10
2 Analysis of Stress
Fig. 2.4 Stress components
acting on parallelopiped
otherwise, it is written as
S =
⎡
⎣
σ x τ xy τ xz
τ yx σ y τ yz
τ zx τ zy σ z
⎤
⎦
(2.4)
if we use ordinary expression in matrix form.
2.5 Spherical and Deviatorial Stress Tensors
A general stress tensor can be conveniently divided into two parts as shown above.
Let us now define a new stress term (σ m ) as the mean stress, so that
σ m =
σ x + σ y + σ z
3
(2.5)
Imagine a hydrostatic type of stress having all the normal stresses equal to σ m ,
and all the shear stresses are zero. We can divide the stress tensor into two parts,
one having only the “hydrostatic stress” and the other, “deviatorial stress”. The
hydrostatic type of stress is given by
2 Analysis of Stress
Fig. 2.4 Stress components
acting on parallelopiped
otherwise, it is written as
S =
⎡
⎣
σ x τ xy τ xz
τ yx σ y τ yz
τ zx τ zy σ z
⎤
⎦
(2.4)
if we use ordinary expression in matrix form.
2.5 Spherical and Deviatorial Stress Tensors
A general stress tensor can be conveniently divided into two parts as shown above.
Let us now define a new stress term (σ m ) as the mean stress, so that
σ m =
σ x + σ y + σ z
3
(2.5)
Imagine a hydrostatic type of stress having all the normal stresses equal to σ m ,
and all the shear stresses are zero. We can divide the stress tensor into two parts,
one having only the “hydrostatic stress” and the other, “deviatorial stress”. The
hydrostatic type of stress is given by