Imperfection sensitivity of shear banding in gradient-dependent Cam-clay plasticity model

• Autorzy: Stankiewicz A.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the numerical simulation of strain localization in granular two-phase material. A gradient enhancement of modified Cam-clay model is introduced to overcome the problem of spurious discretization sensitivity of finite element solution. Two- and three-field finite elements implemented in the finite element analysis program (FEAP) are used in numerical simulations. The attention is focused on imperfection sensitivity of shear banding simulations. An application of the modelling framework to the slope stability problem is also included.

Słowa kluczowe

EN

two-phase medium; finite element method; plasticity; Cam-Clay model; gradient regularization; localization; imperfection sensitivity

PL

ośrodek dwufazowy; metoda elementów skończonych; plastyczność; Cam-Clay; uregulowanie gradientu; lokalizacja

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2015
• Tom: Vol. 22, no. 2
• Strony: 115--139
• Opis fizyczny: Bibliogr. 72 poz., rys., wykr.

Twórcy

autor

Stankiewicz A.

• Cracow University of Technology, Faculty of Civil Engineering Institute for Computational Civil Engineering Warszawska 24, 31-155 Cracow, Poland

Bibliografia

• [1] E.C. Aifantis. Gradient material mechanics: perspectives and prospects. Acta Mechanica, 225: 999–1012, 2014.
• [2] H. Askes, A.S.J. Suiker, L.J. Sluys. A classification of higher-order strain-gradient models – linear analysis. Archive of Applied Mechanics, 72(2-3): 171–188, 2002.
• [3] I. Babuška, J.M. Melenk. The partition of unity method. Int. J. Numer. Meth. Eng., 40(4): 727–758, 1997.
• [4] Z.P. Bažant, G. Pijaudier-Cabot. Nonlocal continuum damage, localization instability and convergence. ASME J. Appl. Mech., 55: 287–293, 1988.
• [5] A. Benallal, J.-J. Marigo. Bifurcation and stability issues in gradient theories with softening. Modelling and Simulation in Materials Science and Engineering, 15(1): 283–295, 2007.
• [6] J. Bobiński. Implementation and application examples of nonlinear concrete models with nonlocal softening. Ph.D. dissertation, Gdańsk University of Technology, Gdańsk, 2006. (in Polish).
• [7] R. Borja. Cam-Clay plasticity. Part V: A mathematical framework for three-phase deformation and strain localization analyses of partially saturated porous media. Comput. Methods Appl. Mech. Eng., 193: 5301–5338, 2004.
• [8] R.I. Borja, X. Song, W. Wu. Critical state plasticity. Part VII: Triggering a shear band in variably saturated porous media. Comput. Methods Appl. Mech. Eng., 261–262: 66–82, 2013.
• [9] R. de Borst. Simulation of strain localisation: A reappraisal of the Cosserat continuum. Eng. Comput., 8: 317–332, 1991.
• [10] R. de Borst, M.-A. Abellan. Dispersion and internal length scales in strain-softening two-phase media. In G. Meschke et al. [Ed.], Proc. EURO-C 2006 Int. Conf. Computational Modelling of Concrete Structures, pp. 549–556, Taylor & Francis, London/Leiden, 2006.
• [11] R. de Borst, H.-B. Mühlhaus. Gradient-dependent plasticity: formulation and algorithmic aspects. Int. J. Numer. Meth. Eng., 35: 521–539, 1992.
• [12] R. de Borst, J. Pamin. Some novel developments in finite element procedures for gradient-dependent plasticity. Int. J. Numer. Meth. Eng., 39: 2477–2505, 1996.
• [13] R. de Borst, L.J. Sluys, H.-B. Mühlhaus, J. Pamin. Fundamental issues in finite element analyses of localization of deformation. Eng. Comput., 10: 99–121, 1993.
• [14] R. de Borst, E. van der Giessen, editors. Material Instabilities in Solids, Chichester, 1998. IUTAM, John Wiley & Sons.
• [15] R.A.B. Engelen, M.G.D. Geers, F.P.T. Baaijens. Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour. Int. J. Plasticity, 19(4): 403–433, 2003.
• [16] S. Forest, E. Lorentz. Localization phenomena and regularization methods. In J. Besson [Ed.], Local approach to fracture, pp. 311–370. Les Presses de l’Ecole des Mines, Paris, 2004.
• [17] T.-P. Fries, T. Belytschko. The extended/generalized finite element method: an overview of the method and its applications. Int. J. Numer. Meth. Eng., 84(3): 253–304, 2010.
• [18] A. Gajo, D. Bigoni, D. Muir Wood. Multiple shear band development and related instabilities in granular materials. Journal of the Mechanics and Physics of Solids, 52: 2683–2724, 2004.
