21. In this test, the only non-zero component of the stress tensor is T 11. 22. This proves that the first Piola Kirchhoff stress tensor is "'not objective " '. 23. The 1st Piola Kirchhoff stress tensor , \ boldsymbol { P } is one possible solution to this problem. 24. Where I is the 3 x 3 identity matrix and \ boldsymbol \ tau is the deviatoric stress tensor . 25. However, the stress tensor still has some important uses, especially in formulating boundary conditions at fluid interfaces. 26. In this case the differential equations that define the stress tensor are linear, and the problem becomes much easier. 27. These constraints on the stress tensor are known as the " Beltrami-Michell " equations of compatibility: 28. A exact solutions that are non-vacuum solutions, solutions in which the stress tensor is non-zero. 29. From this, the stress tensor of the system can be calculated and usually is calculated by the numerical package. 30. Here we consider a three-dimensional Oldroyd-B model coupled with the momentum equation and the total stress tensor .
