Octahedral Based Incremental Stress-Strain Matrices

by David W. Murray, (M.ASCE), Prof.; Dept. of Civ. Engrg., Univ. of Alberta, Edmonton, Alberta, Cananda,

Serial Information: Journal of the Engineering Mechanics Division, 1979, Vol. 105, Issue 4, Pg. 501-513

Document Type: Journal Paper


Some Investigators have recently suggested that appropriate nonlinear stress-strain relationships for concrete can be obtained by deriving expressions for bulk and shearing moduli based upon experimental data presented in terms of octahedral stresses and strains. The paper reviews octahedral stress-strain relationships and derives appropriate stiffness matrices, both secant and tangent, for plane stress, plane strain, and three-dimensional applications. It is shown that proper tangent stiffness matrices cannot be obtained simply by replacing secant moduli with tangent moduli. Incremental matrices suitable for implementation in nonlinear finite-element programs are presented and considered.

Subject Headings: Stress strain relations | Matrix (mathematics) | Stiffening | Nonlinear finite element analysis | Concrete | Shear stress | Shear modulus | Plane strain

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