Albrecht Bertram Livres

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.

Focusing on material theory, this book introduces key concepts such as elasticity, plasticity, and viscoelasticity, making these advanced topics accessible to engineers, physicists, and mathematicians without prior knowledge. Each section begins with a literature comment, guiding readers towards further exploration of the subject. This structured approach ensures a comprehensive understanding while staying aligned with contemporary advancements in the field.

The book provides comprehensive frameworks for modeling gradient materials across various fields such as elasticity, plasticity, viscosity, and thermomechanics. It begins with fundamental balance laws applicable to all gradient materials, followed by detailed modeling of second and third-order materials under finite deformations. It then narrows its focus to small deformations within geometrically linear theory. Additionally, it explores internal constraints in gradient materials and concludes with a study of incompressible viscous gradient fluids, addressing applications like turbulent flows.

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.

This careful and detailed introduction to non-linear continuum mechanics and to elasticity and platicity, with a unique mathematical foundation, starts right from the basics. The general theory of mechanical behaviour is particularized for the broad and important classes of elasticity and plasticity. Brings the reader to the forefront of today's knowledge. A list of notations and an index help the reader finding specific topics.