Initial Stresses and Strains
Initial stresses and strains refer to a stress and strain state that would exist even without the external loads. Initial stresses and strains are not initial values in the mathematical sense. They apply all through the solution, and may even vary with time or solution parameters. They should rather be considered as an offset to the stress and strain state in the constitutive relation.
The initial strain is subtracted from the total strain, before the constitutive law is applied for computing the stresses. The initial stress is added to the stress computed by using the constitutive law. As an example, linear elasticity including both in initial strain ε0 and an initial stress s0 can be written as
It can also be noted that the effect of the initial strain is analogous to, for example, a thermal strain or other inelastic strain contributions.
Use either the initial strain or the initial stress (but not both) when you have results from another analysis or another physics interface, which you want to incorporate into the stress-strain relation.
Both the initial stress and strain are tensor variables defined via components in the local coordinate system for each domain.
In case of nearly incompressible material (mixed formulation), the components of the total initial stress (that is, without volumetric-deviatoric split) are still input. The initial pressure in the equation for the pressure help variable pw is computed as
In the case of geometric nonlinearity, the initial stress represents the second Piola–Kirchhoff stress, not the Cauchy stress. The initial strain is interpreted as a Green–Lagrange strain.
Other Possible Uses of Initial Strains and Stresses
Many inelastic effects in solids mechanics (for example creep, plasticity, damping, viscoelasticity, poroelasticity, and so on) are represented by additive contributions to either the total strain or total stress. Then the initial value input fields can be used for coupling the elastic equations (solid mechanics) to the constitutive equations (usually General Form PDEs) modeling such extra effects. When adding stress contributions, you may however find it more convenient to use the External Stress concept.
The Initial Stress and Strain node can be added to Linear Elastic Material, Nonlinear Elastic Materials, Piezoelectricity, Elastoplastic Soil Models, Magnetostriction, or Shape Memory Alloy materials.