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...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.展开更多
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 ...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 of rock mass with VMIB model,and an alternative approach for modeling other multi-cracked body.展开更多
基金Project supported by the National Basic Research Program of China (973 Project) (No. 2002CB412704).
文摘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.
基金the National Natural Science Foundation of China (Grant No. 50609013)
文摘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 of rock mass with VMIB model,and an alternative approach for modeling other multi-cracked body.
