Contact stressed between two elastic solid bodies. Non-linearity is introduced by the fact that the area of contact is not known in advance but
ais a part of the solution.
Physics and modelling
Contact problem between two linear elastic solids. The material behaviour is modelled using the linear (Hookean) stress-strain relationship
and the assumption of small deformations.
Finite Volume stress analysis, while insignificantly small compared to the FEM equivalent FEM methods, offers several interesting advantages when applied to
non-linear problems. The segregated solution algorithm deals with non-linearity in a natural and stable way and offers the prospect of significantly reduced cost
of simulation. The problem under consideration is the simplest form of non-linearity, introduced by the fact that the area of force transfer (contact) needs to be
determined as a part of the solution. Here, we have incorporated the surface-to-surface interaction tools available in the OpenFOAM library into the standard FV
stress analysis solver, stressedFoam and incorporated the update of the contact area into the iteration loop. The result is a quick and robust contact stress analysis
solver.
The test case consists of a cylindrical surface in contact with a flat surface, where both sides deform under the uniform pressure load applied from the top. The
test case does not involve friction forces between the two surface, although their addition would be straightforward.
OpenFOAM solver
contactStressFoam
Images and animations
The pictures below show the deformed geometry and the stress isolines in the two bodies. Notice the smooth transition of the stress between
the two bodies as well as the fact that the solution has been obtained on non-matching surface meshes.
Figure 3:
Deformed geometry.
Figure 4:
Normal stress distribution.
Figure 5:
Equivalent stress distribution.
The final picture shows the application of the contact stress methodology to a dynamic crack propagation problem. The test case consists of a titanium striker hitting a plastic
specimen with an initialized crack at the plane of symmetry. The specimen is supported on two steel cylinders and the impact speed is 1 m/s. The figure shows the
distribution of normal stresses and clearly indicates the region of contact. Simulation and results courtesy of Dr. Vlado Tropsa , Imperial College of Science, Technology and
Medicine, London. http://www.me.ic.ac.uk.
Figure 6:
Impact test.
Author
Simulation by Nabla Ltd. and Dr Vlado Tropsa of Imperial College of Science, Technology and Medicine, London.
