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Finite element analysis of anisotropic non‐linear incompressible elastic solids by a mixed model
Author(s) -
Srinivasan Ramakrishnan,
Perucchio Renato
Publication year - 1994
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.1620371805
Subject(s) - hyperelastic material , finite element method , compressibility , anisotropy , isotropy , mathematics , mixed finite element method , mathematical analysis , hydrostatic pressure , displacement (psychology) , transverse isotropy , mechanics , geometry , physics , structural engineering , engineering , psychology , quantum mechanics , psychotherapist
Abstract A mixed finite element method is presented for geometrically and materially non‐linear analysis of anisotropic incompressible hyperelastic materials. An incremental iteractive total Lagrangian formulation is adopted. The nodal displacements and the hydrostatic pressure are independently interpolated leading to a mixed system of equations, with characteristic zero diagonal terms. Computations are carried out using a three‐dimensional linear displacement, constant pressure element. A mixed penalty approximation is then employed to eliminate the pressure variables at the element level. The anisotropic material handling capability of the formulation is tested through a number of transversely isotropic problems and the results compared to analytical solutions. To demonstrate the applicability of this formulation to model complex anisotropic problems, the inflation of a cut toroidal tube with helical fibre orientation is analysed.