Should we not use abbreviations at all in academic writing? [duplicate]

Contractions generally sound a little more informal than their non-contracted equivalents. However, they also sound more natural, as non-contracted forms are practically never used in speech (except e.g. for emphasis or in cases where contractions are not grammatical).

Whether a particular piece of writing is "formal" enough to warrant avoiding contractions is really quite subjective. If you look at many scholarly books and even journal articles, you will find that many (native speaking) authors actually do use contractions and their respective editors have decided that they're happy with them. I would argue that contractions are almost always possible in e-mails: if the context was that formal, you probably wouldn't be communicating by e-mail in the first place. But as I say, it is a subjective decision.

On the other hand, if you are writing in a formal context such as a journal article or a formal letter to a company and can't decide whether or not to use contractions, then I think that avoiding contractions will always be a "safe" decision in such formal contexts.

Try to avoid using the contracted form in formal texts:

Contractions are used sparingly in formal written English. The APA style guide prefers that contractions, including Latin abbreviations, not be used in scholarly papers, and recommends that the equivalent phrase in English be written out.

source

It is frowned upon to use contractions in formal writing. However, these "rules" or "standards" are quickly becoming guidelines. For instance, it's often advised to avoid negations in formal writing. So, "do not" shouldn't be used at all. But there are times when the negated construction doesn't have the same meaning as the positive construction, and meaning is sometimes compromised for form. The author Cormac McCarthy even uses "dont" in his works.

A good piece of writing should be clear and natural. If you find that "don't" is more natural than "do not," use "don't." Don't fall prey to traditionalists.

As with all writing it is important to consider your audience's expectations. You could do a brief analysis of others' writings in the same field and publication type. If they use lots of contractions then it is safe for you to do so too. If they don't and you do, then you may draw attention away from the content of your writing to the style in which it is written. If this is an aim, then fine, but you may undermine your credibility with some readers.

It's also worth pointing out that some contractions (such as the ones in this post: don't, it's) are far more common and therefore more likely to be accepted than others. I would be very wary of using less common contractions such as "they're", "he'll", "mustn't", "would've", etc.