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
Manuel Friedrich

News:

Research interests:

  • Calculus of Variations

  • Multiscale Methods

  • Free-discontinuity problems

  • Atomistic models and discrete-to-continuum limits

  • Geometric rigidity

  • Modeling of materials in elasticity and fracture mechanics

Short vita:

Publications:

  • (with L. Kreutz) Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice. Nonlinearity, to appear [Preprint]

  • (with M. Kruzik, J. Valdman) Numerical approximation of von Kármán viscoelastic plates. DCDS-S, to appear [Preprint]

  • Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials. Mathematics in Engineering, to appear [Preprint]

  • (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 V. Crismale) Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity. Submitted 2019. [Preprint]

  • (with U. Stefanelli) Crystallization in a one-dimensional periodic landscape. Submitted 2019. [Preprint]

  • (with F. Solombrino) Functionals defined on piecewise rigid functions: Integral representation and Γ-convergence. Submitted 2019 [Preprint]

  • (with M. Kruzik) Derivation of von Kármán plate theory in the framework of three-dimensional viscoelasticity. Submitted 2019 [Preprint]

  • (with E. Davoli) Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions. Preprint 2018. [Preprint]

  • (with U. Stefanelli) Ripples in graphene: A variational approach. Submitted 2018. [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]