Wear and Contact Mechanics by Luis Rodríguez-tembleque

By Luis Rodríguez-tembleque

This publication involves the edited types of the papers awarded on the moment overseas convention on Computational tools in touch Mechanics, which was once held in Ferrara, Italy, July 11-13, 1995. the significance of touch mechanics to engineering layout has lengthy been famous. because of nice advances in trendy machine expertise and computational examining ideas, it truly is attainable to unravel complicated touch difficulties related to numerous our bodies. touch difficulties are computationally tough as they're inherently nonlinear. This nonlinearity is because of the relocating boundary and the lifestyles of friction alongside the touch surfaces. Papers inside of this publication current mechanical types together with rolling, impression, surprise and unilateral touch; numerical versions reminiscent of the finite aspect version, boundary aspect approach and essential equations; engineering purposes comparable to fracture mechanics and composite fabrics, in addition to mathematical types.

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Enforcement of the contact conditions The behaviour at the contact interface is governed by the non-penetration condition in the normal direction to the contact zone and the frictional tribological law in the tangential direction. The tribological model used in this work is the Coulomb friction law, a common engineering approximation to the frictional process where normal and tangential tractions are coupled by the normal pressure. When applying the contact conditions, one difficulty reside in the fact that the contact restrictions are expressed by a group of equalities and inequalities, resulting in a constrained problem.

R2 −→ R2 in the following way { [x, y]T if x2 + y 2 ≤ g 2 T PCg (x, y) = (11) √ 2g 2 [x, y] otherwise x +y and introduce the augmented tangential multiplier variable λt (r) = λt + rkt (12) Key Engineering Materials Vol. 618 29 Fig. 3: Exploded view with sign criteria used for the Lagrange multipliers and contact forces in a FEM-FEM contact zone. A relative motion of the two substructures in the indicated direction will produce represented signs on contact forces. e. PCg (λt (r)) = λt (13) obtaining again a strictly non-differentiable function at the stick-slip frontier but with computable directional derivative at that point.

Later, Gonz´alez et al. [21, 22] allowed the contact frame to separate from the substructures in all directions, making the frame a completely free system between the substructures that moves maintaining the contact zone as an unknown. Differences in this work were also in the way of finding the contact states, because the contact conditions were imposed mathematically using an augmented Lagrangian formulation with projection functions, making the trial and error contact search unnecessary. In contact problems the region of interest is usually restricted to a local area around the contact zone where stress concentration with locally plastic deformations can occur, while extensive parts of the solid remain almost unloaded.

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