Some Important and Useful Definitions

In elementary mechanics of materials (Strength of Materials or the first undergraduate course in solid mechanics) as well as in an introductory graduate elasticity course five fundamental assumptions are normally made about the characteristics of the materials for which the analysis is valid. These assumptions require the material to be, 

Provided that a material has these characteristics, be it a metal or polymer, the elementary stress analysis of bars, beams, frames, pressure vessels, columns, etc. using these assumptions is quite accurate and useful. However, when these assumptions are violated serious errors can occur if the 

Linearity Two types of linearity are normally assumed Material linearity (Hookean stress-strain behavior) or linear relation between stress and strain Geometric hnearity or small strains and deformation. 

Elastic Deformations due to external loads are completely and instantaneously reversible upon load removal. 

Continuum Matter is continuously distributed for all size scales, i.e. there are no holes or voids. 

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