Advanced Structural Analysis/Part I - Theory/Materials/Properties/Elasticity

1. Introduction
2. /Tensile Testing/
3. /Broad Implications/
4. /Additional Aspects/

Introduction

All solid materials display an approximately linear response to moderate loads. This is manifested in Hooke's law:

${ϵ}_x=\frac{{\sigma }_x-\nu ({\sigma }_y+{\sigma }_z)}{E}$ 
${ϵ}_y=\frac{{\sigma }_y-\nu ({\sigma }_x+{\sigma }_z)}{E}$
${ϵ}_z=\frac{{\sigma }_z-\nu ({\sigma }_x+{\sigma }_y)}{E}$

Where:
$\sigma =$ the normal stress
$E=$ the elastic modulus (Young's modulus)
$ϵ=$ the normal tension

The figure below illustrates the stress-strain curve of some material. Hooke's law is valid in the linear interval marked "Elastic region". The term elastic, as in elastic deformation, refers to the absence of energy dissipation and permanent deformation. Elastic deformations retract upon unloading.

Generic stress-strain graph for a ductile material.