Quasistatic crack growth in finite elasticity with Lipschitz data

DOI10.1007/s10231-010-0145-2zbMath1215.35156OpenAlexW2027277446MaRDI QIDQ628615

Giuliano Lazzaroni

Publication date: 14 March 2011

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-010-0145-2

zbMATH Keywords

energy minimizationbrittle fracturefinite elasticityvariational modelcrack propagationquasistatic evolution

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Nonlinear elasticity (74B20) Brittle fracture (74R10) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Free boundary problems for PDEs (35R35) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (9)

Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue ⋮ Cohesive fracture in 1D: quasi-static evolution and derivation from static phase-field models ⋮ Phase‐Field Fracture at Finite Strains Based on Modified Invariants: A Note on its Analysis and Simulations ⋮ Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture ⋮ Analysis and simulations for a phase‐field fracture model at finite strains based on modified invariants ⋮ On the quasistatic limit of dynamic evolutions for a peeling test in dimension one ⋮ A density result in \(GSBD^p\) with applications to the approximation of brittle fracture energies ⋮ Lower semicontinuity for nonautonomous surface integrals ⋮ Existence and uniqueness of dynamic evolutions for a peeling test in dimension one

Cites Work

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• Crack growth with non-interpenetration: a simplified proof for the pure Neumann problem
• Quasistatic crack growth in finite elasticity with non-interpenetration
• The variational approach to fracture
• Injectivity and self-contact in nonlinear elasticity
• A density result in two-dimensional linearized elasticity, and applications
• A model for the quasi-static growth of brittle fractures: Existence and approximation results
• Quasistatic crack growth in nonlinear elasticity
• Revisiting brittle fracture as an energy minimization problem
• Some Open Problems in Elasticity
• Non-interpenetration of matter for SBV deformations of hyperelastic brittle materials
• LOWER SEMICONTINUITY RESULTS FOR FREE DISCONTINUITY ENERGIES
• Differentiability of Lipschitzian mappings between Banach spaces
• Existence and convergence for quasi-static evolution in brittle fracture
• VI. The phenomena of rupture and flow in solids
• Existence results for a class of rate-independent material models with nonconvex elastic energies
• A lower semi-continuity result for polyconvex functionals in SBV

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