It is also possible to prescribe a stress contribution that only acts as a load on the structure, but that is not added into the stress tensor definition as described in Equation 3-13. The typical case is when there is a pore pressure in a porous material, a common case in geotechnical engineering. The stress carried by the solid material excluding the pore pressure is often called the
effective stress. The load from the pore pressure helps to balance the external loads, while not contributing to the stress tensor of the solid. The contribution to the virtual work of the external stress (load) is then
With the External Stress feature it is also possible to model residual stresses due to, for instance, manufacturing processes. The Residual stress option augments the stress tensor as defined in
Equation 3-13, and it also removes the deformation created from it by applying an external load with opposite sign, as described in
Equation 3-14. In this way there is no induced deformation in the solid, but the definition of the stress tensor and its invariants are augmented, which has an impact in plasticity, creep, or viscoplasticity.
When External Stress (Nominal) is selected, the external stress tensor does not have to by symmetric, thus the contribution of the external stress acts as an external load, to the virtual work is
The in situ stress is a common residual stress used in geotechnical engineering. The vertical stress,
σv, also called
overburden pressure,
lithostatic pressure, or
confining pressure, represents the stress in a point given by the weight of the overlaying material.
The elevation D is the distance of a point in the soil to the top boundary,
ρ is the density and
g the acceleration of gravity. This analytical expression for the vertical stress is derived for a slab of soil of infinite lateral extension.
The lateral or horizontal stress σh is normally given as a factor or the vertical stress
The factor k0, called the
coefficient of lateral earth pressure, is normally computed from the angle of internal friction, from the Poisson’s ratio, or more complex formulas.
When the z-axis represents the vertical coordinate, the in situ stress tensor is written as