A mathematical study of the plasticity effects in muscle contraction

Hill's three-element model of contracting muscle is expanded by replacing the series and the parallel elastic elements with elastoplastic elements. The contractile element is structurally described making use of the sliding filament theory. The resulting mathematical model is formulated in terms of an evolution variational inequality for a nonlinear and nonlocal transport-type operator. The existence and uniqueness of the solution are described along with a numerical approach.This work was supported by M.P.I. (fondi per la ricerca scientifica) and by I.A.N. of C.N.R. Pavia.