External Stress
You can add the External Stress subnode to several material models, in order to specify an additional stress contribution which is not part of the constitutive relation. The external stress can be added to the total stress tensor, or act only as an extra load contribution.
The External Stress subnode is only available with some COMSOL products (see https://www.comsol.com/products/specifications/).
In many cases External Stress and Initial Stress and Strain are interchangeable when prescribing stresses. In Initial Stress and Strain, the given stress is however always added to the stress tensor.
Shell Properties

This section is only present when External Stress is used in the Layered Shell interface. See the documentation for the External Stress node in the Layered Shell chapter.
External Stress
Select a Stress inputStress tensor (Material), Stress tensor (Spatial), Stress tensor (Nominal), Pore pressure, or In situ stress.
When Stress tensor (Material) is selected, you enter the external stress in the form of a second Piola–Kirchhoff stress tensor. The External stress tensor list will contain all stress tensors announced by any physics interface, and also the entry User defined. When User defined is selected, you can enter the data for the External stress tensor Sext as Isotropic, Diagonal, or Symmetric depending on the properties of the tensor. The tensor components are interpreted in the selected coordinate system. If a stress tensor announced by a physics interface is selected, the coordinate system setting is ignored — the orientation is handled internally. Choose a Contribution type Add to stress tensor, Load contribution only, or Residual stress — to determine the effect of the contribution.
When Stress tensor (Spatial) is selected, you enter the external stress in the form of first Cauchy stress tensor. The components are interpreted in the selected coordinate system. Depending on the properties of the tensor, you can enter the data for the External stress tensor σext as Isotropic, Diagonal, or Symmetric. Choose a Contribution type Add to stress tensor, Load contribution only, or Residual stress — to determine the effect of the contribution.
When Stress tensor (Nominal) is selected, you enter the external stress in the form of first Piola–Kirchhoff stress tensor. The components are interpreted in the selected coordinate system. You can enter the data for the External stress tensor Pext as a full tensor that represents current force per undeformed area. The contribution acts as external load.
When Pore pressure is selected, the Absolute pressure drop down menu will always contain the entry User defined, in which case you manually enter a value or an expression for the absolute pressure pA. If there are other physics interfaces (like Darcy’s Law) that compute and announce a pressure variable, such variables are also present in the list. You can also enter a Reference pressure level pref, which is the pressure level at which the pore pressure does not give any stress contribution. Enter the Biot-Willis coefficient aB to specify the fraction of the pore pressure to use. As a default, its value is taken From material. Choose User defined to enter another value or expression. When using Pore pressure, there is no contribution to the stress tensor, the only effect of the pressure is as a load.
When In situ stress is selected, you enter the external stress in the form of Cauchy stress tensor. The tensor components are interpreted in the selected coordinate system. You can enter the data for the External stress tensor σext as Isotropic, Diagonal, or Symmetric. When using In situ stress, there are both contributions to the stress tensor, as well as a body load.
Selecting a stress tensor announced by the same physics interface as where the External Stress node is added, will result in an error (‘Circular variable dependency detected’). This operation would imply that the computed stress depends on itself.
You can use a stress tensor from the same physics interface, but a previous solution step. Select the User defined input type and enter expressions where the withsol operator is used to point to the intended solution.
Since all stress tensor representations coincide in a geometrically linear analysis, Stress tensor (Spatial) is needed only in the case of a geometrically nonlinear analysis. The stress tensor is entered using a Cauchy stress tensor representation, and is internally transformed to a Second Piola–Kirchhoff stress tensor.
The External stress subnode can be used to account for the effect of pore pressure in a porous material in a Layered Shell interface.
For an example of how the External Stress node is used to describe in situ stresses, see Deep Excavation: Application Library path
Geomechanics_Module/Soil/deep_excavation
Location in User Interface
Context Menus
Ribbon
Physics tab with Linear Elastic Material, Nonlinear Elastic Material, Elastoplastic Soil Material, Hyperelastic Material, or Shape Memory Alloy node selected in the model tree: