A variational model for plastic slip and its regularization via \(\Gamma \)-convergence

DOI10.1007/s10659-012-9390-5zbMath1326.74112OpenAlexW1997542906MaRDI QIDQ1937971

Yanyan Li

Publication date: 1 February 2013

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

Full work available at URL: https://doi.org/10.1007/s10659-012-9390-5

zbMATH Keywords

plasticityvariational modelcohesive fracture\(\Gamma \)-convergenceplastic slipfree-discontinuity problem

Mathematics Subject Classification ID

Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Anelastic fracture and damage (74R20) Energy minimization in equilibrium problems in solid mechanics (74G65) Methods involving semicontinuity and convergence; relaxation (49J45) Brittle damage (74R05)

Related Items (12)

Phase field approximation of cohesive fracture models ⋮ Micromechanics-based elasto-plastic-damage energy formulation for strain gradient solids with granular microstructure ⋮ On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure ⋮ Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy ⋮ Plastic flow as an energy minimization problem. Numerical experiments ⋮ Gradient damage models coupled with plasticity and nucleation of cohesive cracks ⋮ A Modica-Mortola approximation for the Steiner problem ⋮ The Γ-limit for singularly perturbed functionals of Perona–Malik type in arbitrary dimension ⋮ Phase field modeling of frictional slip with slip weakening/strengthening under non-isothermal conditions ⋮ A variational model of elasto-plastic behavior of materials ⋮ Damage-driven fracture with low-order potentials: asymptotic behavior, existence and applications ⋮ Approximation of Length Minimization Problems Among Compact Connected Sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularized variational theories of fracture: a unified approach
• Laws of crack motion and phase-field models of fracture
• Elastic bars with cohesive energy
• Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments
• The variational approach to fracture mechanics. A practical application to the French Panthéon in Paris
• Strain localization in ductile single crystals
• Free-discontinuity problems via functionals involving the \(L^1\)-norm of the gradient and their approximations
• Structured deformations of continua
• An introduction to \(\Gamma\)-convergence
• A density result in two-dimensional linearized elasticity, and applications
• Numerical experiments in revisited brittle fracture
• A mechanical model for the elastic-plastic behavior of metallic bars
• A model for the quasi-static growth of brittle fractures: Existence and approximation results
• Interaction of fractures in tensile bars with non-local spatial dependence
• An approximation result for special functions with bounded deformation
• Revisiting brittle fracture as an energy minimization problem
• A relaxation approach to Hencky's plasticity
• Initiation of cracks with cohesive force models: a variational approach
• Numerical implementation of the variational formulation for quasi-static brittle fracture
• Validation of the energy-balance approach to curve-shaped shear-band propagation in soil
• Approximation of functional depending on jumps by elliptic functional via t-convergence
• The unrestrainable growth of a shear band in a prestressed material
• A density result in SBV with respect to non-isotropic energies
• ON THE VARIATIONAL APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS IN THE VECTORIAL CASE
• The growth of slip surfaces in the progressive failure of over-consolidated clay
• Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case

This page was built for publication: A variational model for plastic slip and its regularization via \(\Gamma \)-convergence