Abstract
Penetration problems in geomechanics involve the insertion or intrusion of solid bodies into the ground. Such problems are extremely difficult to model numerically, because they usually involve severe mesh distortion caused by large deformation and frictional contact. In this paper, an Arbitrary Lagrangian–Eulerian method is used to overcome the mesh distortion problem. Some specific issues associated with the ALE method, such as node relocation and remapping of contact history variables, are discussed. The ALE method, incorporated with an automatic load stepping scheme and a smooth contact discretisation technique, is then used to analyse the penetration of axial displacement piles into the ground.
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References
Abbo AJ, Sloan SW (1996) An automatic load stepping algorithm with error control. Int J Numer Methods Eng 39: 1737–1759
Benson DJ (1989) An efficient, accurate and simple ALE method for nonlinear finite element programs. Comp Methods Appl Mech Eng 72: 305–350
Belytschko T, Kennedy JM (1978) Computer models for subassembly simulation. Nucl Eng Des 49: 17–38
Fischer KA, Wriggers P (2006) Motar based frictional contact formulation for higher order interpolation using the moving friction cone. Comp Methods Appl Mech Eng 195(37–40): 5020–5036
Fischer KA, Sheng D, Abbo AJ (2007) Modeling of pile installation using contact mechanics and quadratic elements. Comp Geotech 34(6): 449–461
Gadala MS, Wang J (1998) ALE formulation and its application in solid mechanics. Comp Methods Appl Mech Eng 167: 33–55
Ghosh S, Kikuchi N (1991) An arbitrary Lagrangian–Eulerian finite element method for large deformation analysis of elastic-viscoplastic solids. Comp Methods Appl Mech Eng 86: 127–188
Hu Y, Randolph MF (1998) A practical numerical approach for large deformation problems in soils. Int J Numer Anal Methods Geomech 22: 327–350
Huang W, Sheng D, Sloan SW, Yu HS (2004) Finite element analysis of cone penetration in cohesionless soil. Comp Geotech 31: 517–528
Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flow. Comp Methods Appl Mech Eng 58: 19–36
Laursen TA (2002) Computational contact and impact mechanics. Springer, Berlin
Liu WK, Belytschko T, Chang H (1986) An arbitrary Lagrangian–Eulerian finite element method for path-dependant materials. Comp Methods Appl Mech Eng 58: 227–245
Liyanapathirana DS, Deeks AJ, Randolph MF (2000) Numerical modelling of large deformations associated with driving of open-ended piles. Int J Numer Anal Meth Geomech 24: 1079–1101
Lopez RJ (2001) Advanced engineering mathematics. Addison Wesley, New York
Nazem M (2006) Numerical algorithms for large deformation problems in geomechanics. Ph.D. thesis, School of Engineering, The University of Newcastle, Australia
Nazem M, Sheng D, Carter JP (2006) Stress integration and meshing refinement for large deformation in geomechanics. Int J Numer Methods Eng 65: 1002–1027
Peric D, Hochard C, Dutko M, Owen DRJ (1996) Transfer operators for solving meshes in small strain elasto-plasticity. Comp Methods Appl Mech Eng 137: 331–344
Peric D, Vaz M Jr, Owen DRJ (1999) On adaptive strategies for large deformations of elasto-plastic solids at finite strains: computational issues and industrial applications. Comp Methods Appl Mech Eng 176: 279–312
Potts DM, Zdravkovic L (2001) Finite element analysis in geotechnical engineering, vol 1, theory. Thomas Telford, London
Sheng D, Axelsson K, Magnusson O (1997) Stress and strain fields around a penetrating cone. In: Pietruszczak S, Pande GN (eds) Numerical models in geomechanics. Balkema, Rotterdam, pp 653–660
Sheng D, Eigenbrod KD, Wriggers P (2005) Finite element analysis of pile installation using large-slip frictional contact. Comp Geotech 32(1): 17–26
Sheng D, Sloan SW, Yu HS (2000) Aspects of finite element implementation of critical state models. Comput Mech 26: 185–196
Sheng D, Sloan SW (2001) Load stepping methods for critical state models. Int J Numer Methods Eng 50: 67–93
Sheng D, Wriggers P, Sloan SW (2006) Improved numerical algorithms for friction contact in pile penetration analysis. Comp Geotech 33: 341–354
Sheng D (2007) Frictional contact for pile installation. In: Wriggers P, Nackenhorst U (eds) IUTAM symposium on computational methods in contact mechanics. Springer, Heidelberg, pp 239–256
Simo JC, Meschke G (1993) A new class of algorithms for classical plasticity extended to finite strains. Appl Geomater Computat Mech 11: 253–278
Sloan SW, Randolph MF (1984) Numerical prediction of collapse loads using finite element methods. Int J Numer Anal Methods Geomechan 6: 47–76
Susila E, Hryciw RD (2003) Large displacement FEM modelling of the cone penetration test (CPT) in normally consolidated sand. Int J Numer Anal Methods Geomech 27: 585–602
Van den Berg P (1994) Analysis of soil penetration. Ph.D. thesis, Technische Universiteit Delft
Wang CX, Carter JP (2002) Deep penetration of strip and circular footings into layered clays. Int J Geomech 2(2): 205–232
Wriggers P (2002) Computational contact mechanics. Wiley, Chichester
Yamada T, Kikuchi F (1993) An arbitrary Lagrangian–Eulerian finite element method for incompressible hyperelasticity. Comp Methods Appl Mech Eng 102: 149–177
Yu HS (2004) Cavity expansion methods in geomechanics. Kluwer, Dordrecht
Zhou H, Randolph MF (2007) Computational techniques and shear band development for cylindrical and spherical penetrometers in strain-softening clay. Int J Geomech ASCE 7(4): 287–295
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Sheng, D., Nazem, M. & Carter, J.P. Some computational aspects for solving deep penetration problems in geomechanics. Comput Mech 44, 549–561 (2009). https://doi.org/10.1007/s00466-009-0391-6
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DOI: https://doi.org/10.1007/s00466-009-0391-6