The faces carry the bending moment as membrane tension and compression; the core carries the shear force. Distance between face centroids d = c + t.

D = E_f(bt³/6 + btd²/2) + E_c,xbc³/12 ≈ E_fbtd²/2, with E_f = 2E_f,tE_f,c/(E_f,t + E_f,c) for a face modulus that differs in tension and compression

S = G_cbd²/c ≈ G_cbc

3-point: δ = PL³/(48D) + PL/(4S), M = PL/4, Q = P/2

4-point, a = (L − L_s)/2: δ = Pa(3L² − 4a²)/(48D) + Pa/(2S), M = Pa/2, Q = P/2

σ_f = M/(btd), τ_c = Q/(bd)

Tension face failure: σ_f = unnotched laminate tension strength (lower face)

Delamination in the tension face: σ_d = √(E_xG_IIc/(0.47 t_block)), after a matrix crack in the run; t_block = thickest same-angle off-axis block on one half of the face; 0.47 fitted to the ply-block tests of Wisnom, Khan and Hallett (2008)

Compression face failure: σ_f = unnotched laminate compression strength (upper face)

Face wrinkling: σ_f = σ_w = 0.5(E_f,cE_cG_c)^1/3, with the compression modulus of the face

Core shear: τ_c = core shear strength, so P = 2τ_cbd

The four failure modes are checked at every load; the first to reach its limit fails the beam. Under a concentrated load without a pad, the core can also crush locally (indentation); test standards use load pads to prevent it, so it is not modelled here. The face modulus of a layup is its membrane modulus along the span from laminate theory, with E_1c on the compression face. Both face strengths come from the shared engine ply-failure.js, the same calculation as the Tension page. Tension: progressive ply discount with in-situ matrix strengths (Camanho et al. 2006), fiber failure at X_T, ±45° plies at S_L when no plies are near 0°, and delamination of a cracked off-axis run. Compression: E_1c along the fibers, fiber failure at σ₁ = −X_C, ±45° plies at S_L when no plies are near 0°, otherwise the first matrix failure; cracks close in compression, so delamination is not checked. Face wrinkling uses the Hoff and Mautner design value. Honeycomb faces can also dimple between cells, and the face-core bond can fail; neither is modelled.

The beam is linear elastic up to the first failure. The load drop after it and the damage drawings are illustrative.

Material data

Sources:

• H.G. Allen, Analysis and Design of Structural Sandwich Panels, Pergamon (1969). doi:10.1016/C2013-0-02134-2
• D. Zenkert, An Introduction to Sandwich Construction, EMAS (1995). No DOI.
• N.J. Hoff and S.E. Mautner, The buckling of sandwich-type panels, J. Aeronaut. Sci. 12 (1945) 285. doi:10.2514/8.11246
• M.R. Wisnom, B. Khan and S.R. Hallett, Size effects in unnotched tensile strength of unidirectional and quasi-isotropic carbon/epoxy composites, Compos. Struct. 84 (2008) 21. doi:10.1016/j.compstruct.2007.06.002
• P.P. Camanho, C.G. Dávila, S.T. Pinho, L. Iannucci and P. Robinson, Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear, Compos. Part A 37 (2006) 165. doi:10.1016/j.compositesa.2005.04.023
• L.J. Gibson and M.F. Ashby, Cellular Solids, 2nd ed., Cambridge University Press (1997). doi:10.1017/CBO9781139878326
• ASTM D7249/D7249M-20, facesheet properties by long beam flexure. doi:10.1520/D7249_D7249M-20
• ASTM D7250/D7250M-20, sandwich beam flexural and shear stiffness. doi:10.1520/D7250_D7250M-20
• ASTM C393/C393M-20, core shear properties by beam flexure. doi:10.1520/C0393_C0393M-20
• Core data: 3A Composites BALTEK SB.100, DIAB Divinycell H100, Evonik ROHACELL 71 WF, Hexcel HexWeb HRH-10 and 5052 aluminium honeycomb data sheets. Ply data: NCAMP qualification data for IM7/8552 and AS4/8552 (test-materials.js); your-material plies estimated from fiber and resin; tape densities from Hexcel 8552 product data.