An aggregate generation and packing algorithm based on Monte-Carlo method is developed to express the aggregate random distribution in cement concrete. A mesoscale model is proposed on the basis of the algorithm. In this model, the concrete con- sists of three parts, namely coarse aggregate, cement matrix and the interracial transition zone （ITZ） between them. To verify the proposed model, a three-point bending beam test was performed and a series of two-dimensional mesoscale concrete mod- els were generated for crack behavior investigation. The results indicate that the numerical model proposed in this study is helpful in modeling crack behavior of concrete, and that treating concrete as heterogeneous material is very important in frac- ture modeling.
Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.
