A hyperelastodynamic ALE formulation based on referential, spatial and material settings of continuum mechanics

Acta Mechanica

Volumn 174, Issue 3-4, 2005, Pages 201-222

  Kuhl, E ^a,b   Steinmann, P ^a  

^a University of Kaiserslautern ^*

^b University of Koblenz Landau   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; FLUID MECHANICS; HAMILTONIANS; LAGRANGE MULTIPLIERS; METAL FORMING; PROBLEM SOLVING; THEOREM PROVING;

HYPERELASTODYNAMICS; REYNOLD'S TRANSPORT THEOREM; SPATIAL COORDINATES; VARIATIONAL ARBITRARY LAGRANGIAN EULERIAN (ALE);

CONTINUUM MECHANICS;

EID: 15544385498     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-004-0200-4     Document Type: Article

References (41)

1. Armero, F., Love, E.: An arbitrary Lagrangian-Eulerian finite element method for finite strain plasticity. Int. J. Num. Meth. Eng. 35, 737-766 (2003).
2. Askes, H.: Advanced spatial discretisation strategies for localized failure. Mesh adaptivity and meshless methods. Ph.D. thesis, Technische Universiteit Delft, Delft, The Nederlands 2000.
3. Askes, H., Bargmann, S., Kuhl, E., Steinmann, P.: Structural optimization by simultaneous equilibration of spatial and material forces. Accepted for publication (2004).
4. Askes, H., Kuhl, E., Steinmann, P.: An ALE formulation based on spatial and material settings of continuum mechanics. Part 2: Classification and applications. Comp. Meth. Appl. Mech. Eng. 193, 4223-4245 (2004).
5. Askes, H., Sluys, L. J.: Remeshing strategies for adaptive ALE analysis of strain localisation. Eur. J. Mech. / A: Solids 51, 447-467 (2000).
6. Belytschko, T., J. M. Kennedy, J. M.: Computer models for subassembly simulation. Nuclear Eng. Design 49, 17-38 (1978).
7. Belytschko, T., Liu, W. K., Moran, B.: Nonlinear finite element analysis for continua and structures. Wiley 2000.
8. Braun, M.: Configurational forces induced by finite-element discretization. Proc. Estonian Acad. Sci. Phys. Math. 46, 24-31 (1997).
9. Braun, M.: Structural optimization by material forces. In: Mechanics of material forces (Steinmann, P., Maugin, G. A., eds.). Kluwer 2003.
10. Donéa, J.: Finite element analysis of transient dynamic fluid-structure interaction. In: Advanced structural dynamics (Donéa, J., ed.), pp. 255-290. London: Applied Science Publishers 1980.
11. Donéa, J.: Arbitrary Lagrangian Eulerian finite element methods. In: Computer: methods for transient analysis (Belytschko, T., Hughes, T. J. R., eds.), pp. 473-516. Amsterdam: Elsevier 1983.
12. Donéa, J., Fasoli-Stella, P., Giuliani, S.: Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems. In: Trans. 4th Int. Conf. on Structural Mechanics in Reactor Technology - Vol. B: Thermal and Fluid/Structure Dynamics Analysis (Jaeger, T. A., Boley, B. A., eds.), B 1/2, pp. 1-12. Amsterdam: North-Holland 1977.
13. Donéa, J., Giuliani, S., Halleux, J. P.: An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comp. Meth. Appl. Mech. Eng. 33, 689-723 (1982).
14. Donéa, J., Huerta, A.: Finite element methods for flow problems. New York Chichester: Wiley 2003.
15. Eshelby, J. D.: The force on an elastic singularity. Phil. Trans. Royal Soc. London 244, 87-112 (1951).
16. Eshelby, J. D.: The elastic energy-momentum tensor. J. Elasticity 5, 321-335 (1975).
17. Gurtin, M. E.: On the nature of Configurational forces. Arch. Rat. Mech. Anal. 131, 67-100 (1995).
18. Gurtin, M. E.: Configurational forces as basic concepts of continuum physics. New York: Springer 2000.
19. Hirt, C. W., Amsden, A. A., Cook, J. L.: An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comp. Phys. 14, 227-253 (1974).
20. Huerta, A., Liu, W. K.: Viscous flow with large free surface motion. Comp. Meth. Appl. Mech. Eng. 69, 227-324 (1988).
21. Hughes, T. J. R., Liu, W. K., Zimmermann, T. K.: Lagrangian-Eulerian finite element formulation for viscous flows. Comp. Meth. Appl. Mech. Eng. 29, 329-349 (1981).
22. Kienzler, R. Herrmann, G.: Mechanics in material space with applications to defect and fracture mechanics. New York: Springer 2000.
23. Kuhl, E., Askes, H., Steinmann, P.: An ALE formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation. Comp. Meth. Appl. Mech. Eng. 193, 4207-4222 (2004).
24. Kuhl, E., Denzer, R., Barth, F. J., Steinmann, P.: Application of the material force method to thermo-hyperelasticity. Comp. Meth. Appl. Mech. Eng. 193, 3303-3326 (2004).
25. Kuhl, E., Steinmann, P.: Computational modeling of healing: An application of the material force method. Biomech. Model. Mechanobiol. 2, 187-203 (2004).
26. Kuhl, E., Steinmann, P.: Material forces in open system mechanics. Comp. Meth. Appl. Mech. Eng. 193, 2357-2381 (2004).
27. Liu, W. K.: Finite element procedures for fluid-structure interactions and application to liquid storage tanks. Nuclear Eng. Design 65, 221-238 (1981).
28. Liu, W. K., Gvildys, J.: Fluid-structure interaction of tanks with an eccentric core barrel. Comp. Meth. Appl. Mech. Eng. 58, 51-77 (1986).
29. Maugin, G. A.: The thermomechanics of plasticity and fracture. Cambridge: Cambridge University Press 1992.
30. Maugin, G. A.: Material inhomogeneities in elasticity. London: Chapman 1993.
31. Maugin, G. A.: Material forces: concepts and applications. Appl. Mech. Rev. 48, 213-245 (1995).
32. Maugin, G. A.: The thermomechanics of nonlinear irreversible behaviors. Singapore: World Scientific 1999.
33. Maugin, G. A.: Geometry of material space: Its consequences in modern computational mechanics. Technische Mechanik 20, 95-104 (2000).
34. Mueller, R., Maugin, G. A.: On material forces and finite element discretizations. Comp. Mech. 29, 52-60 (2002).
35. Steinmann, P.: Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting. Int. J. Solids Struct. 37, 7371-7391 (2000).
36. Steinmann, P.: On spatial and material settings of hyperelastodynamics. Acta Mech. 156, 193-218 (2002).
37. Steinmann, P.: On spatial and material settings of hyperelastostatic crystal defects. J. Mech. Phys. Solids 50, 1743-1766 (2002).
38. Steinmann, P.: On spatial and material settings of thermo-hyperelastodynamics. J. Elasticity 66, 109-157 (2002).
39. Thoutireddy, P.: Variational arbitrary Lagrangian-Eulerian method. Ph.D. thesis, California Institute of Technology, Passadena, California. Available at http://etd.caltech.edu, 2003.
40. Thoutireddy, P., Ortiz, M.: A variational Arbitrary Lagrangian-Eulerian (VALE) method of mesh adaption and optimization in static finite element calculations. Int. J. Num. Meth. Eng. 53, 1337-1351 (2003).
41. Yamada, T., Kikuchi, F.: An arbitrary Lagrangian-Eulerian finite element method for incompressible hyperelasticity. Comp. Meth. Appl. Mech. Eng. 102, 149-177 (1993).