I wonder if it means "make something happen fast" here, like sadden, darken etc.? because if we use this link http://www.oxfordlearnersdictionaries.com/definition/english/fasten?q=fasten+ it doesn't help.
Analysts say high-tensile steel and aluminium will be the more popular alternative for many years to come, considering parts makers would need to overhaul production lines and figure out ways to fasten new materials like cellulose nanofibre onto other car parts.
Source: https://www.cnbc.com/2017/08/14/japanese-auto-parts-could-soon-be-made-out-of-wood.html