Lusin's condition and the distributional determinant for deformations with finite energy

DOI10.1515/acv.2011.016zbMath1252.49016OpenAlexW2013159675MaRDI QIDQ3167326

Duvan Henao, Carlos Mora-Corral

Publication date: 2 November 2012

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv.2011.016

zbMATH Keywords

cavitationsurface energyLusin's conditionelastic deformationsdistributional determinantcreated surfacenon-interpenetration of matter

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Fracture and damage (74R99) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items

Note on Lusin \((N)\) condition and the distributional determinant, Global invertibility of Sobolev maps, Strict limits of planar BV homeomorphisms, Higher order Sobolev homeomorphisms and mappings and the Lusin \((N)\) condition, On the existence of minimizers for the neo-Hookean energy in the axisymmetric setting, A numerical study of void coalescence and fracture in nonlinear elasticity, Weak limit of homeomorphisms in \(W^{1, n-1}\) and (INV) condition, Classification of strict limits of planar \(BV\) homeomorphisms, Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers, Relaxation of nonlinear elastic energies involving the deformed configuration and applications to nematic elastomers, Harmonic dipoles and the relaxation of the neo-Hookean energy in 3D elasticity, On the lack of compactness in the axisymmetric neo-Hookean model, Existence results in large-strain magnetoelasticity, Hausdorff measure of critical set for Luzin \(N\) condition, Optimal Control of Soft Materials Using a Hausdorff Distance Functional, Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity, A structure property of ``vertical integral currents, with an application to the distributional determinant, Example of a smooth homeomorphism violating the Luzin \(N^{-1}\) property, Quasiconvexity at the boundary and the nucleation of austenite, On the Convergence of a Regularization Scheme for Approximating Cavitation Solutions with Prescribed Cavity Volume, A lower bound for the void coalescence load in nonlinearly elastic solids, Orlicz-Sobolev nematic elastomers, Weak regularity of the inverse under minimal assumptions, Energy Estimates and Cavity Interaction for a Critical-Exponent Cavitation Model, Invertibility of Orlicz-Sobolev maps, \(\Gamma\)-convergence approximation of fracture and cavitation in nonlinear elasticity

Cites Work

• Property N of homeomorphisms of the class \(W_ p\)
• Sharpness of the assumptions for the regularity of a homeomorphism
• An extension of the identity Det = det
• Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
• Regularity properties of deformations with finite energy
• Null Lagrangians, weak continuity, and variational problems of arbitrary order
• On the integrability of the Jacobian under minimal hypotheses
• Convexity conditions and existence theorems in nonlinear elasticity
• On cavitation, configurational forces and implications for fracture in a nonlinearly elastic material
• Fractures and vector valued maps
• An existence theory for nonlinear elasticity that allows for cavitation
• Erratum to: Fractures and vector valued maps
• Homeomorphisms of bounded variation
• Regularity of the inverse of a planar Sobolev homeomorphism
• Regularity of the inverse of spatial mappings with finite distortion
• Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
• Some fine properties of currents and applications to distributional Jacobians
• The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity
• Regularity of the inverse of a Sobolev homeomorphism in space
• Parametric surfaces
• On the optimal location of singularities arising in variational problems of nonlinear elasticity
• On the existence of minimizers with prescribed singular points in nonlinear elasticity