Introduction: Fundamental Axioms of Continuum Mechanics

Abstract

Continuum mechanics, including nonlinear continuum mechanics, studies the behavior of material bodies or continua. We can mathematically define a body as follows: it is a set $\mathcal{B}$ consisting of elements $\mathcal{M}$ called material points. The concept of a material point in continuum mechanics is primary, i.e. axiomatic, as is the concept of a geometrical point in elementary geometry.