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A three‐dimensional finite element program for brittle bimodular rock‐like materials
Author(s) -
Khan Akhtar S.,
Yuan Si
Publication year - 1988
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610120603
Subject(s) - finite element method , cartesian coordinate system , elasticity (physics) , ultimate tensile strength , structural engineering , linear elasticity , young's modulus , brittleness , mathematics , materials science , composite material , engineering , geometry
The present paper models the behaviour of bimodular materials (materials with different tensile and compressive moduli) by using a three‐dimensional finite element method. Since there is no explicit and definite expression for the shear modulus G of bimodular materials, the analysis starts with a 3 × 3 elasticity matrix in the principal stress coordinate system, and then uses a transformation from principal to Cartesian coordinates to obtain the 6 × 6 elasticity matrix. A corresponding iterative technique is proposed, and multiloading sequences in non‐proportionate loading—which need more iterations because of the non‐linear elastic property—are also discussed. Numerical examples are presented which show good agreement with analytical results.