As I understand from several sources (e.g) it's meaning is kind of lace/straps. Apparently its a of a medieval origin (encountered that word in Luis Vives 16h century). But I struggle to see how this word came into being: a lone-word? or a new compound word based on stem (like "astrigmen" or so)I was unable to locate.
Astrigmentum is formed from the verb astringere (= prefix ad + stringere), 'to tie up tightly,' and the suffix mentum. In general, this suffix forms 'nouns denoting acts, or means and results of acts' (Allen & Greenough, New Latin grammar §239). Here it denotes 'means' specifically and is added to a de-nasalized form of the present/imperfective verb stem (astring > astrig). Therefore, the word astrigmentum is literally 'a means of tying up.'
The word fragmentum has a similar derivation from a de-nasalized verb stem (of the verb frangere, 'to break') + mentum. However, the suffix denotes 'results' instead of 'means,' so that a fragmentum is literally 'the result of breaking'.
Incidentally, strigmentum, which is mentioned in the other answer, is from the unprefixed root verb of astringere, also de-nasalized. In this case, though, the verb is used with the meaning 'to strip,' 'to shave,' or 'to skim the surface of.' Here too, as for fragmentum, the suffix denotes 'results.'
Looks like one possible etymology means "[material] thoroughly scraped off." Or perhaps "scraped away."
a + strigmentum
a = not (privative alpha)
a = "away from;" "completely, thoroughly;" indicates absence
strigmentum, i, n.
I. In gen., that which is scratched or scraped off, a scraping (post-Aug.), Plin. 20, 3, 8, § 17.— II. In participle, filth or dirt scraped off, Cels. 2, 6 med.; 5, 2, 4; Plin. 9, 51, 74, § 160; 28, 4, 13, § 51; Val. Max. 9, 14, ext. 2 al.
From the Lewis and Short lexicon, via Perseus Word Study Tool