A multiscale mechanical model for materials based on virtual internal bond theory

Abstract

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.KEY WORDS virtual multi-dimensional internal bond, material property dimensionality, multiscale modeling, molecular dynamics, virtual internal bond

Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds

“…The constitutive relation should possess the tensor quality in that it should be independent of the specific coordinate system. Fortunately, Zhang and Ge [12] has theoretically proved the tensor quality of Eq. (1).…”

Modeling of progressive damage in concrete using multidimensional virtual internal bond method

“…The macroscale kinematic measure, deformation gradient F ij , i , j = {1,2,3} is given as 24 where x i and X j denote the i th and j th component of material point co‐ordinates in deformed and undeformed configuration, respectively, and ∂ is the partial derivative operator. Cauchy–Born rule 24–35 is invoked to associate microscale (Figure 2) with macroscale kinematics, thereby providing the position vector of the microbond IJ in its current configuration as l o FX i .Under the assumption of infinitesimal deformation, length of the bond in the deformed configuration can be simplified as where is the small strain measure and δ ij is the Kronecker delta function. The bond energy stored in L‐bond ( U n ) and R‐bond ( U s ) is given by 28 …”

“…Although the available VIB models are successful in capturing several facets of fracture in concrete, still, the effect of asymmetry in fracture strength and especially explicit accounting of failure in tension and compression is missing. Hence, in the present work, the MVIB approach of Zhang et al 28 is modified by imposing independent bond evolution function in tension and compression loading, and its effect is analyzed. The remaining paper is organized as follows.…”

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

“…m takes the values of 0.0, 0.5, 0. 7 Young's modulus of material. The simulated and the experimental results are shown in Figure 5.…”

“…Because the fracture criterion is directly incorporated into the constitutive relation, VIB model presents some advantages in simulating fracture behaviors. Zhang and Ge [4][5][6][7] introduced a shear bond into the original VIB to restrict the relative rotation freedom of pairwise particles. By this modification, VIB can be applied to materials of wider range of Poisson ratio.…”