Computer Simulation of Failure in an Elastic Model with Randomly Distributed Defects

We analyze a simple model of failure in an elastic material with randomly distributed defects. The model that we employ is a two‐dimensional triangular lattice of springs. These springs are linearly elastic up to some small strain and irreversibly break at larger strain. Defects are introduced into the model by breaking a certain fraction of the springs before straining. During the simulation, a uniaxial strain is applied, the equilibrium configuration of the lattice is determined, and then the strain is incremented again. The failure stress is found to decrease as the fraction of springs removed is increased and decreases logarithmically with the linear dimension of the sample, L. The cumulative failure stress distribution is well fitted by the form F (σ) = 1 ‐ exp[‐ cL ‐2 exp(‐ k /σ μ )], where σ is the failure stress, σ is a constant between 1 and 2, and c and k are constants which are characteristic of the microscopic properties of the system.