A micro-mechanical investigation of bifurcation in granular materials

In this paper, the notion of loss of sustainability of a mechanical state in a granular assembly is investigated. The vanishing of the second-order work, defined on the macroscopic scale from tensorial variables, is shown to play a fundamental role in detecting the occurrence of this type of bifurcation. Then a link is established between the macroscopic second-order work on the specimen scale and a discrete local expression that introduces microscopic variables defined on each contact scale. This relation opens up a micro-mechanical interpretation allowing one to examine which micro-structural features are responsible for the vanishing of the macroscopic second-order work. Finally, it is established that both geometrical and material micro-structural origins may combine to induce the occurrence of bifurcation on a specimen scale.

[1]  I. Vardoulakis,et al.  Bifurcation Analysis in Geomechanics , 1995 .

[2]  Rodney Hill,et al.  The essential structure of constitutive laws for metal composites and polycrystals , 1967 .

[3]  Jean-Pierre Bardet,et al.  Observations on the effects of particle rotations on the failure of idealized granular materials , 1994 .

[4]  Farhang Radjai,et al.  Contact forces in a granular packing. , 1999, Chaos.

[5]  François Nicot,et al.  On incremental non‐linearity in granular media: phenomenological and multi‐scale views (Part I) , 2005 .

[6]  Material instability in granular assemblies from fundamentally different models , 2007 .

[7]  Farhang Radjai,et al.  BIMODAL CHARACTER OF STRESS TRANSMISSION IN GRANULAR PACKINGS , 1998 .

[8]  Masanobu Oda,et al.  Experimental micromechanical evaluation of strength of granular materials: Effects of particle rolling , 1982 .

[9]  François Nicot,et al.  Bifurcation and second-order work in geomaterials , 2007 .

[10]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[11]  Davide Bigoni,et al.  Uniqueness and localization—I. Associative and non-associative elastoplasticity , 1991 .

[12]  François Nicot,et al.  A multi-scale approach to granular materials , 2005 .

[13]  J. Mandel.  Conditions de Stabilité et Postulat de Drucker , 1966 .

[14]  Michael R. Horne,et al.  The behaviour of an assembly of rotund, rigid, cohesionless particles. I , 1965, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[15]  Poul V. Lade,et al.  Instability and Plastic Flow of Soils. I: Experimental Observations , 1990 .

[16]  D. C. Drucker.  Some implications of work hardening and ideal plasticity , 1950 .

[17]  D. C. Drucker,et al.  A DEFINITION OF STABLE INELASTIC MATERIAL , 1957 .

[18]  F. Donze,et al.  Identification and Validation of a Discrete Element Model for Concrete , 2004 .

[19]  François Nicot,et al.  Micro-mechanical investigation of material instability in granular assemblies , 2006 .

[20]  Davide Bigoni,et al.  Bifurcation and Instability of Non-Associative Elastoplastic Solids , 2000 .

[21]  R. Hill.  A general theory of uniqueness and stability in elastic-plastic solids , 1958 .

[22]  Félix Darve,et al.  Constitutive modelling and instabilities of soil behaviour , 1995 .

[23]  Félix Darve,et al.  Constitutive Equations and Instabilities of Granular Materials , 2002 .

[24]  R. Nova,et al.  CONTROLLABILITY OF THE INCREMENTAL RESPONSE OF SOIL SPECIMENS SUBJECTED TO ARBITRARY LOADING PROGRAMMES , 1994 .

[25]  Frédéric-Victor Donzé,et al.  Numerical simulations of impacts using a discrete element method , 1998 .

[26]  François Nicot,et al.  On flow rule in granular media: phenomenological and multi-scale views , 2005 .

[27]  H. Petryk,et al.  Theory of Bifurcation and Instability in Time-Independent Plasticity , 1993 .

[28]  F. Darve,et al.  On the Elastic and Plastic Strain Decomposition in Granular Materials , 2006 .

[29]  F. Nicot.  Constitutive modelling of a snow cover with a change in scale , 2003 .

[30]  H. Petryk,et al.  Theory of Material Instability in Incrementally Nonlinear Plasticity , 2000 .

[31]  A. Liapounoff,et al.  Problème général de la stabilité du mouvement , 1907 .

[32]  Félix Darve,et al.  Failure in geomaterials: continuous and discrete analyses , 2004 .

[33]  A. Tordesillas,et al.  Incorporating rolling resistance and contact anisotropy in micromechanical models of granular media , 2002 .

[34]  Instability of dilating sand , 1993 .

[35]  François Nicot,et al.  Constitutive modelling of snow as a cohesive-granular material , 2004 .

[36]  Richard B. Nelson,et al.  INSTABILITY OF GRANULAR MATERIALS WITH NONASSOCIATED FLOW , 1988 .