Mechanics of solids is an interesting branch of science, different points in the material
displace relative to each other, which is nothing but deformation. When a material
deforms it changes the shape of the body but often it also changes the volume of the body.
It depends on the intrinsic properties of the material whether there is a very large change
in volume or if there’s negligible or no change in volume at all.
The ability of the material to change or not
change its volume during deformation is nothing but volumetric behavior.
The materials that do not change their volume during deformation are called
as incompressible materials and the materials that do change their volume
are nothing but compressible materials. But in general, when a material does change its
volume during deformation, not all the deformation results in change in volume. But what do we mean
by that? Let’s look at the strain developed in the model during this deformation.
Typically, the total train developed in the material
is a summation of two types of strains. One component of it results in changing
the volume of the body and this is called as the volumetric strain.
The other component does not result in changing the volume of the body
and this is called as the deviatoric strain. The material tries to resist both the strains,
the resistance it offers to the deviatoric strain is called as its elastic modulus
and the resistance it offers to the volumetric strain is called as the bulk modulus.
But why is it important to what each of these strains mean?
Well, for one thing it helps us understand how materials deform
and for another we can use this information in designing various products.
Let’s for instance look at the bottling of beverages such as wine and champagne. They usually
have a wine stopper made of cork material to stop the beverage from leaking out of the bottle.
Cork is a special type of wood which is both impermeable and compressible. Which means that
it does not absorb any liquids and it can change its volume when it undergoes deformation.
So, this makes cork an ideal material because when it’s inserted into the
bottle its total strain is distributed into deviatoric and volumetric strains.
And since cork is compressible it doesn’t offer much resistance to change in volume.
So, there’s a good amount of strain developed in the part
that is barely resisted, and the best part is that this component is a function of change in volume
which can be controlled by modifying the dimensions of the cork.
This makes bottling of wine bottles a fairly intuitive exercise.
Similarly, many other applications such as designing footwear, or picking a suitable
material for engine gaskets, or any sealing applications where there’s a material deforming
in confined space rely on knowing what percentage of its strain is deviatoric or volumetric.
In this section we will spend some time understanding
how one can decompose the total strain into deviatoric and volumetric components
and how it helps us in understanding the properties of a material.
In the end we’ll look into a few practical examples
to see how this knowledge can be helpful in engineering and other daily applications.