Recently, the ''velocity accommodation'' concept was introduced in tri
bology. In third-body contacts, velocity accommodation can occur in fi
ve sites and according to four modes, giving rise to 20 possible combi
nations, i.e. 20 velocity accommodation mechanisms. The present paper
addresses the role of third and first bodies in elastic and/or plastic
deformations in velocity accommodation. For this, a simplified model
is first proposed to represent third-body contacts separated by wear d
ebris or solid lubricants. Then, by using the finite element method, t
he relative movement between first bodies in contact under different t
ypes of loading is simulated and the deformation of the model as well
as the stress and strain field in the third body is determined numeric
ally. Results quantify the role of the third and first bodies in eithe
r elastic or plastic deformation. When only relative tangential displa
cement is imposed, a simple analytical formula based upon a model of t
wo compliances in series is suggested in order to estimate the displac
ement accommodation of third and first bodies.