On higher complexity for interface/contact laws with arbitrary anisotropy - development of numerical models and their experimental validations.

• Antragsteller: Professor Dr.-Ing. Karl Schweizerhof
• Fachliche Zuordnung: Mechanik
• Förderung: Förderung von 2009 bis 2014
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 133672527

• Erstellungsjahr: 2016

Zusammenfassung der Projektergebnisse

According to the initial goals and the final developments of the project, the following specific findings can be summarized: • Any specific law known in continuum mechanics can be incorporated for the contact interface law. In order to perform this, the relationships are formulated in a covariant form in special coordinate system inherited with the geometry of contact bodies. This generalization allows a much deeper understanding of contact interfaces than the standard Coulomb friction law. • A special convex function is a final characteristic of the interface law. Afterwards, the solution of the principle of maximum dissipation provided in the special curvilinear coordinate system leads to an effective numerical algorithm involving the return-mapping scheme in order to compute the forces and displacements for both the elastic procedure for contact interfaces (“sticking”) and the plastic procedure “sliding”. The result is shown on the experimentally proved contact interface law including: a) the linear elastic part – “static sticking”; b) the softening inelastic part – “threshold value sticking/sliding” and c) the asymptotic part – “dynamic sliding”. • Any contact interface is characterized at least by its structural part and its sliding part, besides the commonly used standard friction such as the Coulomb friction law. On the scale of the interface law formulated via the surface coordinate system, the structural part is characterized by the structural/elastic tensor. This tensor describes the geometrical structure of the surface such as asperities or specific surface geometry after the manufacturing. The sliding part is the characteristic of the stresses/forces computed, or measured during the interaction process. This part can be given by the friction tensor. • The verification process for an interface law including both structural and sliding part is a two scale modeling. The first scale model is provided on the interface and gives the surface characteristic in terms of structural and frictional surface tensor e.g. for anisotropic interface. The characteristics of this model are high numerical efficiency due to the small model (several unknown variables) speeding up the computations. • The second scale modeling is an exact finite element model of the contact interface in terms of the geometry of small asperities or manufactured surfaces. The characteristic is a precise geometry of the contact interface, but low numerical efficiency due to the dimension of the problem – up to several thousand and millions unknown variables. • The two-scale approach has proved numerically the limits and possibilities of a first scale model. • The Nitsche approach is formulated in a geometrically exact fashion as an alternative approach allowing to satisfy exactly the non-penetration condition ξ 3 = 0. • Numerically the Nitsche approach is split into the Gauss point-wise substituted Lagrange multiplier approach (characterized by a high sensitivity to the selection of the order for the Gauss integration) and into the Bubnov-Galerkin-wise partial substituted Lagrange multiplier approach (characterized by a special integration technique in order to determine the Lagrange multipliers locally at each element). This allows to solve the corresponding saddle-problem locally at each element. • A Large Penetration (LP) scheme is a special development in order to allow large load steps during the simulation (penetration is comparable with the characteristic size of the contacting bodies). The initial development for the non-frictional problems allows to reduce the amount of total iterations during the solution process. • The equivalent mechanical system method is the generalization of the LP-scheme efficiency from the non-frictional problem to arbitrary interface problems. The problem is split into a two-phase system which is equivalent to the original one. The first phase is an easily solvable, but simplified system, and the second phase is an original system. A special rule formulated by means of the mechanical equivalency (e.g. softening normal spring or moving tangential spring) allows to introduce a split in an effective manner keeping the speed of computation for both phases. • The special generalization of the interface law into anisotropic friction for curve-to-surface contact pairs requires a covariant formulation using the special Darboux coordinate system of a contact surface. This development allows to generalize the Euler problem (1786) for a rope of a frictional cylinder into the problem for a rope on an orthotropic frictional surface of arbitrary geometry. The problem is solved in the closed form. In addition, the formulated new variational equations can be used directly for numerical “curve-to-surface” contact algorithms.

Projektbezogene Publikationen (Auswahl)

• Implementation of the Nitsche approach for various contact kinematics. PAMM, 2010, 10(1) 169–170
  Izi R., Konyukhov A., Schweizerhof K.
  
• Verification of an anisotropic Coulomb adhesionfriction law for contact surfaces with periodic structure. PAMM, 2010; 10(1) 215–216
  Schmied Ch., Konyukhov A., Schweizerhof K.
  
• On a geometrically exact theory for contact interactions, PAMM, 2011, 11 (1), 959–960
  Konyukhov A., Schweizerhof K.
  
• On a Geometrically Exact Theory for Contact Interactions. In book: Lecture Notes in Applied and Computational Mechanics (G. Zavarise and P. Wriggers (Eds.)), Springer, Berlin, Heidelberg, 2011, 58, 41–56
  Konyukhov A., Schweizerhof K.
  
• On different variational formulations of the Nitsche method. In book: Recent Developments and Innovative Applications in Computational Mechanics (D. Mueller-Hoeppe, S. Loehnert, S. Reese (Eds.)), Springer, Berlin, Heidelberg, 2011, 29–38
  Izi R., Konyukhov A., Schweizerhof K.
  
• Large Penetration Algorithm for 3D Frictionless Contact Problems Based on a Covariant Form. Computer Methods in Applied Mechanics and Engineering, 2012, 217–220, 186–196
  Izi R., Konyukhov A., Schweizerhof K.
  
• 3D Frictionless contact problems with large load-steps based on the covariant description for higher order approximation. Engineering Structures, 50, 107–114, 2013
  Izi R., Konyukhov A., Schweizerhof K.
  
• Contact of ropes and orthotropic rough surfaces. ZAMM, Z. Angew. Math. Mech., 1-18 (2013)
  Konyukhov A.
  
• Geometrically Exact Theory of Contact Interaction – Further developments and Achievements. Scientific Research, Open Access Journal, 15–20, Pub. Date: July 11, 2013
  Konyukhov A., Schweizerhof K.
  
• On a geometrically exact theory for contact interactions. In book: Recent Advances in Contact Mechanics, Lecture Notes in Applied and Computational Mechanics, Ed. G.E. Stavroulakis, Springer, 2013, 56 (4), 31–44
  Konyukhov A., Schweizerhof K.
  
• Contact of ropes and orthotropic rough surfaces. PAMM, 2014 (14), 225–226
  Konyukhov A.
  
• Geometrically exact theory of contact interactions a general approach with a special focus on curve-to-surface contact. GAMM-Mitteilungen, Wiley-VCH, 37 (1), 7-26
  Konyukhov A., Schweizerhof K.