Correlation with continuum mechanics:

Solid mechanics is a branch of mechanics, physics and mathematics that deals with the behavior of solid materials under external forces, temperature fluctuations, displacement and other external actions. Solid mechanics is a part of a broader and wider study known as Continuum mechanics. Solid mechanics makes use of tensors in order to describe strains, stresses and their relationship. On of its most practical applications is the Euler- Bernoulli equation.

Continuum mechanics is the study of the physics of continuous materials. It is composed of solid mechanics, which deals with the study of physics of continuous materials with a defined shape in a state of rest and fluid mechanics, which deals with the study of physics of continuous materials which take the shape of the container in which they are placed. Solid mechanics is further divided into elasticity, which describes materials that return to their shape of rest after a stress is applied on them and plasticity, which describes materials that undergo a permanent deformation after the application of stress.

Every material has a rest shape and its shape changes from the rest shape due to the application of stress. The amount of change or departure from the rest shape is called deformation.  The proportion of deformation to the original shape and size is called strain. If the stress applied externally is low enough, almost any solid material behaves such that the strain and stress vary directly. The coefficient of the proportion is called Young’s modulus or the modulus of elasticity. This area of deformation is called the linearly elastic region. It is quite common for an analyst in solid mechanics to use linear material models as these are easy to compute. Real materials exhibit non-linear behavior.

Questions:

• What is young’s modulus or modulus of elasticity?
• Name and explain the two branches of solid mechanics.