%0 Journal Article
%J Communication in Partial Differential Equations 36 (2011) 2062-2102
%D 2011
%T Large Time Existence for Thin Vibrating Plates
%A Helmut Abels
%A Maria Giovanna Mora
%A Stefan Müller
%X We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.
%B Communication in Partial Differential Equations 36 (2011) 2062-2102
%I Taylor & Francis
%G en_US
%U http://hdl.handle.net/1963/3755
%1 562
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-15T09:12:35Z\\r\\nNo. of bitstreams: 1\\r\\nLongTimeExistence.pdf: 331066 bytes, checksum: eba3dcbc86ddcd7b92e10fddca5964c4 (MD5)
%R 10.1080/03605302.2011.618209
%0 Journal Article
%J Calculus of Variations and Partial Differential Equations 41 (2011) 241-259
%D 2011
%T The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity
%A Helmut Abels
%A Maria Giovanna Mora
%A Stefan Müller
%X The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.
%B Calculus of Variations and Partial Differential Equations 41 (2011) 241-259
%I Springer
%G en_US
%U http://hdl.handle.net/1963/3835
%1 492
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T16:49:12Z\\r\\nNo. of bitstreams: 1\\r\\n0912.4135v1.pdf: 217528 bytes, checksum: 4ee557860670b3d876174b2e053958e4 (MD5)
%R 10.1007/s00526-010-0360-0
%0 Journal Article
%J Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896
%D 2008
%T Convergence of equilibria of three-dimensional thin elastic beams
%A Maria Giovanna Mora
%A Stefan Müller
%X A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.
%B Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896
%G en_US
%U http://hdl.handle.net/1963/1896
%1 2339
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-24T10:09:06Z\\nNo. of bitstreams: 1\\n69M-2006.pdf: 3633291 bytes, checksum: b5dba64c671bbcd8b87e52ce24963341 (MD5)
%R 10.1017/S0308210506001120
%0 Journal Article
%J Indiana Univ. Math. J. 56 (2007) 2413-2438
%D 2007
%T Convergence of equilibria of planar thin elastic beams
%A Maria Giovanna Mora
%A Stefan Müller
%A Maximilian G. Schultz
%X We consider a thin elastic strip of thickness h and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof uses the rigidity estimate for low-energy deformations by Friesecke, James, and Mueller (Comm. Pure Appl. Math. 2002), and a compensated compactness argument in a singular geometry. In addition, possible concentration effects are ruled out by a careful truncation argument.
%B Indiana Univ. Math. J. 56 (2007) 2413-2438
%G en_US
%U http://hdl.handle.net/1963/1830
%1 2386
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-06-08T11:03:04Z\\nNo. of bitstreams: 1\\nmath.fa-0604554.pdf: 263517 bytes, checksum: 1ad7fad8323aa78951b53178a78c3030 (MD5)
%R 10.1512/iumj.2007.56.3023
%0 Report
%D 2007
%T Derivation of a rod theory for phase-transforming materials
%A Maria Giovanna Mora
%A Stefan Müller
%X A rigorous derivation is given of a rod theory for a multiphase material,starting from three-dimensional nonlinear elasticity. The stored energy density is supposed to be nonnegative and to vanish exactly on a set consisting of two copies of the group of rotations SO(3). The two potential wells correspond to the two crystalline configurations preferred by the material. We find the optimal scaling of the energy in terms of the diameter of the rod and we identify the limit, as the diameter goes to zero, in the sense of Gamma-convergence.
%B Calc. Var. Partial Differential Equations 28 (2007) 161-178
%G en_US
%U http://hdl.handle.net/1963/1751
%1 2793
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-16T14:39:50Z\\nNo. of bitstreams: 1\\n21M.pdf: 23269 bytes, checksum: 46cdfa0d7b7b8d6710cc814108473dce (MD5)
%R 10.1007/s00526-006-0039-8
%0 Book Section
%B The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381.
%D 2006
%T Recent analytical developments in micromagnetics
%A Antonio DeSimone
%A Robert V. Kohn
%A Stefan Müller
%A Felix Otto
%B The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381.
%@ 978-0-12-480874-4
%G en_US
%U http://hdl.handle.net/1963/2230
%1 2014
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T15:16:57Z\\nNo. of bitstreams: 1\\nDKMO.pdf: 1644450 bytes, checksum: 4c1079e4854e372d31af9a285f87f400 (MD5)
%0 Journal Article
%J Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549
%D 2005
%T Self-similar folding patterns and energy scaling in compressed elastic sheets
%A Sergio Conti
%A Antonio DeSimone
%A Stefan Müller
%X Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves.
%B Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/3000
%1 1333
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:37:14Z\\nNo. of bitstreams: 1\\npreprint2004_3.pdf: 907333 bytes, checksum: 2b22c209b91ba2ddacc1a1c14a9054a2 (MD5)
%R 10.1016/j.cma.2004.07.044