Material response, isotropy and temperature effect

(a) Elastic and non-elastic response

Linear elastic response obeys Hooke's law, $\sigma = E\varepsilon$.

(b) Isotropic and anisotropic

(c) Homogeneous and continuous

• Homogeneous: properties are the same at every point of the body (they do not change with position). A concrete block with voids and variable aggregate is not exactly homogeneous.
• Continuous: the body has no gaps or voids, so matter is distributed without break and quantities such as stress, strain and displacement are continuous functions of position. This allows calculus to be used.

A body can be homogeneous but anisotropic (a straight timber log of uniform fibre direction).

Effect of temperature

• As temperature rises, $E$ and yield strength fall; the elastic range shortens and the plastic range (ductility) usually increases. Mild steel loses most of its strength near 500 to 600 $^\circ$C.
• At low temperature, yield strength rises but ductility falls, so steel can become brittle (ductile-brittle transition).
• At high temperature under steady load, materials creep (strain increases with time).
• If expansion is restrained, a thermal stress $\sigma = E\alpha\Delta T$ develops.