Transient three-dimensional domain decomposition problems: Frame-indifferent mortar constraints and conserving integration

International Journal for Numerical Methods in Engineering

Volumn 82, Issue 3, 2010, Pages 329-358

  Hesch, Christian ^a   Betsch, Peter ^a  

^a UNIVERSITY OF SIEGEN   (Germany)

Author keywords

Domain decomposition; Energy momentum; Mortar methods

Indexed keywords

AUGMENTATION TECHNIQUES; DEFORMATION DOMAIN; DISCRETIZATIONS; DOMAIN DECOMPOSITION; DOMAIN DECOMPOSITIONS; MORTAR METHODS; NUMERICAL EXAMPLE; NUMERICAL STABILITIES; THREE-DIMENSIONAL DOMAIN; THREE-DIMENSIONAL PROBLEMS;

CONVERGENCE OF NUMERICAL METHODS; MORTAR; PLASTER; THREE DIMENSIONAL;

DOMAIN DECOMPOSITION METHODS;

EID: 77950009195     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2767     Document Type: Article

References (40)

1. Quarteroni A, Valli A. Domain Decomposition Methods for Partial Differential Equations. Oxford Science Publications: Oxford, 1999.
2. Schwarz HA. Ü ber einen Grenzübergang durch alternierendes verfahren. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich 1870; 15:272-286.
3. Hackbusch W. Multi-Grid Methods and Applications. Springer: Berlin, 1985.
4. Wohlmuth BI. Discretization Methods and Iterative Solvers Based on Domain Decomposition. Springer: Berlin, 2000.
5. Widlund OB, Keyes DE (eds). Domain Decomposition Methods in Science and Engineering, vol. XVI. Lecture Notes in Computational Science and Engineering, vol. 55. Springer: Berlin, 2006.
6. Widlund OB, Keyes DE (eds). Domain Decomposition Methods in Science and Engineering, vol. XVII. Lecture Notes in Computational Science and Engineering, vol. 60. Springer: Berlin, 2008.
7. Hallquist JO, Goudreau GL, Benson DJ. Sliding interfaces with contact-impact in large-scale Lagrangian computations. Computer Methods in Applied Mechanics and Engineering 1985; 51:107-137.
8. Laursen TA. Computational Contact and Impact Mechanics. Springer: Berlin, 2002.
9. Wriggers P. Computational Contact Mechanics (2nd edn). Springer: Berlin, 2006.
10. El-Abbasi N, Bathe KJ. Stability and patch test performance of contact discretizations and a new solution algorithm. International Journal for Numerical Methods in Engineering 2001; 79:1473-1486.
11. Bernardi C, Mayday Y, Patera AT. Domain decomposition by the mortar method. In Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, Kaper H et al. (eds). Kluwer Academic Publishers: Dordrecht, The Netherlands, 1993; 269-286.
12. Bernardi C, Mayday Y, Patera AT. A new nonconforming approch to domain decomposition: the mortar element method. In Nonlinear Partial Differential Equations and their Applications, Brezis H, Lions JL (eds). Longman Scientific & Technical: Harlow, U.K., 1994; 13-51.
13. Krause R, Wohlmuth BI. Nonconforming domain decomposition techniques for linear elasticity. East-West Journal of Numerical Mathematics 2000; 8(3):177-206.
14. Dohrmann CR, Key SW, Heinstein MW. Methods for connecting dissimilar three-dimensional finite element meshes. International Journal for Numerical Methods in Engineering 2000; 47:1057-1080.
15. Heinstein MW, Laursen TA. A three dimensional surface-to-surface projection algorithm for non-coincident domains. Communications in Numerical Methods in Engineering 2003; 19:421-432.
16. Puso MA. A 3d mortar method for solid mechanics. International Journal for Numerical Methods in Engineering 2004; 59:315-336.
17. Puso MA, Laursen TA, Solberg J. A segment-to-segment mortar contact method for quadratic elements and large deformations. Computer Methods in Applied Mechanics and Engineering 2008; 197:555-566.
18. Yang B, Laursen TA, Meng X. Two dimensional mortar contact methods for large deformation frictional sliding. International Journal for Numerical Methods in Engineering 2005; 62:1183-1225.
