On the contact law of open-cell poro-granular materials

The contact stiffness between a poro-elastic spherical grain, made out of an open-cell foam, and a plane is studied with the aim of determining the contact law, and in particular verifying if the Hertz interaction potential, originally derived in the frame of continuum mechanics, holds. The contact law is studied experimentally by compressing a half-sphere of melamine foam into a rigid flat surface, and numerically by mean of a finite element model where the porous half-sphere is modeled by irregular tetrakaidecahedral cells. Both approaches reveal two regimes, at low and at high deformations in respect to the size of the cells. Above a cutoff value of the indentation, larger than the ligament length, a Hertzian interaction is observed. The latter is reliably described in terms of the radii of curvature of the contacting bodies and the effective elasticity of the foam structure. Below the cutoff, at the microscale, a more complex trend emerges because of the discrete nature of the foam and in particular the small number of ligaments in contact with the plane, which is function of the sphere radius at the macroscale and the cells shape at the mesoscale. Such microscopic features are akin to a surface roughness between continuous materials. These findings have practical implications to accurately describe the mechanical response of poro-granular media, used for instance in sound and vibration insulation.