Sound production in musical instruments is the consequence of interactions and wave propagation that include nonlinear phenomena. Simulating these phenomena will enable sound synthesis softwares (such as Modalys, developed at IRCAM) to produce more realistic sounds. In order to do so, nonlinear physical models will be implemented in Modalys software using Green-Volterra kernels. Green-Volterra kernels are used to simulate space-time non-linear dynamical problems. This formalism allows to keep the modal approach and simulate nonlinear dynamics until a given order in the Green-Volterra series. This numerical method has been chosen in order to keep ”near real-time” computation time. Interactions solving requires to compute the inverse problem, i.e. compute a force using known displacement or velocity. Green-Volterra kernels of a nonlinear string model and interaction definition will be presented with associated numerical results.