On the inverse formulation of the problem of brittle fracture statistics

A new formulation of the problem of brittle fracture statistics is presented. It is shown that it is possible to devise a mathematical approach by which a strength distribution function corresponding to a given form of a size-mean-strength relationship can be obtained rather than by fitting test data to an a priori assumed form of strength distribution function. The problem in effect is shown to reduce to the solution of a nonlinear integral equation, and a method of its solution is presented. To illustrate the feasibility of the method, the well-known distribution function due to Weibull is derived.