Fracture of disordered three-dimensional spring networks: A computer simulation methodology

In this paper a computational technique is proposed to describe brittle fracture of highly porous random media. Geometrical heterogeneity in the "open cell foam" structure of the porous medium on a mesoscopic length scale ({~}100 nm) is mapped directly onto a three-dimensional (3D) elastic network by using molecular dynamics techniques to generate starting configurations. The aspects in our description are that the elastic properties of an irregular $3D$-network are described using not only a potential with a two-body term (change in bond length, or linear elastic tension) and a three-body term (change in bond angle, or bending), but also a four-body term (torsion). The equations for minimum energy are written and solved in matrix form. If the changes in bond lengths, bond- or torsion angles exceed pre-set threshold values, then the corresponding bonds are irreversibly removed from the network. Brittleness is mimicked by choosing small ({~}1%) threshold values. The applied stress is increased until the network falls apart into two or more pieces.