# Variational Principles of Continuum Mechanics

## II. Applications

Part of the Interaction of Mechanics and Mathematics book series (IMM)

Part of the Interaction of Mechanics and Mathematics book series (IMM)

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems.

Berdichevsky’s work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given.

This book, the second volume, describes how the variational approach can be applied to constructing models of continuum media, such as the theory of elastic plates; shells and beams; shallow water theory; heterogeneous mixtures; granular materials; and turbulence. It goes on to apply the variational approach to asymptotical analysis of problems with small parameters, such as the derivation of the theory of elastic plates, shells and beams from three-dimensional elasticity theory; and the basics of homogenization theory. A theory of stochastic variational problems is considered in detail too, along with applications to the homogenization of continua with random microstructures.

Elastic Body Fluids Variational Principles continuum mechanics development mechanics microstructure

- DOI https://doi.org/10.1007/978-3-540-88469-9
- Copyright Information Springer-Verlag Berlin Heidelberg 2009
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Engineering
- Print ISBN 978-3-540-88468-2
- Online ISBN 978-3-540-88469-9
- Series Print ISSN 1860-6245
- Series Online ISSN 1860-6253
- About this book