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Virtual multi-dimensional internal bonds model and its application in simulation of rock mass

Science china(Technological Sciences) 2008年第2期51卷 192-201页

作者： zhang zhennan1,2 & ge xiurun3.4 1 department of civil engineering,shanghai university,shanghai 200072,china 2 shanghai Institute of Applied Mathematics and Mechanics,shanghai university,shanghai 200072, china 3 Institute of geotechnical engineering,shanghai Jiao Tong university,shanghai 200030,china 4 Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan 430071,china 1. department of civil engineering Shanghai University Shanghai 200072 China 2. shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China 3. Institute of geotechnical engineering Shanghai Jiao Tong University Shanghai 200030 China 4. Institute of Rock and Soil Mechanics Chinese Academy of Sciences Wuhan 430071 China

VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory,the solid mate-rial is considered to consist of random-distributed material particles in microscale. These particles are connected with normal bonds. The macro constitutive relation is derived from the cohesive law between particles. However,in VMIB,the micro particles are connected with both normal and shear bonds. The macro constitutive relation is derived in terms of bond stiffness coefficients. It has been theoretically certified that there exists a corresponding relationship between the two bond stiffness coefficients and the two macro material constants,i.e. the Young’s modulus and Poisson ratio. This corresponding relationship suggests that it should be necessary and sufficient to simultaneously account for the normal and shear interactions between particles. Due to the fact that the fracture criterion is directly incorporated into the constitutive relation,both VIB and VMIB present many advantages in simulating fractures of materials. In the damage model of rock mass,a damage tensor is usually defined to describe the distribution of cracks. The damage value in one direction determines the relative stiffness of rock mass in this direction. In VMIB solid,the relative distribution density of micro bonds in one direction determines the relative macro stiffness of the material in this direction. The effects of the damage value and the relative distribution density of bonds are consistent. To simulate the failure behavior of rock mass with VMIB,the presented paper sets up a quantitative relationship between the damage tensor and the rela-tive distribution density of bonds. Comparison of the theoretical and the experi-mental results shows that VMIB model can represent the effect of distributed cracks on rock mass with this relationship. The presented work provides a founda-tion for further simulating fracture behavior

关键词： VMIB (virtual multi-dimensional internal bonds) rock mass VIB (virtual internal bonds) multi-cracked body numerical simulation

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A MULTISCALE MECHANICAL MODEL FOR MATERIALS BASED ON VIRTUAL INTERNAL BOND THEORY

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Acta Mechanica Solida Sinica 2006年第3期19卷 196-202页

作者： zhang zhennan ge xiurun Li Yonghe department of civil engineering Shanghai University Shanghai 200072 China shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China Institute of geotechnical engineering Shanghai Jiaotong University Shanghai 200030 China Institute of Rock and Soil Mechanics the Chinese Academy of Sciences Wuhan 430071 China

Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson＇s ratio and Young＇s modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds （VMIB） model, is proposed by incorporating a shear bond into the virtual internal bond （VIB） model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. From the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found.

关键词： virtual multi-dimensional internal bond material property dimensionality multiscale modeling molecular dynamics virtual internal bond

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Triangular element partition method with consideration of crack tip

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Science china(Technological Sciences) 2013年第10期56卷 2081-2088页

作者： zhang zhennan ZHENG Hong ge xiurun School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong University Institute of Rock and Soil Mechanics Chinese Academy of Sciences

In fracture simulation,how to model the pre-existing cracks and simulate their propagation without remeshing is an important *** newly developed triangular element partition method(TEPM)provides an efficient approach to this *** firstly meshes the cracked body regardless of the geometry integrity of the interesting object with triangular *** the meshing procedure is completed,some elements are intersected by *** the element intersected by a crack,the TEPM takes the element partition technique to incorporate the discontinuity into the numerical model without any interpolation *** this approach,the TEPM can simulate fracture without mesh *** the TEPM,all the cracked elements are treated as the usual partitioned elements in which the crack runs *** virtual node pairs(the intersection points of crack faces and elements)at the opposite faces of the crack move *** displacements are respectively determined by their neighbor real nodes(nodes formatted in the original mesh scheme)at the same side of the ***,among these cracked elements,the element containing a crack tip,referred to as the crack tip element thereafter,behaves differently from those cut through by the *** influence on the singular field at the vicinity of the fracture tip becomes increasingly significant with the element size *** the crack tip element,the virtual node pair at the crack tip move consistently before fracture occurs while the virtual node pair separate and each virtual node moves independently after the fracture ***,the crack tip element is automatically transformed into the usual partitioned *** the present paper,the crack tip element is introduced into the TEPM to account for the effect of the crack *** examples indicate that the present method is almost free from the element size *** can reach the same precision as the conventional finite element met

关键词： triangular element partition method crack tip element fracture simulation multi-cracked body

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