The stress divergence kernel handles the calculation of the residual, , from the governing equation and the calculation of the Jacobian. From the strong form of the governing equation for mechanics, neglecting body forces, (1) the weak form, using Galerkin's method and the Gauss divergence theorem, becomes (2) in which is the test function. The second term of the weak form equation is the residual contribution calculated by the stress divergence kernel.

The calculation of the Jacobian can be approximated with the elasticity tensor if the simulation solve type is JFNK:

(3) which is nonzero for .

If the solve type for the simulation is set to NEWTON the finite deformation Jacobian will need to be calculated. Set the parameter use_finite_deform_jacobian = true in this case.

note:Use of the Tensor Mechanics Master Action Recommended

The use_displaced_mesh parameter must be set correcting to ensure consistency in the equilibrium equation: if the stress is calculated with respect to the deformed mesh, the test function gradients must also be calculated with respect to the deformed mesh. The Tensor Mechanics MasterAction is designed to automatically determine and set the parameter correctly for the selected strain formulation. We recommend that users employ the Tensor Mechanics MasterAction whenever possible to ensure consistency between the test function gradients and the strain formulation selected.