Il Problema Centrale della Teoria dell'Elasticità Non-Lineare Secondo Signorini

Saccomandi, Giuseppe

Matematica, cultura e società, Série 1, Tome 9 (2024) no. 1, pp. 5-27

Résumé

In 1942, Antonio Signorini, speaking about the theory of non-linear elasticity at an international conference at INDAM, declared that within the framework of this theory:“ ... before any numerical calculations one has to deal with an extremely difficult problem of true mathematical physics: the choice of the complete expression of the elastic potential.” Signorini was thinking of numerical calculations that could indicate the theory of non-linear elasticity as a mathematical model suitable for describing the behavior of certain materials. This note illustrates how Signorini's problem from 1942 to the present day has attracted the attention not only of mechanics community but also of many mathematicians. The main results obtained in these eighty years are also illustrated from a historical point of view, and some of the problems that are still open are indicated.