Fracture surfaces and the regularity of inverses for BV deformations
From MaRDI portal
Publication:715310
DOI10.1007/s00205-010-0395-6zbMath1262.74007OpenAlexW2041768928MaRDI QIDQ715310
Carlos Mora-Corral, Duvan Henao
Publication date: 5 November 2012
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/20.500.11824/584
Nonlinear elasticity (74B20) Regularity of solutions in optimal control (49N60) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Kinematics of deformation (74A05)
Related Items (27)
A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation ⋮ Global invertibility of Sobolev maps ⋮ Strict limits of planar BV homeomorphisms ⋮ 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 ⋮ 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 ⋮ Optimal control and design of magnetic field-responsive smart polymer composites ⋮ Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions ⋮ Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity ⋮ Energy minimizing \(N\)-covering maps in two dimensions ⋮ Optimal Control of Soft Materials Using a Hausdorff Distance Functional ⋮ A Calibration Method for Estimating Critical Cavitation Loads from Below in Three Dimensional Nonlinear Elasticity ⋮ Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity ⋮ Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity ⋮ Quasiconvexity at the boundary and the nucleation of austenite ⋮ 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 ⋮ Frank energy for nematic elastomers: a nonlinear model ⋮ \(\Gamma\)-convergence approximation of fracture and cavitation in nonlinear elasticity
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Sharpness of the assumptions for the regularity of a homeomorphism
- The variational approach to fracture
- Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
- Regularity properties of deformations with finite energy
- A new proof of the SBV compactness theorem
- An existence theory for nonlinear elasticity that allows for cavitation
- Revisiting brittle fracture as an energy minimization problem
- Homeomorphisms of bounded variation
- Regularity of the inverse of a planar Sobolev homeomorphism
- Regularity of the inverse of spatial mappings with finite distortion
- On the weak differentiability of $u\circ f^{-1}$
- Some Open Problems in Elasticity
- Homeomorphisms in the Sobolev space W 1,n–1
- Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
- Weakly Differentiable Functions
- A General Chain Rule for Distributional Derivatives
- Regularity of the inverse of a Sobolev homeomorphism in space
This page was built for publication: Fracture surfaces and the regularity of inverses for BV deformations