• [19] M.G.D. Geers. Experimental analysis and computational modelling of damage and fracture. Ph.D. dissertation, Eindhoven University of Technology, Eindhoven, 1997.
• [20] A. Gens, D.M. Potts. Critical state models in computational geomechanics. Eng. Comput., 5: 178–197, 1988.
• [21] A. Glema. Analysis of wave nature in plastic strain localization in solids. Technical Report Monograph 379, Poznań University of Technology, Poznań, 2004. (in Polish).
• [22] A. Glema, T. Łodygowski. On importance of imperfections in plastic strain localization problems in materials under impact loading. Arch. Mech., 54(5–6): 411–423, 2002.
• [23] P. Grassl, M. Jir´asek. Plastic model with non-local damage applied to concrete. Int. J. Num. Anal. Meth. Geomech., 30: 71–90, 2006.
• [24] A. Groen. Three-dimensional elasto-plastic analysis of soils. Ph.D. dissertation, Delft University of Technology, Delft, 1997.
• [25] M. Gryczmański. State of the art in modelling of soil behaviour at small strains. Architecture Civil Engineering Environment, 2(1): 61–80, 2009.
• [26] R. Hill. A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids, 6: 236–249, 1958.
• [27] T.J.R. Hughes. The Finite Element Method.: linear static and dynamic analysis. Prentice-Hall, New Jersey, 1987.
• [28] M. Jirásek. Nonlocal models for damage and fracture: comparison of approaches. Int. J. Solids Struct., 35(31– 32): 4133–4145, 1998.
• [29] E. Kuhl, E. Ramm, R. de Borst. An anisotropic gradient damage model for quasi-brittle materials. Comput. Methods Appl. Mech. Eng., 183(1–2): 87–103, 2000.
• [30] T. Liebe, P. Steinmann. Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity. Int. J. Numer. Meth. Eng., 51: 1437–1467, 2001.
• [31] T. Liebe, P. Steinmann, A. Benallal. Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage. Comput. Methods Appl. Mech. Eng., 190: 6555–6576, 2001.
• [32] A. Scarpas, X. Liu, J. Blaauwendraad. Numerical modelling of nonlinear response of soil. Part 2: strain localization investigation on sand. Int. J. Solids Struct., 42: 1883–1907, 2005.
• [33] T. Łodygowski. Numerical solutions of initial boundary value problems for metals and soils. In Perzyna [46], pp. 392–468.
• [34] G. Maier, T. Hueckel. Nonassociated and coupled flow rules of elastoplasticity for rock-like materials. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 16: 77–92, 1979.
• [35] N. Moës, J. Dolbow, T. Belytschko. A finite element method for crack growth without remeshing. Int. J. Numer. Meth. Eng., 46(1): 131–150, 1999.
• [36] Z. Mróz. On forms of constitutive laws for elastic-plastic solids. Arch. Mech., 18: 3–34, 1966.
• [37] H.-B. Mühlhaus, E.C. Aifantis. A variational principle for gradient plasticity. Int. J. Solids Struct., 28: 845–857, 1991.
• [38] H.-B. Mühlhaus, I. Vardoulakis. The thickness of shear bands in granular materials. Geotechnique, 37: 271–283, 1987.
• [39] M.K. Neilsen, H.L. Schreyer. Bifurcations in elastic-plastic materials. Int. J. Solids Struct., 30: 521–544, 1993.
• [40] M. Ortiz, Y. Leroy, A. Needleman. A finite element method for localized failure analysis. Comput. Methods Appl. Mech. Eng., 61: 189–214, 1987.
• [41] M. Ortiz, A. Pandolfi. A variational Cam-clay theory of plasticity. Comput. Methods Appl. Mech. Eng., 193: 2645–2666, 2004.
• [42] N.S. Ottosen, K. Runesson. Properties of discontinuous bifurcation solutions in elasto-plasticity. Int. J. Solids Struct., 27(4): 401–421, 1991.
• [43] J. Pamin. Gradient-dependent plasticity in numerical simulation of localization phenomena. Ph.D. dissertation, Delft University of Technology, Delft, 1994.
• [44] J. Pamin. Numerical models of localized deformations (in Polish). In Biliński W. and Piszczek K., editors, Proc. XVII Conf. Computer Methods in Design and Analysis of Hydrostructures, pp. 77–86 Cracow University of Technology, Drukarnia “GS”, Cracow, 2005.
• [45] R.H.J. Peerlings, R. de Borst, W.A.M. Brekelmans, J.H.P. de Vree. Gradient-enhanced damage for quasi-brittle materials. Int. J. Numer. Meth. Eng., 39: 3391–3403, 1996.
• [46] P. Perzyna, editor. Localization and fracture phenomena in inelastic solids. CISM Course Lecture Notes No. 386, Springer-Verlag, Wien – New York, 1998.
