  Discrete simulation methods are efficient tools to investigate the complex
behaviors of complex fluids made of either dry granular materials or dilute
suspensions. By contrast, materials made of soft and/or concentrated units
(emulsions, foams, vesicles, dense suspensions) can exhibit both significant
elastic particle deflections (Hertz-like response) and strong viscous forces
(squeezed liquid). We point out that the gap between two particles is then not
determined solely by the positions of their centers, but rather exhibits its
own dynamics. We provide a new discrete numerical method, named Soft Dynamics,
to simulate the combined dynamics of particles and contacts. As an
illustration, we present the results for the approach of two particles. We
recover the scaling behaviors expected in three limits: the Stokes limit for
very large gaps, the Poiseuille-lubricated limit for small gaps and even
smaller surface deflections, and the Hertz limit for significant surface
deflections. Larger scale simulations with this new method are a promising tool
for investigating the collective behaviors of many complex materials.
