PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surface, successfully applied to a direct variational approach to the nonlinear shell stability problems. Until now most Pogorelov's monographs were written in Russian, which limited the diffusion of his ideas among the international scientific community. The present book is intended to assist and encourage the researches in this field to apply the geometric method and the related results to everyday engineering practice.

This second volume of the series Lecture Notes in Applied and Computational Mechanics is the second part of the compendium of reviewed articles presented at the 11th EUROMECH-MECAMAT conference entitled "Mechanics of microstructured solids: cellular materials, fibre reinforced solids and soft tissues", which took place in Torino (Italy) in March 10-14, 2008, at the Museo Regional delle Scienze. This EUROMECH-MECAMAT conference was jointly organized by the Dipartimento di Matematica dell'Universita di Torino, Italy and the INPL Institute (LEMTA, Nancy-Universite, France). Prof. Franco Pastrone and Prof. Jean-Francois Ganghoffer were the co-chairmen.

This special volume of the series Lecture Notes in Applied and Computational Mechanics is a compendium of reviewed articles presented at the 11th EUROMECH-MECAMAT conference entitled "Mechanics of microstructured solids: cellular materials, fibre reinforced solids and soft tissues", which took place in Torino (Italy) in March 10-14, 2008, at the Museo Regional delle Scienze. This EUROMECH-MECAMAT conference was jointly organized by the Dipar- mento di Matematica dell'Universita di Torino, Italy and the INPL Institute (LEMTA, Nancy-Universite, France). Prof. Franco Pastrone and Prof. Jean- Francois Ganghoffer were the co-chairmen. The conference brought together 50 scientists from 11 European countries, and was aimed at defining the current state of the art in the growing field of cellular and fibrous materials in Europe. Participants had interests in the constitutive m- els of micro-structured solids, non-linear wave propagation, setting up of models and identification of fibre reinforced solids, and soft tissue behaviour in a bio- chanical context. The conference covered most of the mechanical and material aspects, grouped in the following four sessions: * Fibre reinforced materials; * Soft biological tissues; * Generalized continua: models and materials; * Non-linear wave propagation. The high quality talks showed a good balance between modelling and material - pects. An important part of the colloquium, with 12 presentations, was devoted to various aspects of the biomechanics of soft tissues, such as cell adhesion, consti- tive models of soft tissues (brain; arteries), or models of blood flow.

This second volume of the series Lecture Notes in Applied and Computational Mechanics is the second part of the compendium of reviewed articles presented at the 11th EUROMECH-MECAMAT conference entitled "Mechanics of microstructured solids: cellular materials, fibre reinforced solids and soft tissues," which took place in Torino (Italy) in March 10-14, 2008, at the Museo Regional delle Scienze. This EUROMECH-MECAMAT conference was jointly organized by the Dipartimento di Matematica dell'Universita di Torino, Italy and the INPL Institute (LEMTA, Nancy-Universite, France). Prof. Franco Pastrone and Prof. Jean-Francois Ganghoffer were the co-chairmen.

This special volume of the series Lecture Notes in Applied and Computational Mechanics is a compendium of reviewed articles presented at the 11th EUROMECH-MECAMAT conference entitled "Mechanics of microstructured solids: cellular materials, fibre reinforced solids and soft tissues", which took place in Torino (Italy) in March 10-14, 2008, at the Museo Regional delle Scienze. This EUROMECH-MECAMAT conference was jointly organized by the Dipar- mento di Matematica dell'Universita di Torino, Italy and the INPL Institute (LEMTA, Nancy-Universite, France). Prof. Franco Pastrone and Prof. Jean- Francois Ganghoffer were the co-chairmen. The conference brought together 50 scientists from 11 European countries, and was aimed at defining the current state of the art in the growing field of cellular and fibrous materials in Europe. Participants had interests in the constitutive m- els of micro-structured solids, non-linear wave propagation, setting up of models and identification of fibre reinforced solids, and soft tissue behaviour in a bio- chanical context. The conference covered most of the mechanical and material aspects, grouped in the following four sessions: * Fibre reinforced materials; * Soft biological tissues; * Generalized continua: models and materials; * Non-linear wave propagation. The high quality talks showed a good balance between modelling and material - pects. An important part of the colloquium, with 12 presentations, was devoted to various aspects of the biomechanics of soft tissues, such as cell adhesion, consti- tive models of soft tissues (brain; arteries), or models of blood flow.

This book deals with the new developments and application of the geometric method to the nonlinear stability problem for thin non-elastic shells. A.V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicityly the asymptotic formulas for the upper and lower critical loads. The geometric method by Pogorelov is one of the most importanty analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the post critical form of a deformed shell surface, successfully applied to a direct variational approach to the nonlinear shell stability problems. Until now, most of Pogorelov's monographs were written in Russian, which limited the diffusion of his ideas among the international scientific community. The present book is intended to assist and encourage the researchers in this field to apply the geometric method and the related results to everyday engineering practice. Further developments of the geometric method are carried out in this book and are directed to stability of thin shells in the case of elastic anisotropy, elastic anisotropy with linear memory and elasto-plastic properties of the shell material. This book is intended to serve both as a textbook for post-graduate students in structural engineering and applied mathematics, and as a revference monograph for academic and industrial researchers.