Plasticity in Reinforced Concrete

Notation

Stresses and strains

e ij

= deviatoric strain tensor

s ij

= deviatoric stress tensor

s 1, s 2, s 3

= principal-stress deviators

?

= engineering shear strain

? oct

= = octahedral engineering shear strain

? ij

= strain tensor

? oct

= = octahedral normal strain

? v

= I' 1, = volumetric strain

? 1, ? 2, ? 3

= principal strains, tensile strain positive

?

= normal stress

? ij

= stress tensor

? m

= ? oct = mean normal stress

? oct

= = octahedral normal stress

? 1, ? 2, ? 3

= principal stresses, tensile stress positive

?

= shear stress

? m

= = mean shear stress

? oct

= = octahedral shear stress

Invariants

I 1 = I 1 = ? 1 + ? 2 + ? 3 = ? ii

= first invariant of stress tensor

I' 1 = I' 1

= ? 1 + ? 2 + ? 3 = ? v = first invariant of strain tensor

I 2

= ? 1 ? 2 + ? 2 ? 3 + ? 3 ? 1 = second invariant of stress tensor

I 3

= ? ij

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