Capturing strain localization in dense sands with random density

International Journal for Numerical Methods in Engineering

Volumn 67, Issue 11, 2006, Pages 1531-1564

  Andrade, José E ^a   Borja, Ronaldo I ^a  

^a Stanford University   (United States)

Author keywords

Granular materials; Random density; Strain localization

Indexed keywords

ALGORITHMS; BOUNDARY VALUE PROBLEMS; ELASTOPLASTICITY; GRANULAR MATERIALS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PLASTIC DEFORMATION; PLASTICITY; RANDOM PROCESSES; STRAIN; STRESSES; YIELD STRESS;

DENSE SANDS; DENSITY FIELDS; GEOMATERIALS; RANDOM DENSITY; STRAIN LOCALIZATION;

SAND;

ALGORITHMS; BOUNDARY VALUE PROBLEMS; ELASTOPLASTICITY; GRANULAR MATERIALS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PLASTIC DEFORMATION; PLASTICITY; RANDOM PROCESSES; SAND; STRAIN; STRESSES; YIELD STRESS;

EID: 33748439376     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1673     Document Type: Article

References (49)

1. Borja RI, Aydin A. Computational modeling of deformation bands in granular media. I. Geological and mathematical framework. Computer Methods in Applied Mechanics and Engineering 2004; 193:2667-2698.
2. Desrues J, Viggiani G. Strain localization in sand: an overview of the experimental results obtained in grenoble using stereophotogrammetry. International Journal for Numerical and Analytical Methods in Geomechanics 2004; 28:279-321.
3. Rechenmacher AL, Finno RJ. Shear band displacements and void ratio evolution to critical state in dilative sands. In Bifurcation and Instabilities in Geomaterials, Labuz JF, Drescher A (eds). A. A. Blakema Publishers: Rotterdam, 2003; 13-22.
4. Rechenmacher AL, Finno RJ. Digital image correlation to evaluate shear banding in dilative sands. Geotechnical Testing Journal 2004; 27:13-22.
5. Jefferies MG. Nor-Sand: a simple critical state model for sand. Géotechnique 1993; 43:91-103.
6. Borja RI, Andrade JE. Critical state plasticity, part VI: meso-scale finite element simulation of strain localization in discrete granular materials. Computer Methods in Applied Mechanics and Engineering 2006, in press (John Argyris Memorial special issue).
7. Been K, Jefferies MG. A state parameter for sands. Géotechnique 1985; 35:99-112.
8. Manzari MT, Dafalias YF. A critical state two-surface plasticity model for sands. Géotechnique 1997; 43:255-272.
9. Roscoe KH, Burland JH. On the generalized stress-strain behaviour of 'wet' clay. In Engineering Plasticity, Heyman J, Leckie FA (eds). Cambridge University Press: Cambridge, 1968; 535-609.
10. Borja RI, Lee SR. Cam-Clay plasticity, part I: implicit integration of elasto-plastic constitutive relations. Computer Methods in Applied Mechanics and Engineering 1990; 78:49-72.
11. Borja RI. Cam-Clay plasticity, part II: implicit integration of constitutive equation based on nonlinear elastic stress predictor. Computer Methods in Applied Mechanics and Engineering 1991; 88:225-240.
12. Borja RI, Tamagnini C. Cam-Clay plasticity, part III: extension of the infinitesimal model to include finite strains. Computer Methods in Applied Mechanics and Engineering 1998; 155:73-95.
13. Peric D, Ayari MA. Influence of Lode's angle on the pore pressure generation in soils. International Journal of Plasticity 2002; 18:1039-1059.
14. Peric D, Ayari MA. On the analytical solutions for the three-invariant Cam Clay model. International Journal of Plasticity 2002; 18:1061-1082.
15. Borja RI, Sama KM, Sanz PF. On the numerical integration of three-invariant elastoplastic constitutive models. Computer Methods in Applied Mechanics and Engineering 2003; 192:1227-1258.
16. Borja RI. Computational modeling of deformation bands in granular media. II. Numerical simulations. Computer Methods in Applied Mechanics and Engineering 2004; 193:2699-2718.
17. Lode W. Versuche ueber den einfluss der mitt leren Hauptspannung auf das Fliessen der Metalle Eisen Kupfer und Nickel. Zeitschrift fuer Physik 1926; 36:913-939.
18. Borja RI. Bifurcation of elastoplastic solids to shear band mode at finite strains. Computer Methods in Applied Mechanics and Engineering 2002; 191:5287-5314.
19. Lee EH. Elastic-plastic deformation at finite strain. Journal of Applied Mechanics 1969; 36:1-6.
20. Holzapfel GA. Nonlinear Solid Mechanics. Wiley: West Sussex, U.K., 2000.
