A Brief Introduction to Some General Concepts in Elasticity

Abstract

This chapter is not intended to be an introduction to elasticity. It is merely a very quick survey of those definitions and axioms that relate strictly to the mathematical problems studied in the remainder of the book. For a deep and exhaustive treatment of the matter we refer, e.g., to TRUESDELL & TOUPIN [1960], TRUESDELL & NOLL [1965], WANG & TRUESDELL [1973], TRUESDELL [1974, 1977], GURTIN [1981], MARSDEN & HUGHES [1983], and CIARLET [1986]. What we will say has a physical meaning if n = 3. Nevertheless, since the definitions, axioms, and problems considered in this book generalize spontaneously to an n-dimensionai setting (n ≧ 1), we prefer to present the theory directly in the n-dimensional form while still using the terminology relative to the three-dimensional case.