Study of an elastoplastic model with an infinite number of internal degrees of freedom

We treat the dynamical behavior of the continuous elastoplastic model of Masing, consisting of an infinite number of springs and dry-friction elements. Using the theory of differential inclusions we prove existence and uniqueness result. Moreover, we prove that the continuous model is the limit of the discrete Masing model when the number of degrees of freedom tends to infinity. Starting from known results of numerical analysis, we build an implicit Euler-like numerical scheme of order one.