The work is focused on the formulation of a thermodynamically–based constitutive theory for granular, cemented geomaterials, often characterized by a open structure with high porosity and voids of large diameter. Upon mechanical degradation processes such as bond rupture and grain crushing, these material undergo large volumetric and shear strains, and in some cases the deformations are so large that the usual assumption of linearized kinematics may be not applicable. In the first part of this work, the theory of hyperplasticity is extended to the finite deformation regime by adopting a multiplicative split of the deformation gradient into an elastic and a plastic part, under the assumption of material isotropy. Grain breakage and bond damage processes are accounted for through two micromechanically–inspired internal variables. A specific constitutive model for carbonatic cemented sands and calcarenites is proposed as a relevant example of application. In the second part, an implicit stress–point algorithm has been developed which is amenable to closed form linearization, for the implementation of the model into standard FE platforms. A series of numerical tests have demonstrated the accuracy and efficiency of the proposed algorithm. The simulation of plane strain biaxial tests, modeled as boundary–value problems, has highlighted the role played by geometric non–linearity in determining the evolution of the specimen deformation upon reaching a bifurcation condition.

Revised: 2020-08-07

Accepted: 2020-09-28

Published online: 2020-11-16

Keywords: Hard soils, Soft rocks, Hyperplasticity, Breakage mechanics, Finite deformations, Multiplicative plasticity, Stress–point algorithm, Consistent linearization

@article{OGEO_2020__2__A4_0, author = {Oliynyk, Kateryna and Tamagnini, Claudio}, title = {Finite deformation hyperplasticity theory for crushable, cemented granular materials}, journal = {Open Geomechanics}, eid = {4}, publisher = {Alert Geomaterials}, volume = {2}, year = {2020}, doi = {10.5802/ogeo.8}, language = {en}, url = {opengeomechanics.centre-mersenne.org/item/OGEO_2020__2__A4_0/} }

Oliynyk, Kateryna; Tamagnini, Claudio. Finite deformation hyperplasticity theory for crushable, cemented granular materials. Open Geomechanics, Volume 2 (2020) , article no. 4, 33 p. doi : 10.5802/ogeo.8. https://opengeomechanics.centre-mersenne.org/item/OGEO_2020__2__A4_0/

[1] The mechanical behaviour of a pyroclastic rock: yield strength and ”destructuration” effects, Rock Mechanics and Rock Engineering, Volume 31 (1998) no. 1, pp. 25-42

[2] Triaxial testing of naturally cemented carbonate soil, J. Geotech. Engng., ASCE, Volume 119 (1993) no. 9, pp. 1379-1398

[3] The underground cavity network of south-eastern Rome (Italy): an evolutionary geological model oriented to hazard assessment, Bulletin of Engineering Geology and the Environment, Volume 70 (2011) no. 4, pp. 533-542

[4] Plasticity: Modeling & Computation, Springer Science & Business, 2013

[5] On the numerical integration of three-invariant elastoplastic constitutive models, Comp. Meth. Appl. Mech. Engng., Volume 192 (2003) no. 9-10, pp. 1227-1258

[6] Cam–Clay plasticity, Part III: Extension of the infinitesimal model to include finite strains, Comp. Meth. Appl. Mech. Engng., Volume 155 (1998), pp. 73-95

[7] The mechanics of cemented carbonate sands, Geotechnique, Volume 43 (1993) no. 1, pp. 53-67

[8] A finite-strain Cam-clay model in the framework of multiplicative elasto-plasticity, Int. J. of Plasticity, Volume 14 (1998) no. 12, pp. 1155-1187

[9] On the mechanics of structured sands, Géotechnique, Volume 49 (1999) no. 6, pp. 741-760

[10] Effects of mineral suspension and dissolution on strength and compressibility of soft carbonate rocks, Engineering Geology, Volume 184 (2015), pp. 1-18

[11] Experimental study on the water-induced weakening of calcarenites, Rock Mechanics and Rock Engineering, Volume 48 (2014) no. 2, pp. 441-461

[12] Extension of plasticity theory to debonding, grain dissolution, and chemical damage of calcarenites, Int. J. Num. Anal. Meth. Geomech., Volume 40 (2016) no. 3, pp. 315-343

