GEOMATERIALS: CONTINUUM OR DISCONTINUUM, THAT IS THE QUESTION

Different numerical models within the framework of computational mate- rial mechanics will be presented allowing completely diverse insights into the material behaviour at the mesoscopic level. In order to obtain an anisotropic damage evolution in a natural and conceptually simple way geomaterials are modelled as a discrete granular particle assembly composed of convex polygons that are linked together by simple beams accounting for cohesive effects. An internal length scale is incorporated intrinsically into the model by a statistically controlled particle generation process. Compression simula- tions with different boundary conditions are used to verify the qualitative application of the model. A transition from a continuous to a discontinuous state of the material results as a naturally output of the simulation. The continuous approach presented in the sec- ond part is based on the microplane concept allowing for directional dependent stiffness degradation at the material point level. Different concepts regarding the enhancement of the microplane formulation are outlined. Among these are versions for elasto-damage, elasto-plasticity and their combination on the one hand and a gradient enhancement on the other hand. Finally, a comparison of both, discrete and continuous models, namely the discrete element model and the continuous elastic microplane model, shows some re- markable similarties between both schemes. This allows a schematic comparison noting the corresponding inter-relations between both models.

[1]  P. Stroeven,et al.  Some aspects of the micromechanics of concrete , 1973 .

[2]  J. Mier Fracture Processes of Concrete , 1997 .

[3]  Erik Schlangen,et al.  Experimental and numerical analysis of micromechanisms of fracture of cement-based composites , 1992 .

[4]  Hans J. Herrmann,et al.  A study of fragmentation processes using a discrete element method , 1995, cond-mat/9512017.

[5]  Gian Antonio D'Addetta,et al.  A comparison of discrete granular material models with continuous microplane formulations , 2000 .

[6]  Ignacio Carol,et al.  Damage and plasticity in microplane theory , 1997 .

[7]  Milan Jirásek,et al.  A thermodynamically consistent approach to microplane theory. Part I. Free energy and consistent microplane stresses , 2001 .

[8]  E. Ramm,et al.  Failure analysis of elasto-plastic material models on different levels of observation , 2000 .

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

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

[11]  R. A. Vonk,et al.  Softening of concrete loaded in compression , 1992 .

[12]  Ekkehard Ramm,et al.  Two-dimensional dynamic simulation of fracture and fragmentation of solids , 1999 .

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

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

[15]  F. Kun,et al.  Fragmentation of colliding discs , 1996 .

[16]  Ekkehard Ramm,et al.  An anisotropic gradient damage model for quasi-brittle materials , 2000 .

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

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

[19]  Hans J. Herrmann,et al.  Simulating deformations of granular solids under shear , 1995 .

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

[21]  E. Stein,et al.  Error indicators and mesh refinements for finite-element-computations of elastoplastic deformations , 1998 .

[22]  Hans J. Herrmann,et al.  A vectorizable random lattice , 1992 .

[23]  Roux,et al.  Fracture of disordered, elastic lattices in two dimensions. , 1989, Physical review. B, Condensed matter.

[24]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .