The Main Problem of Antonio Signorini

Prof Giuseppe Saccomandi (Università degli Studi di Perugia)

Tuesday 21st March, 2023 14:00-15:00 Maths 311B / (ID: 838 0651 2263)

Abstract

In 1942 Antonio Signorini delivers a talk in the framework of an international meeting in Rome organised by the Istituto Nazionale di Alta Matematica, INDAM, and about the theory of nonlinear elasticity:

...prima di ogni calcolo numerico si ha da affrontare un problema estremamente diffcile di vera Fisica matematica: la scelta dell'espressione completa del potenziale elastico¹

The aim of today's seminar is to illustrate what has happened regarding the Signorini problem from 1942 to the present day, following the ideas and approach contained in some of my recent works:

• Puglisi, G., & Saccomandi, G. (2016). Multi-scale modelling of rubber-like materials and soft tissues: an appraisal. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2187), # 20160060;
• Destrade, M., Saccomandi, G., & Sgura, I. (2017). Methodical fitting for mathematical models of rubber-like materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198), # 20160811;
• Destrade, M., Dorfmann, L., & Saccomandi, G. (2022). The Ogden model of rubber mechanics: 50 years of impact on nonlinear elasticity. Philosophical Transactions of the Royal Society A, 380(2234), # 20210332.
  

¹before any numerical calculation one has to face an extremely diffcult problem of true mathematical physics: the choice of the complete expression of the elastic potential.

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