Sangkyu Kim, Yong Hoon Jang, James R. Barber

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We consider discrete two-dimensional elastic systems with Coulomb friction contacts, and investigate the conditions that must be satisfied if these are to be capable of becoming ‘wedged’ --- i.e. of remaining with non-zero elastic deformations when all external loads have been removed. The condition for wedging is reduced to the requirement that a prescribed set of constraint vectors should fail to positively span the N-dimensional vector space of nodal displacements. We also show that the range of admissible wedged states increases monotonically with the coefficient of friction f and that there exists a unique critical coefficient fw such that wedging is impossible for f < fw and possible for f > fw.


Wedging, Coulomb Friction, Positive Span, Contact Mechanics

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Zhechev, M.M., Khramova, M.V., 2008, Geometrical conditions for wedging in mechanical systems with Coulomb friction, Journal of Mechanical Engineering Science, 223, pp. 1171–1179.

Mosemann, M., Wahl, F.M., 2001, Automatic decomposition of planned assembly sequences into skill primitives, IEEE Transactions on Robotics and Automation, 17(5), pp. 709–718.

Sturges, R.H., Laowattana, S., 1996, Virtual wedging in three-dimensional peg insertion tasks, Journal of Mechanical Design, 118(1), pp. 99–105.

Bickford, J.H., 2007, Introduction to the Design and Behavior of Bolted Joints: Non-Gasketed Joints, CRC Press, 4. Ed. Boca Raton.

Falkenberg, A., Drummen, P., Morlock, M.M., Huber, G., 2019, Determination of local micromotion at the stem-neck taper junction of a bi-modular total hip prosthesis design, Medical Engineering and Physics, 65, pp. 31–38.

Hassani, R., Hild, P., Ionescu, I.R., Sakki, N-D., 2003, A mixed finite element method and solution multiplicity for Coulomb frictional contact, Computer Methods in Applied Mechanics and Engineering, 192, pp. 4517–4531.

Hild, P., 2002, On finite element uniqueness studies for Coulomb’s frictional contact model, International Journal of Applied Mathematics and Computer Science, 12, pp. 41–50.

Hild, P., 2004, Non-unique slipping in the Coulomb friction model in two-dimensional linear elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 57, pp. 235–245.

Eck, C., Jarušek, J., 1998, Existence results for the static contact problem with Coulomb friction, Mathematical Models and Methods in Applied Sciences, 8(3), pp. 445–468.

Haslinger, J., Nedlec, J.C., 1983, Approximation of the Signorini problem with friction, obeying the Coulomb law, Mathematical Methods in the Applied Sciences, 5(1), pp. 422–437.

Barber, J.R., Hild, P., 2006, On wedged configurations with Coulomb friction, in: Wriggers P., Nackenhorst U., (Eds.), Analysis and Simulation of Contact Problems, Springer-Verlag, Berlin, pp. 205–213.

Dundurs, J., Stippes, M., 1970, Role of elastic constants in certain contact problems, ASME Journal of Applied Mechanics, 37(4), pp. 965–970.

Thaitirarot, A., Flicek, R.C., Hills, D.A., Barber, J.R., 2014, The use of static reduction in the finite element solution of two-dimensional frictional contact problems, Journal of Mechanical Engineering Science, 228, pp. 1474–1487.

Flicek, R.C., Brake, M.R.W., Hills, D.A., 2017, Predicting a contact’s sensitivity to initial conditions using metrics of frictional coupling, Tribology International, 108, pp. 95-110.

Klarbring, A., 1999, Contact, friction, discrete mechanical structures and discrete frictional systems and mathematical programming, in: Wriggers P., Panagiotopoulos P. (Eds.) New Developments in Contact Problems, Springer, Wien, pp. 55–100.

Andersson, L-E., Barber, J.R., Ahn Y-J, 2013, Attractors in frictional systems subjected to periodic loads, SIAM Journal of Applied Mathematics, 73, pp.1097–1116.

Ahn, Y-J., Bertocchi, E., Barber, J.R., 2008, Shakedown of coupled two-dimensional discrete frictional systems, Journal of the Mechanics and Physics of Solids, 56(12), pp. 3433–3440.

Regis, R.G., 2016, On the properties of positive spanning sets and positive bases, Optimization and Engineering, 17(1), pp. 229–262.

Davis, C., 1954, Theory of positive linear dependence, American Journal of Mathematics, 76, pp. 733–746.



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