• [47] H. Petryk, editor. Material instabilities in elastic and plastic solids. CISM Course Lecture Notes No. 414, Springer-Verlag, Wien – New York, 2000.
• [48] H.E. Read, G.A. Hegemier. Strain softening of rock, soil and concrete – a review article. Mech. Mater., 3: 271–294, 1984.
• [49] S. Rolshoven. Nonlocal plasticity models for localized failure. Ph.D. dissertation, École Polytechnique Fédéralé de Lausanne, Lausanne, 2003.
• [50] K.H. Roscoe, J.B. Burland. On the generalized behaviour of ‘wet’ clay. In Engineering Plasticity, 48: 535–609, Cambridge University Press, Cambridge, 1968.
• [51] J.G. Rots. Computational modeling of concrete fracture. Ph.D. dissertation, Delft University of Technology, Delft, 1988.
• [52] J.W. Rudnicki, J.R. Rice. Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids, 23: 371–394, 1975.
• [53] M.S.A. Siddiquee. FEM simulations of deformation and failure of stiff geomaterials based on element test results. Ph.D. dissertation, University of Tokyo, Tokyo, 1994.
• [54] L.J. Sluys. Wave propagation, localization and dispersion in softening solids. Ph.D. dissertation, Delft University of Technology, Delft, 1992.
• [55] A. Stankiewicz. Numerical analysis of strain localization in one- and two-phase geomaterials. Ph.D. dissertation, Cracow University of Technology, Cracow, 2007.
• [56] A. Stankiewicz, J. Pamin. Finite element analysis of fluid influence on instabilities in two-phase Cam-clay plasticity model. Computer Assisted Mechanics and Engineering Sciences, 13(4): 669–682, 2006.
• [57] A. Stankiewicz, J. Pamin. Gradient-enhanced Cam-clay model in simulation of strain localization in soil. Foundations of Civil and Environmental Engineering, 7: 293–318, 2006.
• [58] T. Svedberg, K. Runesson. A thermodynamically consistent theory of gradient-regularized plasticity coupled to damage. Int. J. Plasticity, 13(6–7): 669–696, 1997.
• [59] J. Tejchman. Influence of a characteristic length on shear zone formation in hypoplasticity with different enhancements. Computers and Geotechnics, 31(8): 595–611, 2004.
• [60] J. Tejchman. Effect of fluctuation of current void ratio on the shear zone formation in granular bodies within micro-polar hypoplasticity. Computers and Geotechnics, 33(1): 29–46, 2006.
• [61] J. Tejchman, W. Wu. Numerical study on patterning of shear bands in a Cosserat continuum. Acta Mechanica, 99(1–4): 61–74, 1993.
• [62] A. Truty. On certain class of mixed and stabilized mixed finite element formulations for single and two-phase geomaterials. Technical Report Monograph 48, Cracow University of Technology, Cracow, 2002.
• [63] I. Vardoulakis, E.C. Aifantis. Gradient dependent dilatancy and its implications in shear banding and liquefaction. Ing.-Arch., 59: 197–208, 1989.
• [64] I. Vardoulakis, J. Sulem. Bifurcation Analysis in Geomechanics. Blackie Academic & Professional, London, 1995.
• [65] G.N. Wells. Discontinuous modelling of strain localisation and failure. Ph.D. dissertation, Delft University of Technology, Delft, 2001.
• [66] K.J. Willam, A. Dietsche. Fundamental aspects of strain-softening descriptions. In Z.P. Bažant [Ed.], Fracture Mechanics of Concrete Structures, pp. 227–238, FRAMCOS, Elsevier Applied Science, London and New York, 1992.
• [67] K.J. Willam, G. Etse. Failure assessment of the extended Leon model for plain concrete. In N. Bićanić et al. [Ed.], Proc. Second Int. Conf. Computer Aided Analysis and Design of Concrete Structures, pp. 851–870, Pineridge Press, Swansea, 1990.
• [68] K. J. Willam, T. Münz, G. Etse, and Ph. Menétrey. Failure conditions and localization in concrete. In H.A. Mang et al., editors, Proc. EURO-C 1994 Int. Conf. Computer Modelling of Concrete Structures, pp. 263–282, Pineridge Press, Swansea, 1994.
• [69] A. Winnicki, C.J. Pearce, N. Bićanić. Viscoplastic Hoffman consistency model for concrete. Comput. & Struct., 79: 7–19, 2001.
• [70] M. Wójcik, J. Tejchman. Modeling of shear localization during confined granular flow in silos within non-local hypoplasticity. Powder Technology, 192(3): 298–310, 2009.
• [71] H.W. Zhang, B.A. Schrefler. Particular aspects of internal length scales in strain localisation analysis of multiphase porous materials. Comput. Methods Appl. Mech. Eng., 193: 2867–2884, 2004.
• [72] O.C. Zienkiewicz, A.H.C. Chan, M. Pastor, B.A. Schrefler, T. Shiomi. Computational Geomechanics. John Wiley & Sons, Chichester, 2000.