Albrecht Bertram - Böcker

Over the past 50 years, strain gradient material theories have been developed for the continuum modeling of size effects in materials and structures in terms of their elasticity, plasticity and fracturing.

Over the past 50 years, strain gradient material theories have been developed for the continuum modeling of size effects in materials and structures in terms of their elasticity, plasticity and fracturing.

This book presents an introduction to material theory and, in particular, to elasticity, plasticity and viscoelasticity, to bring the reader close to the frontiers of today’s knowledge in these particular fields.

This book offers frameworks for the material modeling of gradient materials both for finite and small deformations within elasticity, plasticity, viscosity, and thermomechanics. The next chapters are dedicated to the material modeling of second and third-order materials under finite deformations.

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.

This textbook offers an introduction to modeling the mechanical behavior of solids within continuum mechanics and thermodynamics. To illustrate the fundamental principles, the book starts with an overview of the most important models in one dimension. Tensor calculus, which is called for in three-dimensional modeling, is concisely presented in the second part of the book. Once the reader is equipped with these essential mathematical tools, the third part of the book develops the foundations of continuum mechanics right from the beginning. Lastly, the book’s fourth part focuses on modeling the mechanics of materials and in particular elasticity, viscoelasticity and plasticity. Intended as an introductory textbook for students and for professionals interested in self-study, it also features numerous worked-out examples to aid in understanding.

This textbook offers an introduction to modeling the mechanical behavior of solids within continuum mechanics and thermodynamics. To illustrate the fundamental principles, the book starts with an overview of the most important models in one dimension. Tensor calculus, which is called for in three-dimensional modeling, is concisely presented in the second part of the book. Once the reader is equipped with these essential mathematical tools, the third part of the book develops the foundations of continuum mechanics right from the beginning. Lastly, the book’s fourth part focuses on modeling the mechanics of materials and in particular elasticity, viscoelasticity and plasticity. Intended as an introductory textbook for students and for professionals interested in self-study, it also features numerous worked-out examples to aid in understanding.

Many materials or media in nature and technology possess a microstructure which determines their macroscopic behaviour. The knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of this macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. This book presents the development of new methods in this interdisciplinary field of macro- micro-interactions of different engineering branches like mechanical and process engineering, applied mathematics, theoretical, and computational physics. In particular, solids with microstructures and particle systems are considered.