Convergence of critical points for a phase-field approximation of 1D cohesive fracture energies
DOI10.1007/s00526-024-02786-6zbMATH Open1546.35013MaRDI QIDQ6588093
Marco Bonacini, Flaviana Iurlano
Publication date: 15 August 2024
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
phase-field energies of Ambrosio-Tortorelli typevariational approximation via \(\Gamma\)-convergence
Integro-partial differential equations (45K05) Nonlinear boundary value problems for ordinary differential equations (34B15) Fracture and damage (74R99) Methods involving semicontinuity and convergence; relaxation (49J45) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Singular perturbations for ordinary differential equations (34E15)
Cites Work
- Unnamed Item
- Unnamed Item
- Phase field approximation of cohesive fracture models
- A variational approach to fracture and other inelastic phenomena
- Unilateral gradient flow of the Ambrosio-Tortorelli functional by minimizing movements
- Gradient damage models coupled with plasticity and nucleation of cohesive cracks
- Elastic bars with cohesive energy
- The variational approach to fracture
- Convergence results for critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term
- Variational formulation of softening phenomena in fracture mechanics: The one-dimensional case
- Free-discontinuity problems via functionals involving the \(L^1\)-norm of the gradient and their approximations
- Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures
- The gradient theory of phase transitions and the minimal interface criterion
- The Gibbs-Thompson relation within the gradient theory of phase transitions
- Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
- Revisiting brittle fracture as an energy minimization problem
- Optimal regularity and structure of the free boundary for minimizers in cohesive zone models
- Asymptotic behavior of Allen-Cahn-type energies and Neumann eigenvalues via inner variations
- A general thermodynamical model for adhesive frictional contacts between viscoelastic or poro-viscoelastic bodies at small strains
- Cohesive zone-type delamination in visco-elasticity
- A quasi-static evolution generated by local energy minimizers for an elastic material with a cohesive interface
- Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics
- Convergence of phase-field approximations to the Gibbs-Thomson law
- Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case
- Cohesive fracture in 1D: quasi-static evolution and derivation from static phase-field models
- Linearly constrained evolutions of critical points and an application to cohesive fractures
- Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach
- Approximation of functional depending on jumps by elliptic functional via t-convergence
- A VANISHING VISCOSITY APPROACH TO FRACTURE GROWTH IN A COHESIVE ZONE MODEL WITH PRESCRIBED CRACK PATH
- On the convergence of stable phase transitions
- Image segmentation with a finite element method
- Relaxation results for some free discontinuity problems.
- Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue
- Phase field model with a variable chemical potential
- VARIATIONAL APPROXIMATION OF FREE-DISCONTINUITY ENERGIES WITH LINEAR GROWTH
- Existence, Energy Identity, and Higher Time Regularity of Solutions to a Dynamic Viscoelastic Cohesive Interface Model
- Dynamic cohesive fracture: Models and analysis
- Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
- Convergence of discrete and continuous unilateral flows for Ambrosio–Tortorelli energies and application to mechanics
- Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening
- Quasi-static crack growth for a cohesive zone model with prescribed crack path
- A note on the one-dimensional critical points of the Ambrosio–Tortorelli functional
- On a phase‐field model of damage for hybrid laminates with cohesive interface
- Energetic evolutions for linearly elastic plates with cohesive slip
- Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy
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