Stress, Strain

Synonyms

Deformation

Definition

A stress is a force F distributed over a flat supporting surface.

Strain is a parameter which describes the relative displacement of particles within a deforming body.

Theory and Application

Stress

A stress is a force F distributed over a flat supporting surface of Area A.

Stress at a point, identified with σ, is given by

$$ \mathrm{limit} \mathrm{a}\mathrm{s} \updelta \mathrm{A}\to 0 \mathrm{of} \updelta \mathrm{F}/\updelta \mathrm{A}=\mathrm{d}\mathrm{F}/\mathrm{d}\mathrm{A} $$

Stress may vary over surface.

Stress may act as an arbitrary angle.

It is appropriate to transform into components in x, y, and z system.

Choosing x as normal to surface with y and z being tangential:

$$ {\sigma}_{\mathrm{x}\mathrm{x}}={\mathrm{dF}}_{\mathrm{x}}/\mathrm{d}\mathrm{A} $$

$$ {\sigma}_{\mathrm{xy}}={\mathrm{dF}}_{\mathrm{y}}/\mathrm{d}\mathrm{A} $$

$$ {\sigma}_{\mathrm{xz}}={\mathrm{dF}}_{\mathrm{z}}/\mathrm{d}\mathrm{A} $$

Suffix notation: first suffix – direction...