The formation of teeth, also known as odontogenesis, is a complex process that begins in utero, around the sixth week of embryonic development. There are three stages to this process: the bud stage, the cap stage, and the bell stage.
In the bud stage, the tooth germ (an aggregation of cells) starts to form in the developing jawbone. During the cap stage, the tooth germ differentiates into enamel organ, dental papilla, and dental sac, which will later develop into the tooth's enamel, dentin and...

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...