# Solid Mechanics – Basics and Usage

### What is solid mechanics?

A branch of continuum mechanics is known as solid mechanics & this essentially studies the behaviour of the solid materials in general & motion in specific. In addition to this, the deformation under action of forces besides the phase or the temperature changes along with the other internal or the external agents form a part of this subject. In other words, we can say that this solid mechanics is just a branch of mechanics clubbed together with mathematics & physics which further concerns as to how the solid matter works under the external actions. Finally, when it comes to the practical applications of this solid mechanics, then it is stated to be the Euler – Bernoulli beam equation.

### Euler – Bernoulli beam equation

In the above equation  means deflection of beam in  direction where  is the position &  is distributed load,  means elastic modulus &  is 2nd moment of area.

### Solid mechanics as fundamental & its usage

In addition to the above stated things, this solid mechanics makes itself to be the fundamental for the following things – aerospace, civil, nuclear & the mechanical engineering, geology among other branches of physics like that of the materials science. When the talk revolves around the other areas then solid mechanics comes across as being used for specific applications like that of the anatomy of the living being apart from the design of that of the surgical implants & the dental prostheses. Besides this, solid mechanics makes use of the tensors to a great extent when it has to describe strains, stress or the relation between them.

### What are the response models?

Essentially a material comes forward with a rest shape however, its shape moves away from the rest shape & the reason for this is the stress. Hence, deformation can be termed to be amount of departure from the rest shape while strain is the proportion of the deformation to the original size. In addition to this, when the applied stress turns out to be quite low then quite a number of solid materials behave as if strain happens to be directly proportional to stress therefore, coefficient of proportion is known as the modulus of elasticity. And the region of deformation is well – known to be linearly elastic region.

### Types of response models

Elastically – when the applied stress is removed then the material comes back to its undeformed state. Viscoelastically is when the materials behave elastically but have the damping as well (this happens whenever stress is applied apart from being removed). Plastically – the materials which behave elastically basically do so only when the applied stress is lower than that of the yield value. As deformation will only occur when the yield is permanent. Thermoelasticity is essentially used when the elastic solids are concerned & which are those conditions that are neither adiabatic nor isothermal. Finally, real materials generally have non – linear behaviour while analysts use linear material models.