Macroscopic fracture characteristics of random particle systems

This paper deals with determination of macroscopic fracture characteristics of random particle systems, which represents a fundamental but little explored problem of micromechanics of quasibrittle materials. The particle locations are randomly generated and the mechanical properties are characterized by a triangular softening force-displacement diagram for the interparticle links. An efficient algorithm, which is used to repetitively solve large systems, is developed. This algorithm is based on the replacement of stiffness changes by inelastic forces applied as external loads. It makes it possible to calculate the exact displacement increments in each step without iterations and using only the elastic stiffness matrix. The size effect method is used to determine the dependence of the mean macroscopic fracture energy and the mean effective process zone size of two-dimensional particle systems on the basic microscopic characteristics such as the microscopic fracture energy, the dominant inhomogeneity spacing (particle size) and the coefficients of variation of the microstrength and the microductility. Some general trends are revealed and discussed.

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