The question is pretty simple: What is stormtrooper armor made of, and how is it constructed?
Galactic empire - Disney Canon
It was made from Plastoid composite (src: Star Wars Rebels: The Visual Guide and "Battlefront - Twilight Company"). The books were Synth-leather.
She slid her feet into her white synth-leather boots and then—always left first, then right—snapped her plastoid greaves onto her legs. The soft click and hum of mechanisms assured her she’d attached the pieces correctly, and their perfect sculpt felt far more natural than anything she could buy as a civilian. Belt and crotch plate came next, then the torso piece—locked into the belt, finally making her feel clothed.
Please note that plastoid wasn't explicitly designed for armor - according to Ezra's Gamble novel, it was also used for buildings:
Ezra walked around the corner and proceeded toward the end of the block. Ake’s Tavern was on the ground floor of a three-story plastoid building with wide, dark windows.
Amusingly, it was made from plants (all quotes from Battlefront)
Twilight had come to devastate Nakadia’s plastoid factories, where millions of tonnes of farm crops were processed into armor-grade polymers and synthetic resins. Namir hadn’t realized such conversions were possible—he couldn’t imagine how plants could be transmuted into industrial materials—but no one else seemed surprised and he’d kept his questions to himself. Looking stupid in front of his colleagues wouldn’t inspire confidence.
Galactic empire - EU/Legends
The outer white plate armor layer was made of plastoid composite. Source: "Star Wars: The Visual Dictionary", section on "Imperial Stormtroopers", p. 34
The black layer was a "body glove" of unspecified material.
The body plate material wasn't specified (possibly still plastoid?).
However, according to TFA Visual Dictionary, at least 2 elements were made of a new material: both the "ballistic riot shield", and the helmet, were made with "composite betaplast".
Composite Betaplast helmet with integral polarized lenses ("Stormtroopers", p.16)
Lightweight composite betaplast ballistic riot shield ("Close Combat", p.17)
Guess they couldn't afford the final, non-beta, version.