Differences in masses inferred from dynamics, such as velocity dispersions or X-rays, and those inferred from lensing are a generic prediction of modified gravity theories. Viable models however must include some non-linear mechanism to restore General Relativity (GR) in dense environments, which is necessary to pass Solar System constraints on precisely these deviations. In this paper, we study the dynamics within virialized structures in the context of two modified gravity models, f(R) gravity and DGP. The non-linear mechanisms to restore GR, which f(R) and DGP implement in very different ways, have a strong impact on the dynamics in bound objects; they leave distinctive signatures in the dynamical mass-lensing mass relation as a function of mass and radius. We present measurements from N-body simulations of f(R) and DGP, as well as semi-analytical models which match the simulation results to surprising accuracy in both cases. The semi-analytical models are useful for making the connection to observations. Our results confirm that the environment- and scale-dependence of the modified gravity effects have to be taken into account when confronting gravity theories with observations of dynamics in galaxies and clusters.

18 pages, 16 figures; submitted to PRD; v2: typos corrected, references added, minor additions (Sec. IID)