Metamaterials are artificially engineered composites whose microstructure is optimized in order to improve structural performances. The interest in metamaterials is due to their unusual properties, which arise as the by-product of their complex microstructures. Due to their importance for industrial applications, metamaterials are an increasingly active field of research at the interface between materials science, physics, engineering, and mathematics. The project aims at developing a multiscale homogenization analysis of the effective behavior of a special class of metamaterials, that is those exhibiting a periodic strong-difference (high contrast) between the material properties of the components.The PI of the project is Elisa Davoli (TU Wien). Our research is supported by the Austrian Science Fund (FWF), opens an external URL in a new window. We collect below a list of all papers which have been published or submitted within the project.


  1. E. Davoli, E. Rocca, L. Scarpa, L. Trussardi
    Local asymptotics and optimal control for a viscous Cahn-Hilliard-reaction-diffusion model for tumor growth
    Submitted, 2023 (preprint)
  2. C. Gavioli, P. P.Krejčí
    Long time behavior of a porous medium model with degenerate hysteresis
    Submitted, 2023 (preprint)
  3. L. D'Elia, M. Eleuteri, E. Zappale
    Homogenization of supremal functionals in vectorial setting (via power-law approximation)
    Submitted, 2023 (preprint)
  4. G. Bonfanti, E. Davoli, R. Rossi
    A coupled rate-dependent/rate-independent system for adhesive contact in Kirchhoff-Love plates
    Submitted, 2023 (preprint)
  5. E. Davoli, L. D'Elia, J. Ingmanns
    Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions
    Submitted, 2023 (preprint)
  6. E. Davoli, R. Ferreira, I. Fonseca, J.A. Iglesias
    Dyadic partition-based training schemes for TV/TGV denoising
    Submitted, 2023 (preprint)
  7. E. Davoli, G. Di Fratta, A. Fiorenza, L. Happ
    A modular Poincaré-Wirtinger type inequality on Lipschitz domains for Sobolev spaces with variable exponents
    Submitted, 2023 (preprint)
  8. C. Gavioli, P.Krejčí
    Degenerate diffusion with Preisach hysteresis
    Submitted, 2023 (preprint)
  9. E. Davoli, G. Di Fratta, V. Pagliari
    Sharp conditions for the validity of the Bourgain-Brezis-Mironescu formula
    Submitted, 2023 (preprint)
  10. M. Buzancic, E. Davoli, I. Velcic
    Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure
    Submitted, 2022 (preprint)
  11. E. Davoli, C. Gavioli, V. Pagliari
    Homogenization of high-contrast media in finite-strain elastoplasticity
    Submitted, 2022 (preprint)
  12. E. Davoli, C. Gavioli, V. Pagliari
    A homogenization result in finite plasticity
    Submitted, 2022 (preprint)

Published and accepted papers

  1. M. Buzancic, E. Davoli, I. Velcic
    Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: the limiting regimes
    Adv. Calc. Var. (2023), to appear. (preprint)
  2. E. Davoli, R. Ferreira, C. Kreisbeck, H. Schönberger
    Structural changes in nonlocal denoising models arising through bi-level parameter learning
    Applied Mathematics and Optimization 88 (2023), Art. 9 (preprint)
  3. A. Braides, L. D'Elia
    Homogenization of discrete thin structures
    Nonlinear Analysis (2022), to appear
  4. S. Almi, E. Davoli, M. Friedrich
    Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture
    J. Math. Pure Appl. (preprint)
  5. B. Detmann, C. Gavioli, P. Krejčí, J. Lamač, Y. Namlyeyeva
    A model for lime consolidation of porous solids
    Nonlinear Anal. Real World Appl., 65 (2022), 103483
  6. C. Gavioli, P. Krejčí
    Phase transitions in porous media
    Nonlinear Differential Equations and Applications NoDEA, 29 (2022), 72 (preprint)
  7. E. Davoli, K. Nik, U. Stefanelli
    Existence results for a morphoelastic model
    ZAMM- Zeitschrift für Angewandte Mathematik und Mechanik (2022), to appear.
  8. E. Davoli, I. Mazari, U. Stefanelli
    Spectral optimization of inhomogeneous plates
    SIAM Journal on Control and Optimization (SICON) 61 (2023), 852-871 (preprint)
  9. E. Davoli, M. Kružík, V. Pagliari
    Homogenization of high-contrast composites under differential constraints
    Advances in Calculus of Variations (2022). (preprint)
  10. M. Bresciani, E. Davoli, M. Kružík
    Existence results in large-strain magnetoelasticity
    Ann. Inst. H. Poincare Anal. Nonlineaire 40 (2023),no. 3, 557-592 (preprint)
  11. E. Davoli, G. Di Fratta, D. Praetorius, M. Ruggeri
    Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction
    Math. Models Methods Appl. Sci. 32 (2022), 911-939.
  12. E. Davoli, M. Friedrich
    Two-well linearization for solid-solid phase transitions
    JEMS (2022), to appear (preprint)
  13. E. Davoli, I. Fonseca, P. Liu
    Adaptive image processing: first order PDE constraint regularizers and a bilevel training scheme
    Journal of Nonlinear Science 33 (2023), Art.41 (preprint)
  14. E. Davoli, C. Kreisbeck
    On static and evolutionary homogenization in crystal plasticity for stratified composites
    In: Research in the Mathematics of Materials Science. Springer AWM series (2022), to appear (preprint)
  15. E. Davoli, A. Molchanova, U. Stefanelli
    Equilibria of charged hyperelastic solids
    SIAM Journal of Mathematical Analysis 54 (2022), 1470--1487 (preprint)
  16. E. Davoli, M. Kružík, P. Pelech
    Separately global solutions to rate-independent processes in large-strain inelasticity
    Nonlinear Analysis 215 (2022), 112668
  17. E. Davoli, L. Scarpa, L. Trussardi
    Local asymptotics for nonlocal convective Cahn-Hilliard equations with $W^{1,1}$ kernel and singular potential
    Journal of Differential Equations 289 (2021), 35 – 58
  18. E. Davoli, T. Roubíček, U. Stefanelli
    A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains
    Mathematics and Mechanics of Solids 26(10) (2021), 1483 – 1497
  19. E. Davoli, L. Scarpa, L. Trussardi
    Nonlocal-to-local convergence of Cahn-Hilliard equations: Neumann boundary conditions and viscosity terms
    Archive for Rational Mechanics and Analysis 239(1) (2021), 117 – 149
  20. E. Davoli, M. Kružík, P. Piovano, U. Stefanelli
    Magnetoelastic thin films at large strains
    Continuum Mechanics and Thermodynamics 33 (2021), 327 – 341
  21. E. Davoli, R.A. Ferreira, C.C. Kreisbeck
    Homogenization in BV of a model for layered composites in finite crystal plasticity
    Adv. Calc. Var. 14(3) (2021), 441 – 473
  22. E. Davoli, M. Friedrich
    Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions
    Calc. Var. Partial Differential Equations 59(44) (2020)
  23. E. Davoli, G. Di Fratta
    Homogenization of chiral magnetic materials - A mathematical evidence of Dzyaloshinskii's predictions on helical structures
    Journal of Nonlinear Science 30 (2020), 1229 – 1262
  24. E. Davoli, P. Piovano
    Derivation of a heteroepitaxial thin-film model
    Interfaces and Free Boundaries 22 (2020), 1 – 26
  25. E. Davoli, H. Ranetbauer, L. Scarpa, L. Trussardi
    Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics
    Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), 627 – 651