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 nc whose failure statistics are the same as the known statistics for nc elements failing under mean-field stress transfer. The large n statistics are found analytically. Strength scales as √ln(n), accurate to ≥10¹¹ elements. These results suggest new concepts for understanding scaling of failure in heterogeneous materials.