A new approach for modelling slip lines in geological materials with cohesive models

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 30, Issue 11, 2006, Pages 1159-1172

  Rabczuk, Timon ^a   Areias, P M A ^a  

^a Northwestern University   (United States)

Author keywords

Loss of hyperbolicity; Meshfree methods; Slip line; Traction separation laws

Indexed keywords

GALERKIN METHODS; MATHEMATICAL MODELS; TRACTION (FRICTION);

DRUCKER-PRAGER MATERIAL MODEL; SLIP LINES; TRACTION-SEPARATION LAWS;

CONTINUUM MECHANICS;

CONTINUUM MECHANICS; GALERKIN METHODS; MATHEMATICAL MODELS; TRACTION (FRICTION);

COHESION; CONTINUUM MECHANICS; DISCONTINUITY; DISPLACEMENT; GALERKIN METHOD; NUMERICAL MODEL;

EID: 33748268284     PISSN: 03639061     EISSN: 10969853     Source Type: Journal    
DOI: 10.1002/nag.522     Document Type: Article

References (35)

1. Belytschko T, Fish J, Englemann B. A finite element method with embedded localization zones. Computer Methods in Applied Mechanics and Engineering 1989; 70:59-99.
2. Armero F, Garikipati K. An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. International Journal of Solids and Structures 1996; 33(20-22):2963-2895.
3. Oliver J, Cervera M, Manzoli O. Strong discontinuities and continuum plasticity models: the strong discontinuity approach. International Journal of Plasticity 1999; 15:319-351.
4. Xu X-P, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42:1397-1434.
5. Camacho GT, Ortiz M. Computational modeling of impact damage in brittle materials. International Journal of Solids and Structures 1996; 33:2899-2939.
6. Ortiz M, Leroy Y, Needleman A. Finite element method for localized failure analysis. Computer Methods in Applied Mechanics and Engineering 1987; 61(2):189-214.
7. Zhou F, Molinari JF. Dynamic crack propagation with cohesive elements: a methodology to address mesh dependence. International Journal for Numerical Methods in Engineering 2004; 59(1):1-24.
8. Yang Q, Mota A, Ortiz M. A class of variational strain-localization finite elements. International Journal for Numerical Methods in Engineering 2005; 62(8):1013-1037.
9. Falk ML, Needleman A, Rice JR. A critical evaluation of cohesive zone models of dynamic fracture. Journal of Physics IV 2001; 11(PR5):43-50.
10. Moes N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics 2002; 69:813-834.
11. Moes N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46(1):133-150.
12. Gravouil A, Moes N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets - Part ii: level set update. International Journal for Numerical Methods in Engineering 2002; 53:2569-2586.
13. Belytschko T, Chen H, Xu J, Zi G. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. International Journal for Numerical Methods in Engineering 2003; 58(12):1873-1905.
14. Ventura G, Moran B, Belytschko T. Dislocations by partition of unity. International Journal for Numerical Methods in Engineering 2005; 62(11):1463-1487.
15. Areias PMA, Belytschko T. Two scale shear band evolution with adaptive bandwidth by local partition of unity. International Journal for Numerical Methods in Engineering, in press.
16. Samaniego E, Belytschko T. Continuum-discontinuum modelling of shear bands. International Journal for Numerical Methods in Engineering 2005; 62:1857-1872.
17. Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 2004; 61(13):2316-2343.
18. Rabczuk T, Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, in progress.
19. Simo JC, Oliver J, Armero F. An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Computational Mechanics 1993; 12:277-296.
20. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: Chichester, 2000.
21. Marsden JE, Hughes TJR. Mathematical Foundations of Elasticity. Dover Publications Inc.: New York, 1983.
22. Silhavy M. The Mechanics and Thermodynamics of Continuous Media. Springer: Berlin, 1997.
23. Dugdale D. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 1960; 8:100-108.
24. Barenblatt G. The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Fracture 1962; 7:55-129.
25. Chen W, Han D. Plasticity for Structural Engineers. Springer: Berlin, 1988.
26. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an over-view and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139:3-47.
27. Belytschko T, Lu YY. Element-free Galerkin methods for static and dynamic fracture. International Journal of Solids and Structures 1995; 32:2547-2570.
28. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
29. Rabczuk T, Belytschko T, Xiao SP. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering 2004; 193:1035-1063.
30. Vardoulakis I, Goldscheider M, Gudehus G. Formation of shear bands in sand bodies as a bifurcation problem. International Journal for Numerical and Analytical Methods in Geomechanics 1978; 2:99-128.
31. Han C, Drescher A. Shear bands in biaxial tests on dry coarse sand. Soils and Foundations 1993; 33(1):118-132.
32. Anand L, Gu C. Granular materials: constitutive equations and strain localization. Journal of the Mechanics and Physics of Solids 2000; 48:1701-1733.
33. Regueiro RA, Borja RI. Finite element analysis of strain localization in geologic materials taking a strong discontinuity approach. John A. Blume Earthquake Engineering Center 1998; 14.
34. Alsiny A, Vardoulakis I, Drescher A. Deformation localization in cavity inflation experiments on dry sand. Geotechnique 1992; 42:395-410.
35. Rabczuk T, Belytschko T. Adaptivity for structured meshfree particle methods in 2D and 3D. International Journal for Numerical Methods in Engineering 2005; 63(11):1559-1582.