Before answering this question, keep in mind that I am a 2 year Biology student, with limited experience in studying chemistry. I am going to make assumptions which I explain, feel free to correct them.
Firstly, it would be great to have a scientific definition of material. The Wikipedia definition is as follows,
Material is a substance or mixture of substances that constitutes an object.
It is worth knowing the Google dictionary definition of substance, so that we are all on the same page,
A particular kind of matter with uniform properties.
From these definitions I suspect that a material can be classified as being composed of one or more atoms (correct me if I am wrong), if the later is true, those atoms may be of the same or of a different element. If a molecule is considered a substance, it would follow that a material may be composed of one or more molecules, again, of the same type, or a different type. Тhus, I assume that the flexibility of a material, consisting of one molecule, may depend on the molecule's flexibility. On the other hand, I would expect the flexibility of a material consisting of two or more molecules of the same or different type, to depend on the weakness of intramolecular and intermolecular attractions, respectively.
Initially (thinking too hard on the atomic scale), I believed that in order for a material to have a different flexibility to another material, the chemical bonds of its constituent atoms would need to be more flexible. I had thought 'bond flexibility' could differ between molecules, perhaps, because the atoms of certain elements might have their energy dispersed over a greater distance (e.g., an a atom could have the positive charge of its proton spread over a greater distance). Thus, allowing two atoms to be separated over a great distance without 'losing' their bond. This was utter speculation and I now am nearly certain this is incorrect.
According to this source,
Free rotation around C—C bonds allows long polymer molecules to curl up and and tangle very much like spaghetti. Branching - straight, unbranched chains can pack together more closely than highly branched chains, giving polymers that have higher density, are more crystalline and therefore stronger. The spaghetti-like entanglements of polymer molecules tend to produce amorphous solids, but it often happens that some parts can become sufficiently aligned to produce a region exhibiting crystal-like order, so it is not uncommon for some polymeric solids to consist of a random mixture of amorphous and crystalline regions. As might be expected, shorter and less-branched polymer chains can more easily organize themselves into ordered layers than have can long chains.
Therefore, I would expect materials consisting of several long and branched polymers to be more flexible compared to materials composed of several short, and unbranched polymers, because long, and branched polymers could not form as many intermolecular (and perhaps intramolecular) bonds or interactions with other molecules.
Anyway, from what I have read in this post,
Flexibility in polymers at the molecular level is determined by the flexibility of the individual polymer chains and the interactions between the chains.
Sachan goes on to explain that polymer flexibility is explained by the chemical nature of the monomers that make up the polymer chain. For example, monomers with polar groups increase intramolecular hydrogen bonding, or in other words, interchain interactions, thus, I imagine these interactions facilitate bonding between monomers of the polymer, by placing chain monomers closer together, allowing bonds between parts of the chain to occur. They also may facilitate hydrogen bonding between other polymers and thus, cross-linking between molecules, preventing each molecule from rotating independently.
Lower from the first link explains this concept similarly,
Side groups - polar side groups (including those that lead to hydrogen bonding) give stronger attraction between polymer chains, making the polymer stronger.
I would expect bonds between monomers of the polymer chain to make the polymer rigid to a higher degree than, weaker hydrogen bonds by preventing parts of the molecule from independently rotating (i.e., I suppose, two bonded monomers would make the polymer less flexible as a whole, compared to the two same unbonded monomers). Hydrogen bonds would also add resistance to parts of the molecule from separating and thus, rotating independently. In my head, I am thinking of two separate cysteine monomers, apart of a linear polymer chain, both containing sulfhydryl groups, where the sulphur is bonded to a hydrogen. If both hydrogens were removed and the sulphurs of two cysteine monomer bonded, the monomers could not rotate as before, because they would now be bonded to each other and the other monomers as before. It is really hard to visualise why this is the reason, but intuitively the atoms in a folded chain would be less free to rotate compared to the atoms in a linear chain. Adding atoms to a molecule does not necessarily decrease its flexibility, which I would have expected. If anyone can explain the logic behind this more clearly I would appreciate that.
Lastly, I envisage a material stretching in different directions due to atoms rotating around single bonds in the molecule/s that compose that material.
My final assumptions are that: non-polar polymers, composed of predominantly non-polar monomers are more flexible since cross-linking and hydrogen bonding do not impede the rotation of parts of the molecule, by allowing more atoms to be single bonded. Furthermore, Are polymers consisting of more double bonds, less flexible than polymer consisting of more single bonds, on the macroscopic scale? Are branched polymers more flexible compared to unbranched polymers?