Publikationen – Department Mathematik

List of publications:

Preprints:

(with S. Almi, R. Badal, S. Schwarzacher) Thermo-elastodynamics of nonlinearly viscous solids. Submitted 2024. [Preprint]
(with R. Badal, M. Kruzik, L. Machill) Positive temperature in nonlinear thermoviscoelasticity and the derivation of linearized models . Submitted 2024. [Preprint]
(with M. Bresciani) Quasistatic growth of cavities and cracks in the plane . Submitted 2024. [Preprint]
(with W. Górny, U. Stefanelli) The ℓ1 double-bubble problem in three dimensions. Submitted 2024. [Preprint]
(with C. Labourie, K. Stinson) Strong existence for free discontinuity problems in linear elasticity. Submitted 2024. [Preprint]
(with J. Seutter) Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials. Submitted 2024. [Preprint]
(with A. F. Donnarumma) Stochastic homogenisation for functionals defined on asymptotically piecewise rigid functions. Submitted 2023. [Preprint]
(with C. Labourie, K. Stinson) On regularity for Griffith almost-minimizers in the plane. Submitted 2023. [Preprint]
(with W. Górny, U. Stefanelli) A characterization of ℓ1 double bubbles with general interface interaction. Submitted 2023. [Preprint]
(with S. Almi, M. Caponi, F. Solombrino) Geometric rigidity on Sobolev spaces with variable exponent and applications. Submitted 2023. [Preprint]

Publications:

