Giuseppe Saccomandi - Böcker

This book pursues a twofold objective: to introduce the methodologies of Italian Rational Mechanics to an international audience—hoping they may prove valuable to teachers and students in Engineering, Physics, and Mathematics—and to offer essential material for engineering students in Italy whose courses are taught in English. Readers are expected to have a background in Calculus and Linear Algebra, along with a basic familiarity with the fundamental principles of Newtonian Mechanics. Rational Mechanics is a mathematical discipline that spans from Newtonian to analytical and applied mechanics. It follows a rigorous deductive approach and has traditionally provided a foundational framework that bridges mathematics, physics, and engineering. This book builds on the long-standing Italian tradition of teaching Rational Mechanics at the undergraduate level. It is particularly well suited for courses that guide students from first principles to progressively more advanced topics, culminating in the sophisticated modeling of real-world phenomena. Historically, Rational Mechanics has often been the first course in which students of Engineering, Physics, or Mathematics encounter a rigorous and comprehensive framework for mathematical modeling, making its educational value especially significant. The presentation of fundamental concepts is consistently oriented toward applications, with the aim of fostering synergies in teaching, particularly in interdisciplinary contexts. The structure of the book reflects this approach, with special emphasis on sections that are often treated in a more abstract way—such as constraints, the Principle of Virtual Work, d’Alembert’s Principle, and Analytical Mechanics.

More than fifty years ago, Professor R. S. Rivlin pioneered developments in both the theory and experiments of rubber elasticity. These together with his other fundamental studies contributed to a revitalization of the theory of finite elasticity, which had been dormant, since the basic understanding was completed in the nineteenth century. This book with chapters on foundation, models, universal results, wave propagation, qualitative theory and phase transitions, indicates that the subject he reinvigorated has remainded remarkably vibran and has continued to present significant deep mathematical and experimental challenges.

This book presents a series of challenging mathematical problems which arise in the modeling of Non-Newtonian fluid dynamics. It focuses in particular on the mathematical and physical modeling of a variety of contemporary problems, and provides some results. The flow properties of Non-Newtonian fluids differ in many ways from those of Newtonian fluids. Many biological fluids (blood, for instance) exhibit a non-Newtonian behavior, as do many naturally occurring or technologically relevant fluids such as molten polymers, oil, mud, lava, salt solutions, paint, and so on. The term "complex flows" usually refers to those fluids presenting an "internal structure" (fluid mixtures, solutions, multiphase flows, and so on). Modern research on complex flows has increased considerably in recent years due to the many biological and industrial applications.