Interaction between oscillations and singular perturbations in a one-dimensional phase-field model

DOI10.1007/978-3-031-04496-0_1zbMath1501.74061OpenAlexW4312938196MaRDI QIDQ2080543

Teresa Esposito, Caterina Ida Zeppieri, Annika Bach, Roberta Marziani

Publication date: 9 October 2022

Full work available at URL: https://doi.org/10.1007/978-3-031-04496-0_1

zbMATH Keywords

gamma-convergenceAmbrosio-Tortorelli modelfine-scale heterogeneityMumford-Shah limit functional

Mathematics Subject Classification ID

Phase transformations in solids (74N99) Homogenization in equilibrium problems of solid mechanics (74Q05) Brittle damage (74R05) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (3)

Gradient Damage Models for Heterogeneous Materials ⋮ Γ-convergence and stochastic homogenisation of phase-transition functionals ⋮ A phase‐field porous media fracture model based on homogenization theory

Cites Work

• The variational approach to damage. II: The gradient damage models
• Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy
• Approximation of free-discontinuity problems
• The gradient theory of phase transitions and the minimal interface criterion
• Fracture models as \(\Gamma\)-limits of damage models
• Approximation of functional depending on jumps by elliptic functional via t-convergence
• Gradient theory of phase transitions in composite media
• ON THE VARIATIONAL APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS IN THE VECTORIAL CASE
• Fracture and plastic models as Γ-limits of damage models under different regimes
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