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The other conditions are classical. We start from (201), which is equivalent to (202). (203) is also valid. In (201) we note that 8Uij,j = 0 in Vaj if we set 8Pi = 0 on aV a outside A c, then 1. Set 8Pr = 8g = OJ this is the normal contact problem. We obtain, by the independence of the 8pz o ~ (u z + h)8pz = e8pz sub pz 2 o. If pz > 0 :::} 8pz is bilateral, and e = 0 (contact). If pz = 0 :::} 8pz 20, and e 2 0 (no contact). Here we define the contact ares as the region where pz > 0 ("Force" definition).

6 ~tsirn FASTSIM is an algorithm to determine the traction in the general case (notably nonvanishing ip). We recall Eq. (141), where we insert the simplified theoretic hypothesis: c+(u-u/)/k c + L(p - p/)/k, s where c creep Xl - X2 P present traction = (Pz[(x,y),t),py[(x,y),t)f previous traction = p(x + vk), t - k) p' We follow a particle on its path. At the leading edge a(y, t), p We work by induction. Suppose p' is known. What is p? p = p' = 0, that is, known. + (k/L)[s - c) On the right-hand side, only the slip s is unknown.

GLADWELL (1980), Contact problems in the classical theory of elasticity. Sijthoff and Noordhoff, Alphen aid Rijn, the Netherlands. [4] E. JAHNKE, F. EMDE (1943), Tables of functions. Dover publications, New York. L. JOHNSON (1959), The influence of elastic deformation upon the motion of a ball rolling between two surfaces. Proceedings of the Institution of Mechanical Engineers 173, p. 795-810. H. LOVE (1926), A treatise on the theory of elasticity. 4th Ed. Cambridge University Press. T. B. PIRES (1983), Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity.

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