Welcome to the homepage of the "FWF-GAČR Joint Project: Large Strain Challenges in Materials Science"
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.
Preprints
- E. Davoli, G. Di Fratta, V. Pagliari
Sharp conditions for the validity of the Bourgain-Brezis-Mironescu formula
Submitted, 2023 (preprint) - M. Buzancic, E. Davoli, I. Velcic
Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure
Submitted, 2022 (preprint) - E. Davoli, C. Gavioli, V. Pagliari
Homogenization of high-contrast media in finite-strain elastoplasticity
Submitted, 2022 (preprint) - E. Davoli, C. Gavioli, V. Pagliari
A homogenization result in finite plasticity
Submitted, 2022 (preprint)
Published and accepted papers
- 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) - M. Bresciani
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions
Calc. Var. 62 (2023), no. 7, Article no. 181. (preprint) - 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) - S. Almi, E. Davoli, M. Friedrich
Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture
J. Math. Pure Appl. (preprint) - 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) - E. Davoli, K. Nik, U. Stefanelli
Existence results for a morphoelastic model
ZAMM- Zeitschrift für Angewandte Mathematik und Mechanik (2022), to appear. - 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) - E. Davoli, I. Mazari, U. Stefanelli
Spectral optimization of inhomogeneous plates
SIAM Journal on Control and Optimization (SICON) 61 (2023), 852-871 (preprint) - E. Davoli, M. Kružík, V. Pagliari
Homogenization of high-contrast composites under differential constraints
Advances in Calculus of Variations (2022). (preprint) - 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) - 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. - E. Davoli, M. Friedrich
Two-well linearization for solid-solid phase transitions
JEMS (2022), to appear (preprint) - 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) - 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) - 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) - 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) - E. Davoli, A. Molchanova, U. Stefanelli
Equilibria of charged hyperelastic solids
SIAM Journal of Mathematical Analysis 54 (2022), 1470--1487 (preprint) - 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 - 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 - E. Davoli, M. Kružík, P. Pelech
Separately global solutions to rate-independent processes in large-strain inelasticity
Nonlinear Analysis 215 (2022), 112668 - M. Bresciani
Linearized von Kármán theory for incompressible magnetoelastic plates
M3AS 31(10) (2021), 1987 – 2037 - 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 - 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 - 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 - 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 - 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 - E. Davoli, M. Kružík, P. Piovano, U. Stefanelli
Magnetoelastic thin films at large strains
Continuum Mechanics and Thermodynamics 33 (2021), 327 – 341 - 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 - 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 - A. Chambolle, M. Novaga, V. Pagliari
On the convergence rate of some nonlocal energies
Nonlinear Analysis 200 (2020) - 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) - 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 - E. Davoli, P. Piovano
Derivation of a heteroepitaxial thin-film model
Interfaces and Free Boundaries 22 (2020), 1 – 26 - 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