Advances in Applied Mechanics.

Abstract

name a few of those who have contributed to erecting the "Advances" edifice.The idea for this serial was born before the second worldwide conflict, as early as 1940, but could only materialise, due to various setbacks, in 1948, with the first volume edited by Richard von Mises and Theodore von Kármán [3].The original principle set forth by the first two editors was that "The book is intended for students, scholars, and engineers who are familiar with the contents of text books and handbooks but are unable to follow up all the research papers currently published in periodicals and institutional reports" [3].The idea is that the serial should provide authoritative, didactic and self-contained reviews of a research field in which the author is "actively engaged" and has the latitude to present personal views and solutions [4].This short forty-sixth volume is atypical because it had to be prepared within a very short timeframe.I am deeply indebted to the authors of this volume, who have demonstrated an exemplary level of commitment and responsiveness in order to adhere to the very tight schedule imposed upon them.The book is composed of two articles dealing with variational formulations.Variational formulations have clearly been essential to mechanics and to the study of materials and structures, providing rigorous mathematical grounds to the theories.Advances has devoted much attention to this topic.One can refer, among many others, to the survey by Biot [1] of variational-Lagrangian irreversible thermodynamics, which underlies some of the developments in the second chapter of the present volume.Variational formulations were also discussed in this serial as tools for homogenization of heterogeneous materials, e.g. in the chapter by Willis [5] on variational principles for the