# Manuel Friedrich

Applied Mathematics
Universität Münster
Einsteinstr. 62
Office: 120.017
D-48149 Münster
Tel. : +49 (0)251 83-35148
manuel.friedrich@uni-muenster.de

Contact office: Silvia Wernke
Tel. : +49 (0) 251 83-35052
Fax : +49 (0) 251 83-32729

### Research interests:

• Calculus of Variations

• Multiscale Methods

• Free-discontinuity problems

• Atomistic models and discrete-to-continuum limits

• Geometric rigidity

• Evolution equations

• Modeling of materials in elasticity and fracture mechanics

### Publications:

• (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., to appear. [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, to appear. [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]

### Preprints:

• (with M. Seitz, U. Stefanelli) Tilings with nonflat squares: a characterization. Submitted 2021. [Preprint]

• (with L. Kreutz, K. Zemas) Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces. Submitted 2021. [Preprint]

• (with M. Perugini, F. Solombrino) Gamma-convergence for free-discontinuity problems in linear elasticity: Homogenization and relaxation. Submitted 2020. [Preprint]

• (with L. Bétermin, U. Stefanelli) Angle-rigidity for Z^2 configurations. Submitted 2020. [Preprint]

• (with E. Davoli) Two-well linearization for solid-solid phase transitions. Submitted 2020. [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]

### 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]