The complete works of Gabrio Piola: Volume I
The complete works of Gabrio Piola: Volume I

Author: Francesco dell'Isola

Publisher: Springer

Published: 2014-07-02

Total Pages: 816

ISBN-13: 3319002635

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Gabrio Piola works had an enormous impact on the development of applied mathematics and continuum mechanics. An excellent scientific committee who took it upon themselves to translate his complete works. In a second step, they commented Piola’s work and compared it to modern theories in mechanics in order to stress Piola’s impact on modern science and proofs that he has set milestones in applied mathematics. This book presents Piola's original Italian text together with ist translations and their comments. It shows impressively that Gabrio Piola’s work must still be regarded as a modern theory.

The Complete Works of Gabrio Piola: Volume II
The Complete Works of Gabrio Piola: Volume II

Author: Francesco dell'Isola

Publisher: Springer

Published: 2018-10-06

Total Pages: 954

ISBN-13: 3319706926

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This book presents the second volume of Piola’s original Italian text together with the English-language translation and comments, showing convincingly that Gabrio Piola’s work must still be regarded as a modern theory. Gabrio Piola’s work has had an enormous impact on the development of applied mathematics and continuum mechanics. As such, a committee of scientific experts took it upon themselves to translate his complete works. In a second step, they commented on Piola’s work and compared it to modern theories in mechanics in order to stress Piola’s impact on modern science and prove and confirm that he achieved significant milestones in applied mathematics.

Evaluation of Scientific Sources in Mechanics
Evaluation of Scientific Sources in Mechanics

Author: Francesco dell'Isola

Publisher: Springer Nature

Published: 2021-08-12

Total Pages: 377

ISBN-13: 3030805506

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This book evaluates the importance of various historical sources and discusses their role in the creation and transmission of scientific knowledge. It presents an annotated translation of the introductory words given by Johan Ludvig Heiberg to his translation of the works of Archimedes. Further, it offers English translations of and commentaries on selected fundamental works by Ernst Hellinger and Gabrio Piola, which lay the groundwork for the modern theory of advanced materials, and also examines the criteria used to evaluate scientific works.

Discrete and Continuum Models for Complex Metamaterials
Discrete and Continuum Models for Complex Metamaterials

Author: Francesco dell'Isola

Publisher: Cambridge University Press

Published: 2020-03-12

Total Pages: 409

ISBN-13: 1108850189

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Bringing together contributions on a diverse range of topics, this text explores the relationship between discrete and continuum mechanics as a tool to model new and complex metamaterials. Providing a comprehensive bibliography and historical review of the field, it covers mechanical, acoustic and pantographic metamaterials, discusses Naive Model Theory and Lagrangian discrete models, and their applications, and presents methods for pantographic structures and variational methods for multidisciplinary modeling and computation. The relationship between discrete and continuous models is discussed from both mathematical and engineering viewpoints, making the text ideal for those interested in the foundation of mechanics and computational applications, and innovative viewpoints on the use of discrete systems to model metamaterials are presented for those who want to go deeper into the field. An ideal text for graduate students and researchers interested in continuum approaches to the study of modern materials, in mechanical engineering, civil engineering, applied mathematics, physics, and materials science.

Mathematical Applications in Continuum and Structural Mechanics
Mathematical Applications in Continuum and Structural Mechanics

Author: Francesco Marmo

Publisher: Springer Nature

Published: 2021-11-30

Total Pages: 275

ISBN-13: 3030427072

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This book presents a range of research projects focusing on innovative numerical and modeling strategies for the nonlinear analysis of structures and metamaterials. The topics covered concern various analysis approaches based on classical finite element solutions, structural optimization, and analytical solutions in order to present a comprehensive overview of the latest scientific advances. Although based on pioneering research, the contributions are focused on immediate and direct application in practice, providing valuable tools for researchers and practicing professionals alike.

New Achievements in Continuum Mechanics and Thermodynamics
New Achievements in Continuum Mechanics and Thermodynamics

Author: Bilen Emek Abali

Publisher: Springer

Published: 2019-03-13

Total Pages: 586

ISBN-13: 3030133079

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This book presents a liber amicorum dedicated to Wolfgang H. Müller, and highlights recent advances in Prof. Müller’s major fields of research: continuum mechanics, generalized mechanics, thermodynamics, mechanochemistry, and geomechanics. Over 50 of Prof. Müller’s friends and colleagues contributed to this book, which commemorates his 60th birthday and was published in recognition of his outstanding contributions.

Developments and Novel Approaches in Nonlinear Solid Body Mechanics
Developments and Novel Approaches in Nonlinear Solid Body Mechanics

Author: Bilen Emek Abali

Publisher: Springer Nature

Published: 2020-07-18

Total Pages: 491

ISBN-13: 3030504603

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This book features selected manuscripts presented at ICoNSoM 2019, exploring cutting-edge methods for developing novel models in nonlinear solid mechanics. Innovative methods like additive manufacturing—for example, 3D printing— and miniaturization mean that engineers need more accurate techniques for modeling solid body mechanics. The book focuses on the formulation of continuum and discrete models for complex materials and systems, particularly the design of metamaterials.

Generalized Continua as Models for Classical and Advanced Materials
Generalized Continua as Models for Classical and Advanced Materials

Author: Holm Altenbach

Publisher: Springer

Published: 2016-04-15

Total Pages: 456

ISBN-13: 3319317210

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This volume is devoted to an actual topic which is the focus world-wide of various research groups. It contains contributions describing the material behavior on different scales, new existence and uniqueness theorems, the formulation of constitutive equations for advanced materials. The main emphasis of the contributions is directed on the following items - Modelling and simulation of natural and artificial materials with significant microstructure, - Generalized continua as a result of multi-scale models, - Multi-field actions on materials resulting in generalized material models, - Theories including higher gradients, and - Comparison with discrete modelling approaches

Recent Developments in the Theory of Shells
Recent Developments in the Theory of Shells

Author: Holm Altenbach

Publisher: Springer Nature

Published: 2019-09-25

Total Pages: 799

ISBN-13: 3030177475

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This book commemorates the 80th birthday of Prof. W. Pietraszkiewicz, a prominent specialist in the field of general shell theory. Reflecting Prof. Pietraszkiewicz’s focus, the respective papers address a range of current problems in the theory of shells. In addition, they present other structural mechanics problems involving dimension-reduced models. Lastly, several applications are discussed, including material models for such dimension-reduced structures.

Compendium on Gradient Materials
Compendium on Gradient Materials

Author: Albrecht Bertram

Publisher: Springer Nature

Published: 2022-05-28

Total Pages: 307

ISBN-13: 3031045009

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This book offers frameworks for the material modeling of gradient materials both for finite and small deformations within elasticity, plasticity, viscosity, and thermomechanics. The first chapter focuses on balance laws and holds for all gradient materials. The next chapters are dedicated to the material modeling of second and third-order materials under finite deformations. Afterwards the scope is limited to the geometrically linear theory, i.e., to small deformations. The next chapter offers an extension of the concept of internal constraints to gradient materials. The final chapter is dedicated to incompressible viscous gradient fluids with the intention to describe, among other applications, turbulent flows, as already suggested by Saint-Venant in the middle of the 19th century.