A Multi-laminate Element Method (MEM) is used to model both dynamic and elastoplastic behavior of rocks, with a particular focus on semi-micromechanical behavior of geo-materials. The constitutive equations of this numerical model is derived within the context of elastic behavior of the whole medium and plastic sliding of interfaces of predefined multi-laminate, following the framework of working with six stress/strain components and not missing the directional effects. The formulation incorporates explicitly the notion of the preferred direction, with a description of the medium as an assembly of discrete polyhedron elements that support the overall applied loads through contact friction and cohesion, the overall mechanical response ideally may be described on the basis of micro-mechanical behavior of discrete polyhedron elements interconnections. Naturally, this requires the description of overall stress, characterization of fabric, representation of kinematics, development of local rate constitutive relations and evaluation of the overall differential constitutive relations in terms of the local quantities. Multi-laminate framework by defining the small continuum structural units as an assemblage of particles and voids that fill infinite spaces between the sampling planes, has appropriately justified the contribution of interconnection forces in overall macro-mechanics. Upon these assumptions, plastic deformations are to occur due to sliding, separation/closing of the boundaries and elastic deformations are the overall responses of structural unit bodies. Therefore, the overall deformation of any small part of the medium is composed of total elastic response and an appropriate summation of sliding, separation/closing phenomenon under the current effective normal and shear stresses on sampling planes. These assumptions adopt overall sliding, separation/closing of intergranular points of grains included in one structural unit (discrete polyhedron elements) are summed up and contributed as the result of sliding, separation/closing surrounding boundary planes. This simply implies yielding/failure or even ill-conditioning, bifurcation response damage and fragmentation phenomena to be possible over any of the randomly oriented sampling planes. Consequently, plasticity control such as yielding should be checked at each of the planes and those of the planes that are sliding will contribute to plastic deformation. Therefore, the geo-material mass has an infinite number of yield functions usually one for each of the planes in the physical space. Compact and isotropic synthetic media are generated automatically and are used to investigate the mechanical behavior of these low-porosity materials. In the case of micro-mechanics, the model considers the twophase, aggregate and cement medium, at a macroscopic scale. The proposed multi-laminate based model is capable of predicting the behavior of geo-materials on the basis of plastic sliding mechanisms, elastic behavior of particles and possibilities to see the micro-fabric effects as natural anisotropy as well as induced anisotropy in plasticity. The model is capable of predicting the behavior under different orientation of bedding plane, history of strain progression during the application of any stress/strain paths. The influences of rotation of the direction of principal stress and strain axes and induced anisotropy are included in arational way without any additional hypotheses.
Numerical Study Of Rock And Concrete Behavior By Multilaminate Element Modeling
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Sadrnejad, S.A. "Numerical Study Of Rock And Concrete Behavior By Multilaminate Element Modeling." Paper presented at the ISRM International Symposium - 5th Asian Rock Mechanics Symposium, Tehran, Iran, November 2008.
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