Premium
B‐bar FEMs for anisotropic elasticity
Author(s) -
Oberrecht S.P.,
Novák J.,
Krysl P.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4621
Subject(s) - elasticity (physics) , anisotropy , isotropy , hydrostatic equilibrium , compressibility , hydrostatic pressure , hydrostatic stress , materials science , bar (unit) , finite element method , mechanics , structural engineering , physics , composite material , engineering , optics , quantum mechanics , meteorology
SUMMARY Anisotropic elastic materials, such as the homogenized model of a fiber‐reinforced matrix, can display near rigidity under certain applied stress–the resulting strains are small compared with the strains that would occur for other stresses of comparable magnitude. The anisotropic material could be rigid under hydrostatic pressure if the material were incompressible, as in isotropic elasticity, but also for other stresses. Some commonly used finite elements are effective in dealing with incompressibility, but are ill‐equipped to handle materials that lock under non‐hydrostatic stress states (e.g., uniformly reduced serendipity and Q1/Q0 B‐bar hexahedra). The failure of the original B‐bar method is attributed to the assumption that the mode of deformation to be relieved is one of near incompressibility. The remedy proposed here is based on the spectral decomposition of the compliance matrix of the material. The spectrum can be interpreted to separate nearly‐rigid and flexible modes of stress and strain, which leads naturally to a generalized selective reduced integration. Furthermore, the spectral decomposition also enables a three‐field elasticity formulation that results in a B‐bar method that is effective for general anisotropic materials with an arbitrary nearly‐rigid mode of deformation.Copyright © 2014 John Wiley & Sons, Ltd.