Review of Stress and strain
Normal stress
- Normal stress is the resultant normal force over a given area
\[\sigma = \frac{P}{A}\]
Shear stress
- Shear stress is the resultant shear force over a given area
\[\tau = \frac{V}{A}\]
Stresses on arbitrary planes
- Since different “cuts” must yield the same resultant force, the
stress depends on your plane of observation
- Each type of stress is simultaneously present
- A body can fail in shear even when loaded by normal
stress
- Ductile materials typically yield due to shear stress
- Brittle materials typically crack due to normal stress
Stress
Note
- Stresses result from equilibrium (ie the sum of forces)
- It is possible to have stress without strain
- Example: thermal expansion/contraction
- Exothermic reactions such as bone cement
- Cement then adjusts to body temperature
- Constrained by bone and implant \(\rightarrow\) stress
