The Marvels of Strain Energy


Ever hopped using a pogo-stick? The bounciness felt while doing so is attributed to the spring attached to the stick. We’re all well aware of the fundamental property of a spring: storing energy upon being elongated or compressed and releasing the absorbed energy back upon recoil. There are, of course, a great many ways, mechanical, chemical, electrical, thermal and so on, of storing energy until it is wanted. The energy that a spring stores has a specific name, strain energy. However, springs are only a special case of the behavior of any solid when it is loaded.

When external forces are applied to a body, the mechanical work done by those forces is, in general, converted into kinetic and potential energies. But in case of an elastic body constrained to prevent motion, all of this work is converted into elastic potential energy, commonly called the strain energy. From a mechanical engineering standpoint, at a miniscule level, any component or system can be represented by three basic elements: mass (m), spring (k), and damper (c).


It is the elastic potential energy stored by this spring that makes a part of the total strain energy in the body. While in some bodies, these springs can be very stiff (high ‘k’), in others they can be very resilient (relatively lower ‘k’). The best structural components are the ones having the right trade-off between the two properties. In practice, this stored strain energy of a spring has widespread applications ranging from Engineering to Biology. How Biology?

Well, the very reason how we run fast, how we sustain the impact upon jumping from a safe height, how we decelerate while running, how skiers maneuver through bumpy ski-runs (yes, ski-runs are bumpy in spite of the snow covering), how kangaroos use hopping as an efficient mode of locomotion, et cetera lies in the fundamental strain energy storage capacity of muscles and tendons. It’s amazing how precisely the bodies of human beings and animals are adapted biologically so as to store and make use of strain energy. 


How does our body generate energy to carry out various physical tasks? It’s the muscles in our body that absorb oxygen from the air we breathe to break down glucose, thus producing useful energy (called metabolic energy). It is due to this fact that upon exercising or running, our muscles make more energy as a result of which, its oxygen demand rises and we respire more. But there’s a catch in the way locomotion mechanism works. Is it really that the amount of energy required for locomotion and the amount of metabolic energy that the leg muscles actually consume almost equal (considering inevitable losses)? In other words, does all the metabolic energy that the leg muscles make get used up in locomotion? Well, a study done at the University of Leeds doesn’t agree with this and the experimental results obtained in this regard are quite thought-provoking.


Back to the pogo-stick. A hopping kangaroo can be thought of as a child on a pogo stick. For that matter, the same principles apply to a running person, horses, and other animals. To investigate the correlation between the amount of metabolic energy consumed by the muscles and the amount of energy required for locomotion, measurements were made of the rate of oxygen consumption and the corresponding metabolic energy consumed as the animals walked, ran and hopped. Results? Only less than 50% of the total metabolic energy produced was actually used up for locomotion while running and hopping! Majority of it was saved. Well, then where did the remaining energy required for locomotion come from?

The spring comes to the rescue! But we don’t actually have springs in our feet!

Yes, we do have in the form of tendons. Tendons are the tissues that join muscles to bones and form an integral part of our bodies for a vital reason. As aforementioned, an elastic body can be assumed to be made up of a large number of springs that store strain energy. Tendons do the same. To know how, let’s look at the diagram below. The answer as to where the remaining locomotion energy came from will be apparent from the discussion that follows.

Schematic of the tendon (blue spring-like) shock-absorbing mechanism while landing from a jump. The rate of energy storage (2nd phase) is faster than the rate of energy release (3rd phase). Released energy lengthens the muscle (red) which slowly dissipates it as heat.

In landing from a jump, an impact force acts on the sole of the foot and also, a force acts on the muscle-tendon unit. This force stretches the tendon when the rear part of the foot lands down and due to its springy nature (hence, resilience), it stores strain energy. Now, this stored energy can be used (released) for two purposes, either to re-accelerate the body in a step of walking or running or it can be dissipated by lengthening the muscle fibers. The mechanism by which either of the two is carried out is nothing less than a representative of the fact that indeed, our legs are designed in a manner too intricate than we think.

Tendons can be thought of as analogous to capacitors. A capacitor stores electrical energy temporarily and depending upon its time constant, it can deliver the energy quickly or slowly. So for a given amount of stored energy, it can manipulate the power output. A tendon functions in a similar way. To re-accelerate the body, the tendon will release its strain energy quicker than the time it needed to store it. But during dissipation (when coming to rest from a jump or decelerating from a run), the rate at which it releases energy is slower than the rate of energy storage, hence less power output. Thus, energy remaining constant, the timing of energy flow dictates what function the body will carry out. Talking about efficiency, it has been found that a tendon releases almost 93% of its stored energy, thus resembling a very resilient spring.


Having mentioned about skiers, they decelerate frequently while maneuvering through the ski-run and in such cases, the tendons act as shock-absorbers, storing large amounts of strain energy and releasing it slowly to the muscles, thus minimizing the strain on muscles. It may come as a surprise to an engineer that even for a typical car with steel suspensions, driving on ski-runs (assuming sufficient traction availability) would be dangerous while a skier has no problem doing so. The reason lies in the fact that the strain energy storage per unit weight is about 20 times higher for tendons than modern spring steels, making skiers way more efficient.

It is of no surprise now, why animals like kangaroos, cheetahs, horses, deer etc. are so good at hopping or running fast and swift and changing directions so quickly, since a major proportion of their body weight comprises of tendons, playing to their advantage. Bottom line: In nature and technology, looking at things in terms of energy can be revealing, and it is the basis of the modern approaches to the strength of materials and the behaviour of structures.


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