[13] A constitutive model for granular materials with grain crushing and its application to a pyroclastic soil, Int. J. Num. Anal. Meth. Geomech., Volume 26 (2002) no. 15, pp. 1531-1560

[14] A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests, Int. J. Num. Anal. Meth. Geomech., Volume 26 (2002) no. 13, pp. 1313-1347

[15] Weathering of stressed submerged calcarenites, Géotechnique, Volume 63 (2013), pp. 768-785

[16] Application of thermomechanical principles to the modeling of geotechnical materials, Proc. Royal Soc. London Series A, Volume 453 (1997), pp. 1975-2000

[17] A thermomechanical analysis of a family of soil models, Géotechnique, Volume 52 (2002) no. 7, pp. 507-518

[18] On the relationship between stress–dilatancy, anisotropy, and plastic dissipation for granular materials, Geotechnique, Volume 53 (2003) no. 7, pp. 611-618

[19] A systematic procedure for constructing critical state models in three dimensions, Int. Journal of Solids and Structures, Volume 40 (2003) no. 17, pp. 4379-4397

[20] The mechanics of uncemented carbonate sands, Géotechnique, Volume 40 (1990) no. 4, pp. 607-626

[21] Structural features and mechanical behaviour of a pyroclastic weak rock, Int. J. Num. Anal. Meth. Geomech., Volume 25 (2001) no. 15, pp. 1525-1557

[22] Computational methods for plasticity: theory and applications, John Wiley & Sons, 2011

[23] Stress–dilatancy based modelling of granular materials and extensions to soils with crushable grains, Int. J. Num. Anal. Meth. Geomech., Volume 29 (2005) no. 1, pp. 73-101

[24] A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables. Part II – Validation and localization analysis, Journal of the Mechanics and Physics of Solids, Volume 70 (2014), pp. 382-405

[25] Soft rocks in southern Italy and role of volcanic tuffs in the urbanization of Naples, Proceedings of the II International Symposium on The Geotechnics of Hard Soils and Soft Rocks, Volume 3 (2000), pp. 1243-1267

[30] Shear bands in plane strain compression of loose sand, Géotechnique, Volume 47 (1997) no. 1, pp. 149-165

[31] Practical multiscaling, John Wiley & Sons, 2014

[32] Conceptual bases for a constitutive model for bonded soils and weak rocks, Geotechnical Engineering of Hard Soils–Soft Rocks (1993)

[33] Continuum thermodynamics, J. Appl. Mechanics, ASME, Volume 50 (1983), pp. 1010-1020

[34] A kinematic hardening constitutive model for sands: the multiaxial formulation, Int. J. Num. Anal. Meth. Geomech., Volume 23 (1999), pp. 925-965

[35] Sur les matériaux standards généralisés, Journal de Mécanique, Volume 14 (1975), pp. 39-63

[36] Frictional Plasticity in a Convex Analytical Setting, Open Geomechanics, Volume 1 (2019), pp. 1-10

[37] A study of plasticity theories and their applicability to soils (1981) (Ph. D. Thesis)

[38] A thermomechanical framework for constitutive models for rate-independent dissipative materials, Int. J. of Plasticity, Volume 16 (2000) no. 9, pp. 1017-1047

[39] Principles of hyperplasticity: an approach to plasticity theory based on thermodynamic principles, Springer Science & Business Media, 2007

[40] Plasticity: Mathematical Theory and Numerical Analysis, Springer Verlag, New York, 1999

[41] Numerical implementation of constitutive models: rate–independent deviatoric plasticity, Theoretical Foundations for Large Scale computations of Non Linear Material Behavior (1984), pp. 29-57

[42] Behaviour of piles driven in chalk, Engineering in chalk (2018), pp. 33-51

[43] A framework for the mechanical behavior of cemented Corinth marl, Geotechnical Engineering of Hard Soils–Soft Rocks, Volume 1 (1993), pp. 577-583

[44] On the mechanical behavior of bonded soils, Proc. COMETT Seminar on Large Excavations (1994)

[45] North West Shelf development-the foundation engineering challenge, International conference on calcareous sediments (1988), pp. 333-341

