# Extreme Value Theory and Strength of Materials

## Abstract

Extreme value distributions have found widespread use for the description of strength of materials and mechanical structures, often in combination with stochastic models for the loads and forces acting on the material. Thus it is often assumed that the maximum of several loads follows one of the extreme value distributions for maxima. More important, and also less obvious, is that the strength of a piece of material, such as a strip of paper or glass fibre, is sometimes determined by the strength of its weakest part, and then perhaps follows one of the extreme value distributions for minima. Based on this so-called *weakest link principle* much of the work has been directed towards a study of *size effects* in the testing of materials. By this we mean the empirical fact that the strength of a piece of material varies with its dimensions in a way which is typical for the type of material and the geometrical form of the object. An early attempt towards a statistical theory for this was made more than a century ago by Chaplin (1880, 1882); see also Lieblein (1954) and Harter (1977).

## Keywords

Yield Strength Strength Distribution Paper Strip Weak Part Local Strength## Preview

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