Analytical link between structural strength size effect and material random heterogeneity

TL;DR

This paper develops an analytical scaling law linking the size effect of brittle material strength to material heterogeneity modeled by correlated random fields, extending Weibull law insights.

Contribution

It introduces a new analytical framework connecting size effect and material heterogeneity using excursion set geometry, advancing understanding of brittle material strength.

Findings

Derived a complete probability distribution function for structural strength.

Established a method to compute strength for any failure probability.

Extended Weibull law with a more general, heterogeneity-based model.

Abstract

A theoretical scaling law for the size effect of the strength of brittle materials is presented. To some extend, it can be seen as an extension of the well known Weibull law. For that a correlated Random Fields is used to model the heterogeneities of the material. Thanks to recent results on the geometry of excursion sets, one can analytically compute the whole probability distribution function for the strength of a structure of a given size. Then, using this PDF, the structural strength associated to any failure probability can be derived.