonlinear elasticity ⋮ H\"older estimates for the Neumann problem in a domain with holes and a relation formula between the Dirichlet and Neumann problems ⋮ AN EFFICIENT NUMERICAL METHOD FOR CAVITATION IN NONLINEAR ELASTICITY ⋮ Energy Estimates and Cavity Interaction for a Critical-Exponent Cavitation Model ⋮ Error Analysis of a Dual-parametric Bi-quadratic FEM in Cavitation Computation in Elasticity

Cites Work

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• Regularity properties of deformations with finite energy
• Null Lagrangians, weak continuity, and variational problems of arbitrary order
• Convexity conditions and existence theorems in nonlinear elasticity
• An existence theory for nonlinear elasticity that allows for cavitation
• Global invertibility of Sobolev functions and the interpenetration of matter
• Invertibility and a Topological Property of Sobolev Maps
• The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity
• On the existence of minimizers with prescribed singular points in nonlinear elasticity

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