A variety of complex fluids consist in soft, round objects (foams, emulsions,
assemblies of copolymer micelles or of multilamellar vesicles -- also known as
onions). Their dense packing induces a slight deviation from their prefered
circular or spherical shape. As a frustrated assembly of interacting bodies,
such a material evolves from one conformation to another through a succession
of discrete, topological events driven by finite external forces. As a result,
the material exhibits a finite yield threshold. The individual objects usually
evolve spontaneously (colloidal diffusion, object coalescence, molecular
diffusion), and the material properties under low or vanishing stress may alter
with time, a phenomenon known as aging. We neglect such effects to address the
simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully
tensorial, rheological model, equivalent to the (scalar) Bingham model.
Importantly, the model consistently describes the ability of such soft
materials to deform substantially in the elastic regime (be it compressible or
not) before they undergo (incompressible) plastic creep -- or viscous flow
under even higher stresses.Comment: 69 pages, 29 figure