Stress vs Strain
Stress describes the force applied to a material (per unit area) from an external source, permanent deformations in the materials, and/or uneven heating. It has the units [Pascals].
\vartheta = \frac{Force}{Area}
Normal Stress is the stress applied normal to the face of the material. If the normal stress results in a decreasing of the axial length of the material it is called compressive stress, and if the axial length increases it is called tensile stress.
If the normal stress is applied everywhere on the body (e.g. a glass marble submerged under water) then the normal stress is the pressure.
To visualize the difference between stress and force consider the magician lying on a bed of nails.
Let’s consider an assistant who weighs 200 lbs (91 kg) standing on the magician lying on a bed of 2, 20, 200, and 2000 nails. The force due to the weight of the assistant is constant (mg = 889.0560 N), but the area this force is distributed over will increase as the number of nails increases.
Assuming each nail as an area of 1.13 x 10^-6 and the tensile strength of human skin is around 27.2 MPa1 then,
2 nails in the nail bed will create a stress of 393.4 MPa → Dead magician (R.I.P.)
20 nails in the nail bed will create a stress of 39.34 MPa → Dead magician (R.I.P.)
200 nails in the nail bed will create a stress of 3.934 MPa → Alive magician
2000 nails in the nail bed will create a stress of 0.3934 MPa → Barely feels anything
So it’s the stress NOT the force that decides the magician’s fate!
Strain is the material’s response to the applied stress (e.g. the displacement between particles within the material relative to their starting distance). Because it is reported as a ratio of the change in length to the original total length it is unit-less. Sometimes it is also reported as [meter/meter] for clarity.
\delta = L_{final} - L_{initial}
A tensile (normal) stress will produce a tensile strain in the material (i.e. the material will be stretched out). Alternatively, if the stress is applied in different directions for different planes in the material then there will be a distortion in the angle between previously adjacent particles in the material and this is called a shear strain.
\gamma = \theta_{final} - \theta_{initial}