(with M. Bresciani, C. Mora-Corral) Variational models with Eulerian-Lagrangian formulation allowing for material failure. Arch. Ration. Mech. Anal., to appear. [Preprint]
(with R. Badal, L. Machill) Derivation of a von Kármán plate theory for thermoviscoelastic solids. Math. Models Methods Appl. Sci. (M3AS), to appear. [Preprint]
(with S. Almi, M. Caponi, F. Solombrino) A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations. Mathematische Annalen, to appear. [Preprint]
(with M. Seitz, U. Stefanelli) Discrete-to-continuum linearization in atomistic dynamics. DCDS, to appear. [Preprint, Article]
(with L. Kreutz, K. Zemas) Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces. Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. [Preprint, Article]
(with M. Seitz, U. Stefanelli) Nonlocal-to-local limit in linearized viscoelasticity. Comm. Appl. Ind. Math., to appear. [Preprint]
(with L. Kreutz, K. Zemas) Derivation of effective theories for thin 3D nonlinearly elastic rods with voids. Math. Models Methods Appl. Sci. (M3AS), to appear. [Preprint, Article]
(with L. Kreutz) A proof of finite crystallization via stratification. J. Stat. Phys. 190:199 (2023). [Preprint, Article]
(with W. Górny, U. Stefanelli) The double-bubble problem on the square lattice. Interfaces Free Bound. 26 (2024) pp. 79-134. [Preprint, Article]
(with L. Machill) One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams.
Calc. Var. PDE 62:190 (2023). [Preprint, Article]
(with S. Almi, E. Davoli) Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture. J. Math. Pures Appl.175 (2023) pp. 1-36. [Preprint, Article]
(with L. Kreutz, K. Zemas) From atomistic systems to linearized continuum models for elastic materials with voids. Nonlinearity 36 (2023) pp. 679-735. [Preprint, Article]
(with R. Badal, M. Kruzik) Nonlinear and Linearized Models in Thermoviscoelasticity. Arch. Ration. Mech. Anal. 247: 5 (2023). [Preprint, Article]
(with R. Badal, J. Seutter) Existence of quasi-static crack evolution for atomistic systems. Forces in mechanics 9 (2022), 100138. [Preprint, Article]
(with E. Davoli) Two-well linearization for solid-solid phase transitions. J. Eur. Math. Soc. (JEMS), to appear. [Preprint, Article]
(with M. Seitz, U. Stefanelli) Tilings with nonflat squares: a characterization. Milan Journal of Mathematics 90 (2022), pp. 131-175. [Preprint, Article]
(with M. Perugini, F. Solombrino) Gamma-convergence for free-discontinuity problems in linear elasticity: Homogenization and relaxation. Indiana University Mathematics Journal, to appear. [Preprint, Article]
(with L. Machill) Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons. NoDEA Nonlinear Differential Equations Appl. 59:11 (2022). [Preprint, Article]
(with L. Bétermin, U. Stefanelli) Angle-rigidity for Z^2 configurations. Nonlinearity 34 (2021), pp. 8392-8413. [Preprint, Article]
(with L. Bétermin, U. Stefanelli) Lattice ground states for Embedded-Atom Models in 2D and 3D. Letters in Mathematical Physics 111:107 (2021). [Preprint, Article]
(with L. Kreutz, B. Schmidt) Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy. Arch. Ration. Mech. Anal. 240 (2021), pp. 627-698. [Preprint, Article]
(with M. Perugini, F. Solombrino) Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD. J. Funct. Anal. 280 (2021), 108929. [Preprint, Article]
(with M. Kruzik, U. Stefanelli) Equilibrium of immersed hyperelastic solids. DCDS-S, to appear. [Preprint, Article]
(with V. Crismale, F. Solombrino) Integral representation for energies in linear elasticity with surface discontinuities. Adv. Calc. Var. 15 (2022), pp. 705–733. [Preprint, Article]
(with M. Kruzik) Derivation of von Kármán plate theory in the framework of three-dimensional viscoelasticity. Arch. Ration. Mech. Anal. 238 (2020), pp. 489-540. [Preprint, Article]
(with U. Stefanelli) Crystallization in a one-dimensional periodic landscape. J. Stat.Phys. 179 (2020), pp. 485-501. [Preprint, Article]
(with V. Crismale) Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity. Arch. Ration. Mech. Anal. 237 (2020), pp. 1041-1098. [Preprint, Article]
(with U. Stefanelli) Ripples in graphene: A variational approach. Comm. Math. Phys. 379 (2020), pp. 915–954. [Preprint, Article]
(with F. Solombrino) Functionals defined on piecewise rigid functions: Integral representation and Γ-convergence. Arch. Ration. Mech. Anal. 236 (2020), pp. 1325-1387. [Preprint, Article]
(with E. Davoli) Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions. Calc. Var. PDE 59:44 (2020). [Preprint, Article]
(with L. Kreutz) Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice. Nonlinearity 33 (2020), pp. 1240-1296. [Preprint, Article]
(with M. Kruzik, J. Valdman) Numerical approximation of von Kármán viscoelastic plates. DCDS-S, 14 (2021), pp. 299-319. [Preprint, Article]
Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials. Mathematics in Engineering, 2 (2020), pp. 75-100. [Preprint, Article]
(with L. Kreutz) Crystallization in the hexagonal lattice for ionic dimers. Math. Models Methods Appl. Sci. (M3AS) 29 (2019), pp. 1853-1900. [Preprint, Article]
A compactness result in GSBV^p and applications to Γ-convergence for free discontinuity problems. Calc. Var. PDE 58:86 (2019). [Preprint, Article]
(with E. Mainini, P. Piovano, U. Stefanelli) Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule. Arch. Ration. Mech. Anal. 231 (2019), pp. 465-517. [Preprint, Article]
A piecewise Korn inequality in SBD and applications to embedding and density results. SIAM J. Math. Anal. 50 (2018), pp. 3842-3918. [Preprint, Article]
(with U. Ludacka, M. R. A. Monazam, C. Rentenberger, U. Stefanelli, J. C. Meyer, J. Kotakoski) In situ control over graphene ripples and strain in the electron microscope. npj 2D Materials and Applications 2: 25 (2018). [Article]
(with M. Kruzik) On the passage from nonlinear to linearized viscoelasticity. SIAM J. Math. Anal. 50 (2018), pp. 4426-4456. [Preprint, Article]
(with U. Stefanelli) Graphene ground states. Zeitschrift für angewandte Mathematik und Physik, June 2018, 69:70. [Preprint, Article]
(with F. Solombrino) Quasistatic crack growth in 2d-linearized elasticity. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018) pp. 27-64. [Preprint, Article]
On a decomposition of regular domains into John domains with uniform constants. ESAIM Control Optim. Calc. Var. 24 (2018), pp. 1541-1583. [Preprint, Article]
A Korn-type inequality in SBD for functions with small jump sets. Math. Models Methods Appl. Sci. (M3AS) 27 (2017) pp. 2461-2484. [Preprint, Article]
A derivation of linearized Griffith energies from nonlinear models. Arch. Ration. Mech. Anal. 225 (2017) pp. 425-467. [Preprint, Article]
(with P. Piovano, U. Stefanelli) The geometry of C60: A rigorous approach via Molecular Mechanics. SIAM J. Appl. Math. 76 (2016) pp. 2009-2029. [Preprint, Article]
(with B. Schmidt) On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime. Netw. Heterog. Media 10 (2015) pp. 321-342. [Preprint, Article]
(with B. Schmidt) An analysis of crystal cleavage in the passage from atomistic models to continuum theory. Arch. Ration. Mech. Anal. 217 (2015) pp. 263-308. [Preprint, Article]
(with B. Schmidt) An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem. J. Nonlin. Sci. 24 (2014) pp. 145-183. [Preprint, Article]

Other:

(with E. Mainini, P. Piovano) Atomistic potentials and the Cauchy-Born rule for carbon nanotubes: a review. Rendiconti Sem. Mat. Univ. Pol. Torino. [Preprint]
(with B. Schmidt) A quantitative geometric rigidity result in SBD. Preprint 2015. [Preprint]
A Korn-Poincaré-type inequality for special functions of bounded deformation. Preprint 2015. [Preprint]