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A numerical homogenisation method for sandwich plates based on a plate theory with thickness change
Author(s) -
Helfen C.,
Diebels S.
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201100173
Subject(s) - plate theory , mesoscopic physics , materials science , finite element method , bending of plates , length scale , composite plate , boundary value problem , composite number , composite material , mechanics , structural engineering , mathematics , bending , mathematical analysis , physics , engineering , quantum mechanics
Nowadays composite plates are widely used, especially in the transport industry. Their importance derives from their relatively low weight and good mechanical properties, but their behaviour is complex and cannot be obtained from a simple mixture rule properly. In the scope of this work, the considered composite plate is composed of a complex assembly of metal layers and carbon fibers reinforced polymers (CFRP) layers. Whereas the CFRP can be considered as anisotropic elastic, the metal layers have an elasto‐plastic material behaviour. In this case, the possibility to use the classical plate theory is excluded, because the classical plate theory can only regard small deformations and linear material behaviour. For this reason, the modelling of the mechanical behaviour of the composite plate is based on a numerical homogenisation. The underlying principle is a numerical multi‐scale consideration of the composite plate: on the one hand, the macroscale is considered as a Finite Element computation of a plate which is following a plate theory including a thickness change, i. e. a seven degrees of freedom approach. On the other hand, the mesoscale is obtained with a three‐dimensional modelling which explicitly takes into account the stacking order and the material behaviour of the different layers. From each integration point of the macroscale, the deformations are projected on the boundaries of a Representative Volume Element (RVE) of the mesoscale. In this scale, a boundary value problem is solved, and the macroscopic forces, moments and shear forces are obtained as resultants from the mesoscopic stresses.