No, this is not a philosophical article referencing the vicious circle of cause and consequence. I just used a catchy title to draw your attention. So what I really wish to answer is what is more fundamental: Stress or Strain? Now, a few of you might argue as to why this question and tell that stress-strain always co-exist. To answer that, I must tell you that it is by looking back that we have a clear vision of the future. Thus differentiating the primary from the auxiliary, felicitates us in making groundbreaking discoveries. And besides, it’s always good to know how the human brain works and what is more instinctive to the homo sapiens.
Alright, so let’s get the mess sorted. Probably many of us believe that stress has to be fundamental. We apply a force on a body, it develops stresses and leads to deformations/strains. But, this approach has a basic flaw. How do you measure stresses? All the instruments we presently have all measure deflections and it is by calibrating these instrument do we get the stresses. So, we can imagine that we are measuring stress but it is the strains that we are always measuring. Also consider this view: stress is a quantity that measures the internal forces in a body. So zooming in to the molecular level, we see that the neighbouring molecules cannot exert forces on each other unless and until their mutual equilibrium is disturbed.
So, the case that I have presented until now is strongly in favour of strain. Come to think, this sounds a logical choice. Strain is essentially a normalized form of displacement, and displacement makes no sense without space. And anything to do with space is automatically related to the geometry. Ah! Now we have hit the bull’s-eye. You see, every form of math is but a variant of geometry. Geometry is the first human endeavor to understand nature and its language. The Greeks used geometry to do basic arithmetic: add, subtract, multiply, divide and even take a square root! “Euclid’s Elements” is referred as the most influential textbook ever written. It has never ran out of print(since the inception of printing) and is second only to the Bible in the number of editions published. So, now you can understand why all the fuss around geometry. It took us five and a half centuries to figure out algebra, geometry on the other hand is as natural to us as is sight.
Alright! Now you would say that I always knew that strain was more fundamental than strain, that is why it is always an independent quantity when we plot the famous stress-strain relationship. But, there is a catch in this statement. One can plot strain-stress as good as stress-strain, as long as one uses the natural strain. The problem with our “Engineering” strain is that, we engineers love to live in the world of statics and simplify every system to a static one. We see that the area of the cross-section keeps changing but ah, what the heck. The deformations are small and thus the change in area is small and is generally ignored. When Leonhard Euler first proposed the equation1, Giordano Riccati first played with the idea and later Thomas Young popularized the philosophy, they lived in the elastic range of the material. This range as was later found was surprisingly very narrow when compared to the deformation of the material at failure (The plastic strain can go as high as 8 to 10 times the yield strain and the fracture strain 15 to 30 times). So, the Engineer’s static simplification of area is short lived. But we still adhere to this assumption which gives rise to the problem of having multiple strains for a single value of stress. So, it is the definition of a function which forces the strain to be plotted as the abscissa.
Puff! That was a long discussion. But, I really hope that now you understand that why seeing is believing or why closing your eyes to the assumptions can lead to major mistakes. And of course, we all know that it is not possible for an animal to evolve into another species in a single lifetime and the fact that egg-laying species pre-date the existence of chickens; it is biologically necessary that the egg came first.
1 Robert Hooke in 1678 published a paper suggesting that the displacement under a load is related to the applied force. In 1705, James Bernoulli proposed that the proper way to study deformation of geometry is by giving force per unit area or stress as a function of elongation per unit length, strain. Leonhard Euler, a student of James Bernoulli’s brother Johann Bernoulli, proposed the linear relationship s=E*e.