Stochastic Elasticity
A Nondeterministic Approach to the Nonlinear Field Theory
Seiten
2023
|
1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-06694-8 (ISBN)
Springer International Publishing (Verlag)
978-3-031-06694-8 (ISBN)
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 variablesas 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.
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 variablesas 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.
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.
| Erscheinungsdatum | 05.09.2023 |
|---|---|
| Reihe/Serie | Interdisciplinary Applied Mathematics |
| Zusatzinfo | XVII, 275 p. 94 illus., 90 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 451 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | applied probability • hyperelastic materials • Information Theory • large strain analysis • limit point instability • Liquid Crystal Elastomers • nonlinear elastic deformations • Propagation of Uncertainty • Stochastic Modeling • uncertainty quantification |
| ISBN-10 | 3-031-06694-4 / 3031066944 |
| ISBN-13 | 978-3-031-06694-8 / 9783031066948 |
| Zustand | Neuware |
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