A crucial question in materials science consists in providing accurate mathematical descriptions of phenomena exhibiting an intrinsic nonlinear nature. Many applications, ranging from sensors design to biomechanics, and from the modeling of fracture effects to the simulation of wings behavior in aerospace engineering, are indeed encoded by complex nonlinear mechanical phenomena described by large strain deformations. This project aims at joining the complementary expertise of two research groups, based in Vienna and in Prague, in order to build an international team, and to advance the mathematical modeling of challenging large (finite) strain problems in materials science. The Austrian PI is Elisa Davoli (TU Wien), the Czech PI is Martin Kružík (UTIA, Prague). Our research is supported by the Austrian Science Fund (FWF), opens an external URL in a new window and the Czech Science Fund (GAČR), 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, G. Di Fratta, V. Pagliari
    Sharp conditions for the validity of the Bourgain-Brezis-Mironescu formula
    Submitted, 2023 (preprint)
  2. M. Buzancic, E. Davoli, I. Velcic
    Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure
    Submitted, 2022 (preprint)
  3. E. Davoli, C. Gavioli, V. Pagliari
    Homogenization of high-contrast media in finite-strain elastoplasticity
    Submitted, 2022 (preprint)
  4. 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. M. Bresciani
    Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions
    Calc. Var. 62 (2023), no. 7, Article no. 181. (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. S. Almi, E. Davoli, M. Friedrich
    Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture
    J. Math. Pure Appl. (preprint)
  5. V. Pagliari, K. Papafitsotros, B. Raita, A. Vikelis
    Bilevel training schemes in imaging for total-variation-type functionals with convex integrands
    SIAM Journal on Imaging Sciences Vol. 15, Iss. 4 (2022) (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. M. Bresciani, M. Kružík
    A reduced model for plates arising as low energy $\Gamma$-limit in nonlinear magnetoelasticity
    SIAM J. Math. Anal. 55 (2023), no. 4, 3108-3168 (preprint)
  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. I. Mazari, D. Ruiz-Balet, E. Zuazua
    Constrained control of bistable reaction-diffusion equations: Gene-flow and spatially heterogeneous models
    Ann. Inst. H. Poincaré Anal. Non Linéaire (2022), to appear. (preprint)
  15. I. Mazari, D. Ruiz-Balet
    Quantitative stability for eigenvalues of Schrödinger operator, Quantitative bathtub principle & Application to the turnpike property for a bilinear optimal control problem
    SIAM Journal on Mathematical Analysis 54 (2022), 3848--3883. (preprint)
  16. 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)
  17. E. Davoli, A. Molchanova, U. Stefanelli
    Equilibria of charged hyperelastic solids
    SIAM Journal of Mathematical Analysis 54 (2022), 1470--1487 (preprint)
  18. I. Mazari
    Quantitative estimates for parabolic optimal control problems under $L^{\infty}$ and $L^1$ constraints in the ball: Quantifying parabolic isoperimetric inequalities
    Nonlinear Analysis 215 (2022), 112649
  19. I. Mazari, G. Nadin, Y. Privat
    Shape optimization of a weighted two phase Dirichlet eigenvalue
    Archive for Rational Mechanics and Analysis 243 (2022), 95 – 137
  20. E. Davoli, M. Kružík, P. Pelech
    Separately global solutions to rate-independent processes in large-strain inelasticity
    Nonlinear Analysis 215 (2022), 112668
  21. M. Bresciani
    Linearized von Kármán theory for incompressible magnetoelastic plates
    M3AS 31(10) (2021), 1987 – 2037
  22. I. Mazari, G. Nadin, A.I. Toledo Marrero
    Optimisation of the total population size with respect to the initial condition for semilinear parabolic equations: Two-scale expansions and symmetrisations
    Nonlinearity 34 (2021), 7510
  23. I. Mazari, D. Ruiz-Balet
    A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models
    SIAM journal on Applied Mathematics 81(1) (2021), 153 – 172
  24. 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
  25. 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
  26. 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
  27. E. Davoli, M. Kružík, P. Piovano, U. Stefanelli
    Magnetoelastic thin films at large strains
    Continuum Mechanics and Thermodynamics 33 (2021), 327 – 341
  28. I. Mazari, G. Nadin, Y. Privat
    Optimisation of the total population size for logistic diffusive equations: bang-bang property and fragmentation rate
    Comm. PDEs (2021), to appear
  29. 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
  30. A. Chambolle, M. Novaga, V. Pagliari
    On the convergence rate of some nonlocal energies
    Nonlinear Analysis 200 (2020)
  31. 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)
  32. 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
  33. E. Davoli, P. Piovano
    Derivation of a heteroepitaxial thin-film model
    Interfaces and Free Boundaries 22 (2020), 1 – 26
  34. 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