[46] Particle crushing and deformation behaviour, Soils and foundations, Volume 50 (2010) no. 4, pp. 547-563

[47] A structured Cam Clay model, Can. Geotech. J., Volume 39 (2002) no. 6, pp. 1313-1332

[48] Elastic-plastic deformation at finite strains, J. Appl. Mechanics, ASME, Volume 36 (1968), pp. 1-6

[49] An experimental and theoretical study of the behavior of a calcarenite in triaxial compression, Géotechnique, Volume 45 (1995) no. 4, pp. 633-648

[50] Calcareous sediments: an engineering enigma, International conference on calcareous sediments (1988), pp. 777-784

[51] Thermomechanics of plasticity and fracture, Cambridge University Press, 1992

[52] A stable mesh–independent approach for numerical modelling of structured soils at large strains, Comp. & Geotechnics, Volume 116 (2019), p. 103215

[53] Thermodynamical approach for Camclay–family models with Roscoe–type dilatancy rules, Int. J. Num. Anal. Meth. Geomech., Volume 18 (1994), pp. 133-138

[54] Sur les lois de frottement, de viscosité et de plasticité, C. R. Acad. Sci., Volume 271 (1970), pp. 608-611

[55] A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation, Int. J. Num. Anal. Meth. Geomech., Volume 27 (2003) no. 9, pp. 705-732

[57] Mathematical modelling of natural and engineered geomaterials, European J. of Mechanics, A/Solids, Volume 11 (1992) no. special issue, pp. 135-154

[58] Nonlinear Elastic Deformations, Ellis Horwood, Chichester, 1984

[59] Fundamentals of kinematic hardening hyperplasticity, International journal of solids and structures, Volume 38 (2001) no. 21, pp. 3771-3794

[60] Subsidence above the Ekofisk oil reservoirs, Proceedings of the International Congress on behaviour of offshore structures (1988), pp. 113-128

[62] Internal variable formulations of problems in elastoplasticity: constitutive and algorithmic aspects, Appl. Mech. Reviews, Volume 47 (1993), pp. 429-456

[63] A kinematic hardening constitutive model for natural clays with loss of structure, Géotechnique, Volume 50 (2000) no. 2, pp. 153-164

[64] Computational inelasticity Volume 7, Springer Science & Business Media, 1998

[65] M66INV: Fortran 90 subroutine to compute the inverse of a $6\times 6$ matrix, 2009 https://caps.gsfc.nasa.gov/simpson/software/m66inv_f90.txt (NASA Goddard Space Flight Center)

[66] Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comp. Meth. Appl. Mech. Engng., Volume 99 (1992) no. 1, pp. 61-112

[67] Numerical analysis and simulation of plasticity, Handbook of numerical analysis, Volume 6 (1998), pp. 183-499

[69] Plasticity with generalized hardening: constitutive modeling and computational aspects, Acta Geotechnica, Volume 11 (2016) no. 3, pp. 595-623

[70] A Generalized Backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials, Int. J. Num. Anal. Meth. Geomech., Volume 26 (2002), p. 963-â1004

[71] A constitutive modelling framework predicting critical state in sand undergoing crushing and dilation, Géotechnique, Volume 66 (2016) no. 9, pp. 695-710

[72] A thermomechanical constitutive model for cemented granular materials with quantifiable internal variabes. Part I: Theory, Journal of the Mechanics and Physics of Solids, Volume 70 (2014), pp. 281-296

[73] A micro-mechanical study of cemented granular materials (2015) (Ph. D. Thesis)

[74] Geotechnical properties of two collapsible volcanic soils of low bulk density at the site of two dams in Canary Islands (Spain), Proc. VIII Conf. on Soil Mech. Found. Engng., Volume 2 (1975), pp. 257-264

[75] Full–field measurements in experimental geomechanics: historical perspective, current trends and recent results, Advanced experimental techniques in geomechanics (Viggiani, G.; Hall, S. A.; Romero, E., eds.), ALERT Geomaterials, 2012, pp. 3-67

[76] An introduction to thermomechanics, North Holland, 1983

[77] The derivation of constitutive relations from the free energy and the dissipation function, Advances in applied mechanics (1987), p. 183