How does a folding phone's glass bend without breaking?

Bending strain. Bend a sheet of thickness t so its middle follows a circle of radius R: the middle keeps its length, the outer face stretches and the inner face squeezes by ε = t/(2R). Phone cover glass about 0.5 mm thick folded to R = 2 mm: 0.5 ÷ 4 = 12.5% (the film's “more than ten percent”). Ultra-thin glass 30 µm thick at R = 2 mm: 0.03 ÷ 4 = 0.75% (“about one percent”). In the film and the tool, R is measured at the middle of the glass. A typical human hair is about 70 µm across (hairs range roughly 20–180 µm).

The break line is approximate. Strengthened ultra-thin glass survives roughly 1–1.5% surface strain, so the line is drawn at ≈1.5%, and the tool calls 1.2–1.5% “near the limit”. The real limit depends on the glass, how it was chemically strengthened, its edges and flaws, and how many times it is folded. Glass tolerates squeezing better than stretching, but not strains of several percent.

Glued or sliding. Glued solid, the layers bend as one beam about a single neutral axis at z̄ = Σ E_it_iz_i / Σ E_it_i, and a point at distance y from it is strained by y/(R + offset). In the illustrative stack below, that axis sits 124 µm below the middle of the glass (pulled down by the stiff metal plate), and because the screen side faces the inside of the fold, the glass is squeezed by 5.1–6.5% at R = 2 mm, far past the break line. Free to slide, each layer bends about its own middle and the glass is back to t/(2R) = 0.75%. In-between settings of the “Screen layers” control blend the two limits; that blend is illustrative, not a model of a real adhesive.

Force to fold. Bending stiffness glued: D = Σ E_i(t_i³/12 + t_id_i²), with d_i each layer's distance from the neutral axis; free to slide: D = Σ E_it_i³/12. For n equal layers the ratio is n², 100× for 10 layers. For this stack it is about 130×. The tool shows the force relative to the same layers sliding (in-between settings blend the two).

Slip. Sliding layers keep their own lengths, so in a fold of angle θ two layers whose middles are d apart slip by d·θ at the ends. Top to bottom here that is 255 µm × π ≈ 800 µm for a full 180° fold. It depends only on the angle, not on the radius, like the ends of a bent deck of cards.

Illustrative stack, not Apple's published spec. Apple says only that the iPhone Duo's inner display is made of “more than 10 ultrathin layers” and that optically clear adhesives “let the layers glide” as it folds. The model's stack, from the touch side (thickness, Young's modulus): protective film 50 µm (5 GPa), ultra-thin glass 30 µm (70 GPa), adhesive 25 µm (≈0), polarizer 25 µm (3 GPa), adhesive 25 µm, touch layer 10 µm (5 GPa), OLED on polyimide 30 µm (8 GPa), adhesive 20 µm, polymer support 50 µm (4 GPa), metal plate 30 µm (110 GPa): 295 µm in all. The glass thickness control changes only the glass layer. Presets: normal phone glass 0.5 mm at R = 2 mm; a plastic cover (no glass, an illustrative 80 µm polyimide film like the 2019 Galaxy Fold's) at R = 2 mm; ultra-thin glass (2020) 30 µm at R = 1.5 mm, the low end of the 1.5–2 mm folds such glass was designed for; Duo-style sliding layers at R = 1.9 mm, from the roughly 3.85 mm-wide teardrop HTX Studio measured in the hinge; too tight a fold, R = 1 mm.

The crease. HTX Studio measured the iPhone Duo's crease at 48 µm peak to valley with a slope under 0.1° when new, and 167 µm with a 1.24° slope after 3,000 machine folds. The crease panel models it as a smooth dent whose width is chosen to match those slopes, with a light 40 cm above the screen: a surface tilted by angle α shifts a reflection by about 2α × 40 cm, up to about 17 mm for the worn crease. The matte finish is modeled as tiny lenses that spread reflections by about ±1.5° (an assumption, not a published figure), so the reflection blurs over about 5 cm and the jog blends in. Apple's engineers told MrMobile that the matte texture scatters reflections, which is why the crease is hard to see, and reviewer Tim Pan described the texture as “almost like countless tiny lenses”. John Ternus (Apple) said the inner display's top “isn't a glass surface. It's a polymer surface,” which carries the nano-texture, and Kate Bergeron (Apple) told 9to5Mac that the top cover layer is replaceable. HTX Studio and TechRadar report ultra-thin glass both above and below the OLED; the model keeps one glass layer.

Not modeled. Real adhesives are soft and shear partway, so real stacks sit between the two limits; the hinge curls the screen into a teardrop, not a perfect circle; a sheet's edges, fatigue over thousands of folds, temperature, the second glass layer, and how the layers are held at the hinge are left out. Strains are linear and small-angle; the gauge and colours show the glass's peak strain at the bend.

The pictures. The phone, the deck of cards and the crease close-ups are AI-generated illustrations of a generic foldable, not Apple imagery, with no Apple marks. Every layer, strain, number and reflection comes from the model.

Sources: Apple, iPhone Duo (more than 10 ultrathin layers; adhesives that let the layers glide); Samsung, Samsung Display Introduces Foldable Display with Easily Bendable, Ultra-thin Glass (February 2020: 30 µm ultra-thin glass, 200,000 folds); TechRadar, iPhone Duo hands-on; 9to5Mac, Apple says iPhone Duo has replaceable folding display layer; HTX Studio's crease and hinge measurements (YouTube); Euler–Bernoulli beam theory and Neutral axis.