The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas. It was originally introduced by Clausius in 1865 along abstract lines focusing on thermodynamical irreversibility of macroscopic physical processes. In the next decade, Boltzmann made the genius connection—further developed by Gibbs—of the entropy with the microscopic world, which led to the formulation of a new and impressively successful physical theory, thereafter named statistical mechanics. The extension to quantum mechanical systems was formalized by von Neumann in 1927, and the connections with the theory of communications and, more widely, with the theory of information were respectively introduced by Shannon in 1948 and Jaynes in 1957. Since then, over fifty new entropic functionals emerged in the scientific and technological literature. The most popular among them are the additive Renyi one introduced in 1961, and the nonadditive one introduced in 1988 as a basis for the generalization of the Boltzmann–Gibbs and related equilibrium and nonequilibrium theories, focusing on natural, artificial and social complex systems. Along such lines, theoretical, experimental, observational and computational efforts, and their connections to nonlinear dynamical systems and the theory of probabilities, are currently under progress. Illustrative applications, in physics and elsewhere, of these recent developments are briefly described in the present synopsis.

Entropy

Damage-plastic model for concrete failure

Gabrio Piola’s scientific papers have been underestimated in mathematical physics literature. Indeed, a careful reading of them proves that they are original, deep and far-reaching. Actually, even ...

https://hal.archives-ouvertes.fr/hal-00869677/document

At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola

Finite element modeling of confined concrete-II : plastic-damage model

Gabrio Piola's scientific papers have been underestimated in the mathematical-physics literature. Indeed a careful reading of them proves that they are original, deep and far reaching. Actually -even if his contribution to mechanical sciences is not completely ignored- one can undoubtedly say that the greatest part of his novel contributions to mechanics, although having provided a great impetus and substantial influence on the work of many preminent mechanicians, is in fact generally ignored. It has to be remarked that authors [10] dedicated many efforts to the aim of unveiling the true value of Gabrio Piola as a scientist; however, some deep parts of his scientific results remain not yet sufficiently illustrated. Our aim is to prove that non-local and higher gradient continuum mechanics was conceived already in Piola's works and to try to explain the reasons of the unfortunate circumstance which caused the erasure of the memory of this aspect of Piola's contribution. Some relevant differential relationships obtained in Piola [Piola, 1845-6] are carefully discussed, as they are still nowadays too often ignored in the continuum mechanics literature and can be considered the starting point of Levi-Civita's theory of Connection for Riemannian manifolds.

At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola

A variational model based on isogeometric interpolation for the analysis of cracked bodies

https://hal.archives-ouvertes.fr/hal-00878684/document

A framework of elastic–plastic damaging model for concrete under multiaxial stress states

https://hal.archives-ouvertes.fr/hal-00878757/document

Loredana Contrafatto

Papers

A variational model based on isogeometric interpolation for the analysis of cracked bodies

A framework of elastic–plastic damaging model for concrete under multiaxial stress states

A new thermodynamically consistent continuum model for hardening plasticity coupled with damage

A concrete homogenisation technique at meso-scale level accounting for damaging behaviour of cement paste and aggregates

A reconstructed local B̄ formulation for isogeometric Kirchhoff–Love shells