PT Journal
AU Bîrsan, M
   Ghiba, I
   Martin, R
   Neff, P
TI Refined dimensional reduction for isotropic elastic Cosserat shells with initial curvature
SO Mathematics and Mechanics of Solids
PD 07
PY 2019
BP 4000
EP 4019
VL 24
IS 12
DI 10.1177/1081286519856061
LA en
DE Elastic shells; Cosserat material; Dimensional reduction; Curvature; Bending; Strain energy density
AB 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.
PI Sage UK: London, England
ER