In scientific writing, should I write energy is expended, cost or consumed?
Which term is preferable? As in the example,
Energy is expended/cost/consumed through deformation/vibration/friction.
energy is said to be expended in English scientific texts as in these sentences:
1) Work Work is done when a force F is exerted to move an object over a distance d W = F × d unit of measure: the joule (J), 1 J = 1 N·m
Energy is expended when a force acts over some distance to move an object. Not all forces do work.
2) How much energy is expended in this reaction?
3) It can be seen that for all types of deformation and all metals investigated the percentage of the energy stored is high when the total energy expended during deformation is small, and that it decreases rapidly with increasing work done.
expended means "used up". The words cost and consumed are not used in your context in the form you have provided them. Consumed is used for electricity. Machines consume energy. And cost is about price, literal or not, so, it is irrelevant here.
[[You might want to take care not to expend too much energy in scientific writing. Caveat: joke on the question's wording. ]]
Please note: this answer contains examples. A comment did not provide enough room so I decided to post an answer.
That said, I am no materials scientist (unless you consider being a linguist being a scientist), but I can say this. All other things being equal, for a sentence in the form given by the OP
energy is A, B, or C [past participles of verbs expended, consumed or cost] through process 1, 2, 3 or 4.
It is my opinion that only the verb "expended" works there. Processes expend energy, they don't consume energy and they don't cost energy either.
USAGE, here, therefore is:
The last example posted by the OP is a comment: "for an elastic spring, the energy is expended partly on kinetic energy and partly on potential energy."
Energy is not expended there. Please note: Energy is stored in the elastic spring (compression) and it can be released when the spring elongates.
Proof of this from a professor at Stanford University
In physics, elastic energy refers to the energy released when a spring elongates. When a spring is compressed it stores energy that can be used later, at this point the spring contains elastic potential energy. 2 Releasing the spring, or elongating it, releases the elastic energy, allowing the spring to move.May 11, 2017
The word to use depends a lot on the situation:
The work expended for plastic deformation cannot be gained back completely. Some energy is lost in the process. (Slightly paraphrasing from Handbook of Physics).
Energy is expended to launch a rocket into orbit. However, more specifically, chemical potential energy is converted to kinetic energy and gravitational potential energy when a rocket is launched, although some energy is lost to friction between the rocket and the atmosphere.
A can crusher expends energy to crush a can, while a car running over a can loses energy due to plastic deformation of the can. A perpetual motion machine is impossible because all mechanical systems lose some energy to friction.
Foot contact time... is a strong predictor of locomotor energy costs, but it does not explain the variance in rate of energy expenditure during locomotion.... Nature, Scientific Reports Terrestrial locomotion energy costs vary considerably between species...
There are lots of other examples, and it is best to look for specific examples as similar to your situation as possible. That said, you can generally fall back on energy being expended to do something you want or lost to something you would prefer did not happen.
With respect to energy, the word consumed is rarely used in scientific literature. I could only find it in biology, referring to living things that consume energy, meaning either the energy in the food they eat or the energy they expend on biological processes. Energy consumption is more commonly used in non-scientific literature to talk about the amount of energy used by devices (e.g. refrigerators, cars, lights) or groups of people using devices (e.g. United States per capita energy consumption) without respect to what the energy is used for.
Some more papers to look at: Swimmers spend/expend energy, A quantum refrigerator removes energy, and in the process energy is exchanged, transferred, and redistributed, reaching equilibrium when energy flows are balanced.
Friction dissipates energy.
1a : to break up and drive off
dissipate a crowd
1b : to cause to spread thin or scatter and gradually vanish
one's sympathy is eventually dissipated — Andrew Feinberg
1c physics : to lose (heat, electricity, etc.) irrecoverably
The problem of vibrations in the blades of conventional engines is addressed by including an outer shroud disposed on the outer radius of each blade. Adjacent shrouds come in contact with each other to dissipate energy through friction at the interface, thereby alleviating vibrations. A drawback is that the edges of the shrouds at the point of contact wear out with time and can no longer reduce the vibrations, thus eliminating the mechanism for dissipation of energy.
Energy can neither be destroyed nor created (conservation of energy) hence cannot be consumed per se - expended is your best choice here; Google NGram finds "cost" the least commonly-used construction of those you suggested in your post:
Albeit true that NGram Viewer is not restricted to scientific writings, there have been a number of well received peer reviewed papers demonstrating that in the more recent portions of the Google NGrams English corpus, scientific papers are in fact over-represented in proportion to the rest of the English corpus.
I will add one reference to support this useage: