Stochastic elasticity : a nondeterministic approach to the nonlinear field theory / L. Angela Mihai.
2022
QA931
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Title
Stochastic elasticity : a nondeterministic approach to the nonlinear field theory / L. Angela Mihai.
Author
Mihai, L. Angela, author.
ISBN
9783031066924 (electronic bk.)
3031066928 (electronic bk.)
9783031066917
303106691X
3031066928 (electronic bk.)
9783031066917
303106691X
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource (xvii, 275 pages) : illustrations (chiefly color).
Item Number
10.1007/978-3-031-06692-4 doi
Call Number
QA931
Dewey Decimal Classification
531/.3820151922
Summary
Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains. Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.
Bibliography, etc. Note
Includes bibliographical references and index.
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Source of Description
Description based on print version record.
Series
Interdisciplinary applied mathematics ; v. 55.
Available in Other Form
Stochastic elasticity.
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Table of Contents
1 Introduction
2 Finite elasticity as prior information
3 Are elastic materials like gambling machines?
4 Elastic instabilities
5 Oscillatory motions
6 Liquid crystal elastomers
7 Conclusion
Appendix A Notation
Appendix B Fundamental concepts
Bibliography
Index.
2 Finite elasticity as prior information
3 Are elastic materials like gambling machines?
4 Elastic instabilities
5 Oscillatory motions
6 Liquid crystal elastomers
7 Conclusion
Appendix A Notation
Appendix B Fundamental concepts
Bibliography
Index.