The external stress represents an additional stress contribution which has a source other than the constitutive relation. It is similar to the initial stress described in Initial Stresses and Strains, and the two features can be used interchangeably. As an example, linear elasticity including an external stress σext can be written as

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 3-12. 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 3-12, and it also removes the deformation created from it by applying an external load with opposite sign, as described in Equation 3-13. 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, lithotastic 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 σv 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

The External Stress subnode can be added to Linear Elastic Material, Nonlinear Elastic Materials, Elastoplastic Soil Models, Shape Memory Alloy, or Hyperelastic Material Models.