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An Implicit Method for Frictional Contact, Impact and Rolling
Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization.
2005 (English)In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 24, no 6, p. 1016-1029Article in journal (Refereed) Published
##### Abstract [en]

In this paper an implicit method for frictional contact, impact and rolling is suggested. A nonclassical formulation of a two-dimensional hyperelastic body unilaterally constrained to rigid supports is proposed by following the ideas of Moreau and Jean. A total Lagrangian formulation of the system is given. The elastic properties are defined by coupling the second Piola–Kirchhoff stress to the Green–Lagrange strain via the Kirchhoff–St. Venant law. The equation of motion is written in the spirit of Moreau by using the mean value impulses introduced by Jean. The mean value impulses appear explicitly in the equation of motion. In such manner the treatment of nonconstant kinematic transformation matrices becomes straightforward. The rigid supports are described by smooth functions. By utilizing these functions and the mean value impulses, new contact/impact laws of Signorini and Coulomb type are formulated. The governing equations are solved by a nonsmooth Newton method. This is performed by following the augmented Lagrangian approach and deriving the consistent stiffness matrix as well as the contact stiffness matrices. Three two-dimensional examples are solved by the method: a contact problem, an impact problem and a rolling contact problem.

##### Place, publisher, year, edition, pages
2005. Vol. 24, no 6, p. 1016-1029
##### Keywords [en]
Dynamics, Finite elements, Large rotations, Frictional contact/impact, Newton's method
##### National Category
Mechanical Engineering Mechanical Engineering
##### Identifiers
OAI: oai:DiVA.org:hj-2435DiVA, id: diva2:33255
Available from: 2008-07-08 Created: 2008-07-08 Last updated: 2017-12-12Bibliographically approved

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Strömberg, Niclas

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JTH, Mechanical EngineeringJTH. Research area Engineering mechanics and optimization
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European journal of mechanics. A, Solids
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