Question bank — Sandwich structures — face sheets, core

False — stiffer in bending, yes, but strength depends on failure modes (face wrinkling, core shear, core crush) that a solid plate simply does not have, so a sandwich can be stiffer yet fail earlier at a local defect.

True in the thin-face limit — since $(EI)\approx \frac{E_{f}b{t}_f{h}^2}{2}$ and $h\approx c$ for thin faces, stiffness scales as $h^2$, so $2\times$ depth gives about $4\times$ stiffness.

False — the faces carry the bending (axial) stress because they sit far from the neutral axis; the core's main job is to resist shear and hold the faces apart.

False — even though the core bending term $E_c{I}_{\text{core}}$ is negligible, the core's shear stiffness $G_c$ and its ability to keep the faces separated at distance $h$ are essential; replace it with air and the faces slide independently, collapsing the $h^2$ advantage.

False — beyond some point the faces become prone to wrinkling and the core to shear or crush, and for slender panels shear deflection (the $\frac{VL}{G_{c}bh}$ term) and buckling take over; there is an optimum $h$, not an unbounded one.

False — for long panels the shear-deflection term $\frac{VL}{G_{c}bh}$ becomes significant and must be added, because the low-$G_c$ core deforms noticeably in shear.

False — it is chosen for its high $G_c$ per unit density, its lack of a continuous heat-conduction path (thermal insulation), and its vacuum compatibility (cells vent, no trapped volatiles); Nomex is actually the lower-cost option.

False — it is negligible only when $t_f\ll h$; for thick faces (small $h/t_f$) that term is not small and must be kept, which is why the thin-face assumption must always be stated.

Wrong goal — a denser core adds mass without helping bending; you want the lightest core that still supplies enough shear stiffness and strength and keeps the faces separated. Stiffness comes from face placement, not core density.

Wrong — ${\sigma }_{\text{wr}}$ depends on the core properties $E_c$ and $G_c$ too. Here $C$ is a dimensionless constant (about $0.5$ to $0.82$) that comes from modelling the face as a plate resting on the elastic core, treated as a Winkler foundation, and minimising energy over the wrinkle wavelength; it depends on boundary conditions and is only valid for a face that is thin relative to the wrinkle length. A stiff face on a soft core still wrinkles easily.

Category error — failure is governed by the shear strength ${\tau }_{c,\text{allow}}$ (a stress limit), while $G_c$ is a stiffness property that controls shear deflection. High modulus does not guarantee high strength.

Decimal blunder — $0.005$ m is 5 mm, ten times too thick; it inflates the face mass from 1.92 kg to 19.2 kg. Always confirm whether $t_f$ is in mm or m before substituting.

Approximation stated as exact — the true centroid distance is $d=\frac{h}{2}-\frac{t_f}{2}$; setting $d\approx h/2$ is valid only for thin faces and should always be flagged as an approximation.

Dangerous — honeycomb cores crush under concentrated point loads. Point loads need local reinforcement (solid inserts, potting) to spread the through-thickness pressure.

Wrong formula — a simply-supported uniformly-loaded beam uses $\delta =\frac{5w{L}^4}{384(EI)}$; the support conditions and load type change the numerical coefficient entirely.

Because bending stress $\sigma =My/I$ grows with distance $y$ from the neutral axis, so material at large $y$ carries and resists the most stress — putting strength where the stress is highest maximises capacity per unit mass.

For thin faces $t_f\ll h$, so $t_f^3\ll t_f{h}^2$; the transported term $b{t}_f(h/2{)}^2$ is larger by a factor of about $(h/t_f{)}^2\gg 1$.

Because $E_c{I}_{\text{core}}$ is tiny (typically $E_c/E_f\sim 10^{-3}$) so it adds negligible bending stiffness, but the shear force $V$ must physically pass through the core, and its low $G_c$ makes shear deflection non-trivial in long panels.

Match masses: a solid plate of thickness $t_s$ has the same mass as the two faces when ${\rho }_{s}b{t}_s\approx 2{\rho }_{f}b{t}_f$ (the light core is neglected), so $t_s\approx 2t_f$. The solid inertia is $I_{\text{solid}}=\frac{b{t}_s^3}{12}=\frac{b(2t_f{)}^3}{12}=\frac{8b{t}_f^3}{12}$, and the sandwich inertia is $I_{\text{sand}}\approx \frac{b{t}_f{h}^2}{2}$. Their ratio is $\frac{b{t}_f{h}^2/2}{8b{t}_f^3/12}=\frac{6t_f{h}^2}{8t_f^3}=\frac{3h^2}{4t_f^2}$ — the $\frac{3}{4}$ is exactly $6/8$ from those two coefficients.

The bond transfers the shear between faces and core; a weak or voided bond lets the faces debond and slide, destroying the composite action that the $h^2$ stiffness depends on — see Adhesive Bonding.

Open honeycomb cells vent freely so no gas is trapped to outgas or expand; sealed volumes could hold volatiles or pressurise and delaminate the faces in vacuum.

Launch cost scales with mass, so the payoff is stiffness per kilogram; a material that is stiff but heavy loses to a lighter, slightly less stiff one once mass is charged against orbit cost.

A shear force $V$ over an area $A$ makes an average shear strain $\gamma =\frac{V}{AG}$; over a length $L$ this strain accumulates into a sideways displacement of order $\gamma L=\frac{VL}{AG}$. Putting $A=bh$ (width times depth) and $G=G_c$ (the core does the shearing) gives $\frac{VL}{G_{c}bh}$.

The thin-face formula breaks down — it assumed $t_f\ll h$; at $t_f=h/2$ the panel is a solid plate and you must use $I=\frac{b{h}^3}{12}$ instead.

Then $h\to 2t_f$ and the two faces behave as one solid sheet of thickness $2t_f$; the huge $h^2$ leverage vanishes and you get only the modest stiffness of a thin solid plate.

Core shear governs — the panel fails in the core, not the faces, so redesign by increasing $h$ (which lowers ${\tau }_c\approx V/(bh)$) or choosing a higher-strength core, independent of how strong the faces are.

Shear deflection $\frac{VL}{G_{c}bh}$ dominates and can exceed the bending deflection, so a low-$G_c$ core (foam) may violate the deflection target even if bending stiffness looks adequate.

Local core crushing — the honeycomb collapses under through-thickness compression; the fix is a solid insert or potted region, not a stronger face sheet.

No — the approximation $E_c\ll E_f$ fails, core bending is no longer negligible, and you must treat it as a composite section with all layers contributing; it also loses the lightweight advantage.