Existence of minimizers for the SDRI model in 2d: wetting and dewetting regime with mismatch strain

DOI10.1515/ACV-2022-0053MaRDI QIDQ6566011

Paolo Piovano, Shokhrukh Yusufovich Kholmatov

Publication date: 3 July 2024

Published in: Advances in the Calculus of Variations (Search for Journal in Brave)

regularity existence elastic energy surface energy thin films density estimates fractures minimal configurations interface instabilities crystal cavities SDRI

Mathematics Subject Classification ID

Crystalline structure (74E15) Energy minimization in equilibrium problems in solid mechanics (74G65) Thin films (74K35) Methods involving semicontinuity and convergence; relaxation (49J45) Free boundary problems for PDEs (35R35)

Cites Work

Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model
Existence of minimizers for the \(2d\) stationary Griffith fracture model
Generalised functions of bounded deformation
Study of island formation in epitaxially strained films on unbounded domains
Reduced models for linearly elastic thin films allowing for fracture, debonding or delamination
Material voids in elastic solids with anisotropic surface energies
Equilibrium configurations of epitaxially strained elastic films: second-order minimality conditions and qualitative properties of solutions
A unified model for stress-driven rearrangement instabilities
Capillary drops: contact angle hysteresis and sticking drops
A variational model for fracture and debonding of thin films under in-plane loadings
The variational approach to fracture
A variational method in image segmentation: Existence and approximation results
The stress driven instability in elastic crystals: Mathematical models and physical manifestations
An introduction to \(\Gamma\)-convergence
\(C^\infty\) regularity of the free boundary for a two-dimensional optimal compliance problem
Fracture with healing: a first step towards a new view of cavitation
The surface diffusion flow with elasticity in the plane
A lower semicontinuity result for a free discontinuity functional with a boundary term
Existence of strong minimizers for the Griffith static fracture model in dimension two
A density result in \(GSBD^p\) with applications to the approximation of brittle fracture energies
Evolution of material voids for highly anisotropic surface energy
Existence theorem for a minimum problem with free discontinuity set
Revisiting brittle fracture as an energy minimization problem
Crack patterns in thin films
Derivation of a heteroepitaxial thin-film model
Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity
Existence of strong solutions to the Dirichlet problem for the Griffith energy
Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy
Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law
Equilibrium configurations of epitaxially strained crystalline films: Existence and regularity results
Rectifiable sets, densities and tangent measures
Compactness and lower semicontinuity in \(GSBD\)
Computing the equilibrium configuration of epitaxially strained crystalline films
Korn-Poincarè inequalities for functions with a small jump set
Sets of Finite Perimeter and Geometric Variational Problems
Mixed Mode Cracking in Layered Materials
A GENERALIZATION OF {\RM GO{\L}\c{A}B'S} THEOREM AND APPLICATIONS TO FRACTURE MECHANICS
Analytical validation of the Young–Dupré law for epitaxially-strained thin films
Microscopic Validation of a Variational Model of Epitaxially Strained Crystalline Films
A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems
Scaling Law and Reduced Models for Epitaxially Strained Crystalline Films
A relaxation result for energies defined on pairs set-function and applications
The Asaro-Tiller-Grinfeld instability revisited
Lower semicontinuity properties of functionals with free discontinuities

This page was built for publication: Existence of minimizers for the SDRI model in 2d: wetting and dewetting regime with mismatch strain

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6566011)