%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 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