Why do chocolate bars usually break at the cleavages? 
Why do chocolate bars usually break at the cleavages?
The chocolate bar is less thick at cleavages. How can we relate thickness and fracture point of chocolate bar?
 A: When you tries to break a chocolate bar, a shear stress is applied to the chocolate bar. Once the chocolate reaches its yield strength, the stress at which a material begins to deform plastically, it will break. Thicker materials have higher yield strength than thinner ones, so the thinner cleavages will break first. 
Strength of Materials 
A: When we apply a kind of the twisting load to a chocolate bar, internal reaction forces are generated in the bar. In the kind of twisting one mostly applies to a chocolate bar, the significant internal forces are shear forces. i.e. the forces which are acting along the surface of a cross section. These internal forces deform the actual structure through tiny amounts. This is very roughly and vaguely like a huge bunch of tiny springs put together, each one, in general, in a deformed state. From this 'analogy' it is easy to imagine that a body under the action of internal forces and deformation has some kind of internal elastic energy associated with it at each point of it.  Now the fracture at any point of material occurs because the 'energy density' of this internal elastic energy increases a particular value. This particular value is a property of material mainly. Now this energy density at any point depends on the stress at that point (or strain at that point). In the case of the chocolate bar, where the thickness is low, the stress is higher. Because the shear forces are almost same all over the body but stress is force per area. Due to this high stress in the cleavages, the energy density is high and thus cleavages are the regions where the energy density reaches the value that will be required for fracture.
