Refined dimensional reduction for isotropic elastic Cosserat shells with initial curvature

ORCID
0000-0002-1360-4044
LSF
54461
Zugehörige Organisation
Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Essen, Germany
Bîrsan, Mircea;
ORCID
0000-0002-8466-8010
Zugehörige Organisation
Alexandru Ioan Cuza University of Iaşi, Department of Mathematics, Iaşi, Romania Octav Mayer Institute of Mathematics of the Romanian Academy, Iaşi, Romania
Ghiba, Ionel-Dumitrel;
GND
1104944960
LSF
60113
Martin, Robert J.;
GND
122258886
ORCID
0000-0002-1615-8879
LSF
13332
Zugehörige Organisation
Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Essen, Germany
Neff, Patrizio
Using a geometrically motivated 8-parameter ansatz through the thickness, we reduce a three-dimensional shell-like geometrically nonlinear Cosserat material to a fully two-dimensional shell model. Curvature effects are fully taken into account. For elastic isotropic Cosserat materials, the integration through the thickness can be performed analytically and a generalized plane stress condition allows for a closed-form expression of the thickness stretch and the nonsymmetric shift of the midsurface in bending. We obtain an explicit form of the elastic strain energy density for Cosserat shells, including terms up to order O ( h 5 ) in the shell thickness h . This energy density is expressed as a quadratic function of the nonlinear elastic shell strain tensor and the bending–curvature tensor, with coefficients depending on the initial curvature of the shell.

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