Application of the material force method to isotropic continuum damage

Computational Mechanics

Volumn 30, Issue 3, 2003, Pages 171-184

  Liebe, T ^a   Denzer, R ^a   Steinmann, P ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Computational damage mechanics; Finite element method; Material force method

Indexed keywords

DEFECTS; FINITE ELEMENT METHOD; GALERKIN METHODS; KINEMATICS; MATERIALS SCIENCE;

COMPUTATIONAL DAMAGE MECHANICS;

CONTINUUM MECHANICS;

EID: 0037298494     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0377-0     Document Type: Article

References (33)

1. Braun M (1997) Configurational forces induced by finite-element discretization. Proc. Estonian Acad. Sci. Phys. Math. 46: 24-31
2. Chadwick P (1975) Applications of an energy-momentum tensor in non-linear elastostatics. J. Elasticity 5: 249-258
3. Denzer R, Earth FJ, Steinmann P (2002) Studies in elastic fracture mechanics based on the material force method. Int. J. Num. Meth. Eng. (accepted)
4. Ericksen JL (1998) On nonlinear elasticity theory for crystal defects. Int. J. Plasticity 14: 9-24
5. Eshelby JD (1951) The force on an elastic singularity. Pilosophical Trans. Royal Soc. London A, 244: 87-112
6. Eshelby JD (1975) The elastic energy-momentum tensor. J. Elasticity 5: 321-335
7. Florez-Lopez J, Benallal A, Geymonat G, Billarden R (1994) A two-field finite element formulation for elasticity coupled to damage. CMAME, 114: 193-212
8. Gurtin ME (1999) Configurational Forces as Basic Concepts of Continuum Physics, Springer, New York
9. Hutchinson JW (1968) Plastic stress and strain fields at a crack tip. J. Mech. Phys. Solids 16: 109-114
10. Kuhl E, Steinmann P (2002) On spatial and material settings of thermo-hyperelastodynamics for open systems. Acta Mechanica (accepted)
11. Liebe T, Steinmann P (2001) Theory and numerics of a thermomechanically consistent framework for geometrically linear gradient plasticity. Int. J. Num. Meth. Eng. 51: 1437-1467
12. Liebe T, Steinmann P, Benallal A (2001) Theoretical and computional aspects of a thermodynamically consistent framework for geometrically linear gradient damage. Comp. Meth. Appl. Mech. Eng. 190: 6555-6576
13. Luenberger D (1973) Introduction to Linear and Non-linear Programming. Addison-Wesley Pub., Reading Massachusetts
14. Maugin GA (1993) Material Inhomogeneities in Elasticity. 1st edn. Chapman & Hall, London
15. Maugin GA (1995) Material forces: Concepts and applications. Appl. Mech. Rev. 48: 213-245
16. Maugin GA (1996) Canonical momentum and energy in elastic systems with additional state variables. C. R. Acad. Sci. Paris 323IIb: 407-412
17. Maugin GA (1997) Thermomechanics of inhomogeneous-heterogeneous systems: Applications to the irreversible progress of two- and three-dimesional defects. ARI 50: 41-56
18. Maugin GA (2000) Geometry of material space: Its consequences in modern computational means. Technische Mechanik 20: 95-104
19. Maugin GA (2000) On the universality of the thermomechanics of forces driving singular sets. Arch. Appl. Mech. 70: 31-45
20. Maugin GA, Trimarco C (1992) Pseudomomentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture. Acta Mechanica 94: 1-28
21. M̈ller R, Rolling S, Gross D (2002) On Configurational forces in the context of the Finite Element method. IJNME 53:1557-1574
22. Müller R, Maugin GA (2002) On material forces and Finite Element discretization. Comp. Mech. 29: 52-60
23. Pinsky PM (1987) A finite element formulation for elastoplasticity based on a three-field variational equation. Comput. Meth. Appl. Mech. Eng. 61: 41-60
24. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35: 379-386
25. Rice JR, Rosengren GF (1968) Plane strain deformation near a crack tip in a power-lax hardening material. J. Mech. Phys. Solids 16: 1-16
26. Shield RT (1967) Inverse deformation results in finite elasticity. ZAMP 18: 490-500
27. Simo JC, Ju J (1987) Strain- and stress-based continuum damage models: I. formulation. Int. J. Solids Struct. 23: 821-840
28. Simo JC, Kennedy JG, Taylor RL (1989) Complementary mixed finite element formulations for elastoplasticity. Comput. Meth. Appl. Mech. Eng. 74: 177-206
29. Steinmann P (2000) Application of material forces to hyperelastostatic fracture mechanics. Part I: continuum mechanical setting. Int. J. Solids Struct. 37: 7371-7391
30. Steinmann P (2002) On spatial and material settings of hyperelastodynamics. Acta Mechanica 156: 193-218
31. Steinmann P (2002) On spatial and material settings of thermo-hyperelastodynamics. J. Elasticity 66: 109-187
32. Steinmann P, Ackermann D, Earth FJ (2001) Application of material forces to hyper-elastostatic fracture mechanics. Part II: computational setting. Int. J. Solids Struct. 38: 5509-5526
33. Williams ML (1957) On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24: 109-114