In the dynamic analysis of structural engineering systems, it is common practice to introduce additional damping models to reproduce some of the features observed experimentally. We report here on a preliminary work towards an alternative path for material damping, that aims at reproducing these features through the consideration only of the heterogeneous character of the yield stress field. The heterogeneity is parameterized by a stochastic model, controlled by three parameters only: a mean value, a variance parameter and a correlation length. For a single-degree-of-freedom elasto-plastic system with linear kinematic hardening, we show that such a variability indeed creates the patterns that are classically associated to viscous damping, and that would otherwise be modeled through nonlinear hardening, local hysteresis loops or other such complex constitutive models. A quasi-static force-displacement experiment and the dynamic bending response of a cantilever beam are presented as illustration.