19. Yang B, Laursen TA. A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulation. Computational Mechanics 2008; 41:189-205.
20. Hesch C, Betsch P. A comparison of computational methods for large deformation contact problems of flexible bodies. Zeitschrift für Angewandte Mathematik und Mechanik 2006; 86:818-827.
21. Gonzalez O. Time integration and discrete Hamiltonian systems. Journal of Nonlinear Science 1996; 6:449-467.
22. Gonzalez O. Mechanical systems subject to holonomic constraints: differential-algebraic formulations and conservative integration. Physica D 1999; 132:165-174.
23. Betsch P, Steinmann P. Conserving properties of a time FE method-Part II: time-stepping schemes for non-linear elastodynamics. International Journal for Numerical Methods in Engineering 2001; 50:1931-1955.
24. Betsch P, Steinmann P. Conservation properties of a time FE method. Part III: mechanical systems with holonomic constraints. International Journal for Numerical Methods in Engineering 2002; 53:2271-2304.
25. Armero F, Romero I. On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamics. Computer Methods in Applied Mechanics and Engineering 2001; 190:2603-2649.
26. Armero F, Romero I. On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II: second-order methods. Computer Methods in Applied Mechanics and Engineering 2001; 190:6783-6824.
27. Laursen TA, Chawla V. Design of energy conserving algorithms for frictionless dynamic contact problems. International Journal for Numerical Methods in Engineering 1997; 40:863-886.
28. Armero F, Petöcz E. Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems. Computer Methods in Applied Mechanics and Engineering 1998; 158:269-300.
29. Laursen TA, Love GR. Improved implicit integrators for transient impact problems-geometric admissibility within the conserving framework. International Journal for Numerical Methods in Engineering 2002; 53:245-274.
30. Hauret P, Le Tallec P. Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact. Computer Methods in Applied Mechanics and Engineering 2006; 195:4890-4916.
31. Haikal G, Hjelmstad KD. A finite element formulation of non-smooth contact based on oriented volumes for quadrilateral and hexahedral elements. Computer Methods in Applied Mechanics and Engineering 2007; 196:4690-4711.
32. Betsch P, Hesch C. Energy-momentum conserving schemes for frictionless dynamic contact problems. Part I: NTS method. In IUTAM Symposium on Computational Methods in Contact Mechanics, Wriggers P, Nackenhorst U (eds). IUTAM Bookseries, vol. 3. Springer: Berlin, 2007; 77-96.
33. Hesch C, Betsch P. A mortar method for energy-momentum conserving schemes in frictionless dynamic contact problems. International Journal for Numerical Methods in Engineering 2009; 77:1468-1500.
34. Hughes TJR. The Finite Element Method. Dover: New York, 2000.
35. Truesdell C, Noll W. The Non-Linear Field Theories of Mechanics (3rd edn). Springer: Berlin, 2004.
36. Antman SS. Nonlinear Problems of Elasticity (2nd edn). Springer: Berlin, 2005.
37. Betsch P, Uhlar S. Energy-momentum conserving integration of multibody dynamics. Multibody System Dynamics 2007; 17(4):243-289.
38. Simo JC, Wriggers P, Taylor RL. A perturbed lagrangian formulation for the finite element solution of contact problems. Computer Methods in Applied Mechanics and Engineering 1985; 50:163-180.
39. Hauret P, Le Tallec P. A discontinous stabilized mortar method for general 3D elastic problems. Computer Methods in Applied Mechanics and Engineering 2007; 196:4881-4900.
40. Gonzalez O. Exact energy and momentum conserving algorithms for general models in nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering 2000; 190:1763-1783.