Contact stresses: a short survey of models and methods of computations |
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Authors: | Alfred Zmitrowicz |
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Institution: | (1) Mechanics and Aerospace Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, Canada, M5S 3G8 |
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Abstract: | Contact stresses are identified as normal and tangential forces between contacting solids. The normal stresses are modeled
using unilateral and complementary conditions, elastic response and normal compliance. Friction laws describe the tangential
traction. Friction of materials depends on pressure, sliding velocity, surface temperature, time of contact, surface roughness
and presence of wear debris. Phenomenological, micro-mechanical and atomic-scale models as well as non-classical models of
anisotropic and heterogeneous friction are important steps in the development of friction modeling. Sophisticated friction
models are desirable in vibrating systems, materials processing, rolling contacts, rubber and polymers, geomechanics, bioengineering
and living systems. Main numerical methods in contact mechanics are: finite element method, boundary element method and discrete
element method. To include specific contact constraints, the following computing techniques are applied: Lagrange multipliers,
penalty function, perturbated and augmented Lagrangian methods, mathematical programming methods. The advances of adhesion
and impact modeling are outlined in this paper. |
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Keywords: | |
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