Fundamentals of Continuum Mechanics

John W. Rudnicki

• Publisher: Wiley
• Year: 2014
• ISBN:
  9781118927670
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

A concise introductory course text on continuum mechanics

Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It aims to provide the foundations for further study, not just of these subjects, but also the formulations for much more complex material behaviour and their implementation computationally.

This book is divided into 5 parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations and is a suitable textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics.

• A concise introductory course text on continuum mechanics
• Covers the fundamentals of continuum mechanics
• Uses modern tensor notation
• Contains problems and accompanied by a companion website hosting solutions
• Suitable as a textbook for introductory graduate courses for students in mechanical and civil engineering

Part One
Mathematical Preliminaries

This part provides the foundation for the rest of the book. The treatment is meant to make the book self-contained, assumes little background from the reader, and only covers what is needed later in the book. The treatment begins with vectors. Although most readers will be acquainted with vectors, they are introduced in a way that leads naturally to tensors, introduced in the second chapter, and their representation in terms of dyadics, in the third. Vectors and tensors are introduced in coordinate-free form, appropriate for describing the physical entities that arise in continuum mechanics, before discussing their representation in terms of Cartesian coordinates in the third chapter. This chapter introduces index notation and the summation convention. Chapter 4 discusses the cross product, introduces the permutation symbol, and provides an introduction to the discussion of determinants in the following chapter. Chapter 6 derives the relation between vector and tensor components in coordinate systems that differ by a rotation. This relation provides an alternative method of defining vectors and tensors. Chapter 7 discusses principal values and directions which are pertinent to many of the particular tensors introduced later. Chapter 8 discusses the gradient, but this material is not needed until Part Three, Motion and De...