## Calculations - Slow Soil Penetration

This calculation shows the penetration of a soil by an object. We offer this type of calculation as a consultancy service; the calculation is not possible with the regular Tochnog Professional as distributed to users.

The object stiffness is high relative to the soil stiffness, and thus the object is taken to be rigid (it is not allowed to deform). The soil itself is contained in a rectangular box.

The object is pushed downward into the soil. The calculation is done dynamically, mass inertia is taken into account. The soil is modeled as an elasto-plastic material, using the mohr-coulomb shear failure condition. The soil stiffness is modeled with a power law, which accounts for small stiffness at low stress levels and higher stiffness at high stress levels. An implicit time stepping scheme is used to control non-linear unbalance errors of the numerical calculation. The velocity of the object is small compared to rockets penetrating plates or soils, so that mass inertia is small relative to material stiffness, which makes this a more difficult calculation. Moreover, the very large deformations cannot be covered by a classical Lagrange finite element method; we use a specially adapted Arbitrary Eulerian Lagrangian method to handle the large deformations.

When you click on the picture below you will see a movie of the rectangle penetrating the soil. It can be seen that at the top surface soil is pushed upwards, so the free surface line is being modeled. Also notice that when the object is completely pushed into the soil, the left behind opening is filled again by soil flowing back.