Size scaling of strength in heterogeneous materials

The strength of planar arrays of n elastic elements, having heterogeneous strengths and coupled by elastic stress transfer, is studied by simulation and size-scaling analyses. Failure statistics for large n are shown to be controlled by a critical damage cluster of size n(c) whose failure statistics are the same as the known statistics for n(c) elements failing under mean-field stress transfer. The large n statistics are found analytically. Strength scales as root ln(n), accurate to greater than or equal to 10(11) elements. These results suggest new concepts for understanding scaling of failure in heterogeneous materials.