21. Marsden JE, Hughes TJR. Mathematical Theory of Elasticity. Prentice-Hall: Englewood Cliffs, NJ, 1983.
22. Houlsby GT. The use of a variable shear modulus in elasto-plastic models for clays. Computers and Geotechnics 1985; 1:3-13.
23. Borja RI, Tamagnini C, Amorosi A. Coupling plasticity and energy-conserving elasticity models for clays. Journal of Geotechnical and Geoenvironmental Engineering (ASCE) 1997; 123:949-957.
24. Borja RI. Plasticity Modeling and Computation. Lecture Notes. Stanford University: California, 2005.
25. Gudehus G. Elastoplastische stoffgleichungen fur trockenen sand. Ingenieur-Archiv 1973; 42:151-169.
26. Argyris JH, Faust G, Szimmat, J, Warnke EP, Willam KJ. Recent developments in the finite element analysis of prestressed concrete reactor vessels. Nuclear Engineering and Design 1974; 28:42-75.
27. Jiang J, Pietruszczak. Convexity of yield loci for pressure sensitive materials. Computers and Geotechnics 1988; 5:51-63.
28. Willam KJ, Warnke EP. Constitutive model for the triaxial behaviour of concrete. Concrete Structures Subjected to Triaxial Stresses, ISMES, Bergamo, Italy, May 1974.
29. Dafalias YF. Plastic spin: necessity or redundancy? International Journal of Plasticity 1998; 14:909-931.
30. Simo JC, Hughes TJR. Computational Inelasticity. Prentice-Hall: New York, 1998.
31. Lade PV. Static instability and liquefaction of loose fine sandy slopes. Journal of Geotechnical Engineering (ASCE) 1992; 118:51-71.
32. Lade PV, Duncan JM. Elastoplastic stress-strain theory for cohesionless soil. Journal of the Geotechnical Engineering Division (ASCE) 1975; 101:1037-1053.
33. Simo JC. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering 1992; 99:61-112.
34. Andrade JE, Borja RI. Fully implicit numerical integration of a hyperelastoplastic model for sands based on critical state plasticity. In Computational Fluid and Solid Mechanics, Bathe KJ (ed.). Elsevier Science Ltd.: Amsterdam, 2005; 52-54.
35. Bonet J, Wood RD. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press: Cambridge, U.K., 1997.
36. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: West Sussex, U.K., 2000.
37. Ortiz M, Martin JB. Symmetry-preserving return mapping algorithms and incrementally extremal paths - a unification of concepts. International Journal for Numerical Methods in Engineering 1989; 8:1839-1853.
38. Rudnicki JW, Rice JR. Conditions for localization of deformation in pressure-sensitive dilatant materials. Journal of the Mechanics and Physics of Solids 1975; 23:371-394.
39. Ortiz M, Leroy Y, Needleman A. A finite element method for localized failure analysis. Computer Methods in Applied Mechanics and Engineering 1987; 61:189-214.
40. Willam K. Constitutive models for engineering materials. In Encyclopedia of Physical Science and Technology, vol. 3 (3rd edn). Academic Press: New York, 2002.
41. Oliver J, Huespe AE. Theoretical and computational issues in modeling material failure in strong discontinuity scenarios. Computer Methods in Applied Mechanics and Engineering 2004; 193:2987-3014.
42. Ottosen NS, Runesson K. Properties of discontinuous bifurcation solutions in elasto-plasticity. International Journal of Solids and Structures 1991; 27:401-421.
43. Mosler J. Numerical analyses of discontinuous material bifurcation: strong and weak discontinuities. Computer Methods in Applied Mechanics and Engineering 2005; 194:979-1000.
44. Shahinpoor M. Statistical mechanical considerations on the random packing of granular materials. Powder Technology 1980; 25:163-176.
45. Nübel K, Huang W. A study of localized deformation pattern in granular media. Computer Methods in Applied Mechanics and Engineering 2004; 193:2719-2743.
46. Benjamin JR, Cornell CA. Probability, Statistics, and Decision for Civil Engineers. McGraw-Hill, Inc.: New York, 1970.
47. Nagtegaal JC, Parks DM, Rice JR. On numerically accurate finite element solutions in the fully plastic regime. Computer Methods in Applied Mechanics and Engineering 1974; 4:153-177.
48. Simo JC, Taylor RL, Pister KS. Variational and projection methods for the volume constraint in finite deformation elasto-plasticity. Computer Methods in Applied Mechanics and Engineering 1985; 51:177-208.
49. Hughes TJR. The Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1987.