Tunable (or smart) materials are a special class of metamaterials, characterized by the possibility of adapting their response according to the features of the external environment. As such, tunable materials are considered to be the future for optical-data processing, quantum information, and next-generation technology. An essential first step to build a comprehensive theory for tunable materials is the identification of rigorously deduced macroscopical mathematical models capable of encompassing multiphase features and phase transitions into the description of complex microstructures. This project aims at addressing three fundamental questions: 1) How is the effective material response of a smart material influenced by the geometry of its components? 2) How do nonlocal effects interact with time evolving phase-transitions and with the possible onset of microstructure? 3) How do the chiral properties of active metamaterials interact with macroscopic tunability? 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.

Preprints

  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. S. Almi, E. Tasso
    Generalized bounded deformation in non-Euclidean settings
    Submitted, 2023 (preprint)
  9. C. Gavioli, P.Krejčí
    Degenerate diffusion with Preisach hysteresis
    Submitted, 2023 (preprint)
  10. E. Davoli, G. Di Fratta, V. Pagliari
    Sharp conditions for the validity of the Bourgain-Brezis-Mironescu formula
    Submitted, 2023 (preprint)
  11. S. Almi, E. Tasso
    A general criterion for jump set slicing and applications
    Submitted, 2023 (preprint)
  12. M. Buzancic, E. Davoli, I. Velcic
    Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure
    Submitted, 2022 (preprint)
  13. E. Tasso
    Rectifiability of a class of integralgeometric measures and applications
    Submitted, 2022 (preprint)
  14. E. Davoli, C. Gavioli, V. Pagliari
    Homogenization of high-contrast media in finite-strain elastoplasticity
    Submitted, 2022 (preprint)
  15. E. Davoli, C. Gavioli, V. Pagliari
    A homogenization result in finite plasticity
    Submitted, 2022 (preprint)

Published and accepted papers

  1. S.Riccò, A. Torricelli
    A necessary condition for extremality of solutions to autonomous obstacle problems with general growth
    Nonlinear Analysis: Real World Applications, 76 (2023), 104005 (preprint)
  2. 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)
  3. 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)
  4. A. Braides, L. D'Elia
    Homogenization of discrete thin structures
    Nonlinear Analysis (2022), to appear
  5. S. Almi, E. Davoli, M. Friedrich
    Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture
    J. Math. Pure Appl. (preprint)
  6. E. Davoli, K. Nik, U. Stefanelli
    Existence results for a morphoelastic model
    ZAMM- Zeitschrift für Angewandte Mathematik und Mechanik (2022), to appear.
  7. E. Davoli, I. Mazari, U. Stefanelli
    Spectral optimization of inhomogeneous plates
    SIAM Journal on Control and Optimization (SICON) 61 (2023), 852-871 (preprint)
  8. E. Davoli, M. Kružík, V. Pagliari
    Homogenization of high-contrast composites under differential constraints
    Advances in Calculus of Variations (2022). (preprint)
  9. 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)
  10. E. Davoli, M. Friedrich
    Two-well linearization for solid-solid phase transitions
    JEMS (2022), to appear (preprint)
  11. 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)
  12. E. Davoli, A. Molchanova, U. Stefanelli
    Equilibria of charged hyperelastic solids
    SIAM Journal of Mathematical Analysis 54 (2022), 1470--1487 (preprint)
  13. E. Davoli, M. Kružík, P. Pelech
    Separately global solutions to rate-independent processes in large-strain inelasticity
    Nonlinear Analysis 215 (2022), 112668