Octahedral Based Incremental Stress-Strain Matrices

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.