Many-body interactions in soft jammed materials.

In jammed packings of soft frictionless particles such as foams or emulsions, stress is transmitted via a network of mechanical contacts between neighbors. In generic simplified models of such materials, particle interaction energies are assumed to be pairwise additive. We report ab initio simulations of foam microstructures, showing that in general, this fundamental assumption is not justified: the conservation of bubble volumes introduces a many-body coupling between all the contacts of a given particle. It strongly modifies the relation between forces and displacements at individual contacts, in a way that cannot be captured by an effective two-body interaction. We report the impact of this effect on the linear and nonlinear elastic response of ordered bubble packings with coordination numbers ranging from 6 to 12, used as simple model systems, and we present an analytical model without free parameters which is valid as long as bubbles have an approximately spherical shape. It predicts the many-body coupling of particle contact forces, as well as the macroscopic mechanical response. For packing fractions approaching the jamming transition where contact forces go to zero, we derive an asymptotic two-body interaction law. It contains a logarithmic term, yielding a critical scaling that cannot be approximated by a power law.