A comparison of discrete granular material models with continuous microplane formulations

Abstract The main objective of this paper is the discussion of two different strategies of simulating the constitutive behavior of granular assemblies. For this, we will focus on discrete particle methods which are widely used in physical science and on continuum–based microplane models which are applied by the engineering community. After deriving the overall constitutive equations based on Voigt’s hypothesis, special focus will be dedicated to the comparison of the relations between the microscopic and macroscopic quantities of each model. It will be demonstrated, that the two basically different modelling techniques lead to remarkably similar results for elastic as well as elasto–plastic material behavior.

[1]  Ching S. Chang,et al.  Stress-strain relationship for granular materials based on the hypothesis of best fit , 1997 .

[2]  R. Bathurst,et al.  Micromechanical Aspects of Isotropic Granular Assemblies With Linear Contact Interactions , 1988 .

[3]  Dusan Krajcinovic,et al.  Damage tensors and the crack density distribution , 1993 .

[4]  Pere C. Prat,et al.  Microplane Model for Brittle-Plastic Material: I. Theory , 1988 .

[5]  Ekkehard Ramm,et al.  On the linearization of the microplane model , 1998 .

[6]  F. Emeriault,et al.  Micromechanical modelling of anisotropic non-linear elasticity of granular medium , 1996 .

[7]  P. Bazant,et al.  Efficient Numerical Integration on the Surface of a Sphere , 1986 .

[8]  Zdeněk P. Bažant,et al.  New explicit microplane model for concrete: Theoretical aspects and numerical implementation , 1992 .

[9]  Z. Bažant,et al.  CRACK SHEAR IN CONCRETE: CRACK BAND MICROPLANE MODEL , 1984 .

[10]  F. Sidoroff,et al.  Homogenization for granular materials , 1995 .

[11]  A. Drescher,et al.  Photoelastic verification of a mechanical model for the flow of a granular material , 1972 .

[12]  K. Walton,et al.  The effective elastic moduli of a random packing of spheres , 1987 .

[13]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[14]  S. Nemat-Nasser,et al.  A Micromechanical Description of Granular Material Behavior , 1981 .

[15]  O. Zienkiewicz,et al.  Time-dependent multilaminate model of rocks—a numerical study of deformation and failure of rock masses , 1977 .

[16]  N. P. Kruyt,et al.  Micromechanical Definition of the Strain Tensor for Granular Materials , 1996 .

[17]  Kanatani Ken-Ichi.  DISTRIBUTION OF DIRECTIONAL DATA AND FABRIC TENSORS , 1984 .

[18]  Zdenek P. Bazant,et al.  Microplane Model for Brittle‐Plastic Material: II. Verification , 1988 .