In Mechanics, strain is defined as the ratio of change in dimension to original dimension of a body when it is deformed. It is a dimensionless quantity as it is a ratio between two quantities of same dimension. When a body is under load, it will extend in the direction of the stress (longitudinal strain) and contract in the transverse or lateral direction (lateral strain), in case of longitudinal tensile stress.
To learn with example, take a broken rubber band.
Holding one end in each hand, stretch one of the ends. The length increases. The ratio of change in length to original length is called the longitudinal strain. You will also notice that the rubber band gets thinner as you pull it further apart. The diameter/breadth reduces. The ratio of change in diameter/breadth to original diameter/breadth is called the lateral strain.
Furthermore, the ratio of lateral strain to longitudinal strain is called the Poisson’s ratio.
Poisson’s ratio is independent of cross section. As far as material is concerned, Poisson’s ratio is determined by two independent factors, i.e., the solid rock and dry or wet cracks. The former is influenced by the constituent mineral composition. Poisson’s ratio of the solid rock may be roughly estimated from clay contents for clastic rocks.
Cracks lower the Poisson’s ratio in dry rocks and increase the Poisson’s ratio in wet rocks. The magnitude of change depends on the volume concentration and aspect ratio of cracks. The higher the pore volume concentration and the lower the aspect ratio, the larger is the amount of change in Poisson’s ratio.