New method for simulating fracture using an elastically uniform random geometry lattice

This paper discusses 2D lattice models of beams for simulating the fracture of brittle materials. A simulation of an experiment on a concrete plate subjected to shear, in which two overlapping cracks occur, is used to study the effect of individual beam characteristics and different arrangements of the beams in the overall lattice. It was found that any regular orientation of the beams influences the resulting crack patterns. A method is developed to construct a lattice with a random geometry, but which can represent a homogeneous medium, that eliminates the influence of the beam orientation on a simulated crack pattern. Methods to implement a wide range of Poisson's ratios are also developed, and the use of the random lattice to study arbitrary microstructures is outlined. The crack patterns that are obtained with this lattice are in good agreement with the experimental results. Published by Elsevier Science Ltd