A quasistatic model for an elastic, plastic, viscous foam
Résumé
We suggest a scalar model for deformation and flow a of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic strain, plastic deformation rate and total deformation rate; and three material specific parameters: shear modulus, yield strain and viscosity. We discuss the role of the elastic strain and of the yield function, as well as their link with the microscopical structure. The equations we obtain are quasi-static, that is, limited to deformations and flows slower than the relaxation rate towards mechanical equilibrium. But they are valid both in transient or steady flow regimes, even at large elastic strain; and we discuss why viscosity can be relevent even in this limit. Predictions of the storage and loss moduli agree well with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.