1 - Mathematical Background

Summary

This book assumes a background in the fundamentals of solid mechanics and the mechanical behavior of materials, including elasticity, plasticity, and friction. A previous book by the same authors covers these topics in detail, including derivation or explanation of the most important concepts. It is beyond the scope of the current book to reproduce all of this important information.

In this chapter, the essential equations from this background are reproduced. This serves two purposes: to introduce the notation that will be used throughout the remaining chapters, and to list the principal background equations in one place. Frequent reference to the equations presented in this chapter will be made. However, it should be kept in mind that the full context for these equations is found in Fundamentals of Metal Forming.

Notation

There are many alternate forms of notation used in solid mechanics and finite-element modeling. In some cases, it is clearer to use a form that has become a de facto standard in the area, even though such usage might not be rigorous. In other cases, there is no consensus on notation, so it is less confusing to be consistent with other equations.