Author: Vicente Mataix Ferrándiz
Kratos version: Current head
Source files: Full Hertz
Two meshes are avalaible, a fine mesh as well as a coarser one.
In this test case, we will consider the contact between a demi-sphere and a rigid plane, what is known as Hertz benchmark test. The reference solutions have been taken from the analytical solution of Hertz's work that can be found in the reference section.
The following applications of Kratos are used:
- StructuralMechanicsApplication
- ContactStructuralMechanicsApplication
The problem geometry as well as the boundary conditions are sketched below.
We consider the a sphere of 12.2474 meters of diameter with a load of 1.0e3 Pa.
The structure characteristic parameters are for the spheres:
- Elastic modulus upper body (E1): 1.0E+08 Pa
- Poisson ratio upper body(ν1): 0.29
- Elastic modulus lower body (E2): 1.0E+06 Pa
- Poisson ratio lower body (ν)2: 0.29
The calculation is done in just one static step.
The problem stated above has been solved using an structured mesh of hexahedron. The resulting deformation can be seen in the following image.
As well as the comparation with the reference solution. We will compare the the radius of the contact area and the maximum contact pressure.
- F: 1.0e3 · π · 12.2474^2 = 150000/4 · π = 117808,787 N
- a: 0.6301 vs 0.627 -> 0.5% error
- Pmax: 1.41641e5 vs 1.435467 -> 1.3% error