04557nam a22006015i 4500 978-3-319-70172-1 DE-He213 20210118153345.0 cr nn 008mamaa 171201s2017 gw | s |||| 0|eng d 9783319701721 978-3-319-70172-1 10.1007/978-3-319-70172-1 doi QA71-90 PDE bicssc COM014000 bisacsh PDE thema 004 23 Straughan, Brian. author. aut http://id.loc.gov/vocabulary/relators/aut Mathematical Aspects of Multi–Porosity Continua [electronic resource] / by Brian Straughan. 1st ed. 2017. Cham : Springer International Publishing : Imprint: Springer, 2017. IX, 208 p. 7 illus., 4 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Advances in Mechanics and Mathematics, 1571-8689 ; 38 Introduction -- Models for Double and Triple Porosity -- Double Porosity and Voids -- Comparison of Porosity and Voids Theories -- Uniqueness and Stability by Energy Methods -- Uniqueness Without Definiteness Conditions -- Continuous Dependence in Multi-Porosity Elasticity -- Waves in Double Porosity Elasticity -- Acceleration Waves in Double Voids -- Double Porosity and Second Sound. This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed. Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion. This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications. Computer mathematics. Mechanics. Mechanics, Applied. Mathematical physics. Computational Science and Engineering. http://scigraph.springernature.com/things/product-market-codes/M14026 Solid Mechanics. http://scigraph.springernature.com/things/product-market-codes/T15010 Mathematical Applications in the Physical Sciences. http://scigraph.springernature.com/things/product-market-codes/M13120 SpringerLink (Online service) Springer eBooks Printed edition: 9783319701714 Printed edition: 9783319701738 Printed edition: 9783319888958 Advances in Mechanics and Mathematics, 1571-8689 ; 38 https://doi.org/10.1007/978-3-319-70172-1 ZDB-2-SMA 453454 453454 EB Available to subscribing member institutions only. Доступно лише організаціям членам підписки. Online access from local network of NaUOA. Online access with authorization at https://link.springer.com/ Онлайн-доступ з локальної мережі НаУОА. Онлайн доступ з авторизацією на https://link.springer.com/