Scaling behaviour of damage in the fracture of two-dimensional elastic beam lattices

¹  Department of Physics, NTNU - N-7491 Trondheim, Norway
²  Department of Chemical Engineering, NTNU - N-7491 Trondheim, Norway

Received: 19 April 2007
Accepted: 20 August 2007

Abstract

The response of stress with strain is one of the fundamental quantities used to characterize fracture in materials. Exactly how this relationship appears depends on the microscopic structure, which can vary considerably from material to material. Presently, we study the breaking of materials where the structural disorder is varied within a broad range, using a model based on elastic beams. A large number of system sizes is then generated for each level of disorder in order to study the scaling properties of the force-displacement characteristic. Whereas maximum force and displacement is found to scale trivially, being simply proportional to system size, the scaling exponents relative to the extent of damage in the stable and unstable regimes of fracture are found to scale non-trivially. Our calculations contradict earlier findings which suggested that the scaling is universal with respect to the disorder.