Because the observed size effect follows neither the strength theory nor the linear elastic fracture mechanics, the delamination fracture of laminate-foam sandwiches under uniform bending moment is treated by the cohesive crack model. Both two-dimensional geometrically nonlinear finite element analysis and one-dimensional representation of skin (or facesheet) as a beam on elastic-softening foundation are used. The use of the latter is made possible by realizing that the effective elastic foundation stiffness depends on the ratio of the critical wavelength of periodic skin wrinkles to the foam core thickness, and a simple description of the transition from shortwave to longwave wrinkling is obtained by asymptotic matching. Good agreement between both approaches is achieved. Skin imperfections (considered proportional to the the first eigenmode of wrinkling), are shown to lead to strong size dependence of the nominal strength. For large imperfections, the strength reduction due to size effect can reach 50%. Dents from impact, though not the same as imperfections, might be expected to cause as a similar size effect. Using proper dimensionless variables, numerical simulations of cohesive delamination fracture covering the entire practical range are performed. Their fitting, heeding the shortwave and longwave asymptotics, leads to an approximate imperfection-dependent size effect law of asymptotic matching type. Strong size effect on postpeak energy absorption, important for impact analysis, is also demonstrated. Finally, discrepancies among various existing formulas for critical stress at periodic elastic wrinkling are explained by their applicability to different special cases in the shortwave-longwave transition.

1.
Reissner
,
M. E.
, 1937, “
On the Theory of Beams Resting on a Yielding Foundation
,”
Proc. Natl. Acad. Sci. U.S.A.
0027-8424,
23
, pp.
328
333
.
2.
Gough
,
G. S.
,
Elam
,
C. F.
, and
de Bruyne
,
N. A.
, 1940, “
The Stabilisation of a Thin Sheet by a Continuous Supporting Medium
,”
J. R. Aeronaut. Soc.
0368-3931,
44
, pp.
12
43
.
3.
Hoff
,
N. J.
, and
Mautner
,
S. E.
, 1945, “
The Buckling of Sandwich-Type Panels
,”
J. Aeronaut. Sci.
0095-9812,
12
, pp.
285
297
.
4.
Heath
,
W. G.
, 1960, “
Sandwich Construction, Part 2: The Optimum Design of Flat Sandwich Panels
,”
Aircr. Eng.
0002-2667,
32
, pp.
230
235
.
5.
Niu
,
K.
, and
Talreja
,
R.
, 1999, “
Modeling of Wrinkling in Sandwich Panels Under Compression
,”
J. Eng. Mech.
0733-9399,
125
(
8
), pp.
875
883
.
6.
Bažant
,
Z. P.
, 2002,
Scaling of Structural Strength
, Hermes-Penton, London (and
2nd ed.
,
Elsevier
,
New York
, 2005).
7.
Bažant
,
Z. P.
, and
Cedolin
,
L.
, 1991,
Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories
,
Oxford University Press
,
London
.
8.
Sallam
,
S.
, and
Simitses
,
G. J.
, 1985, “
Delamination Buckling and Growth of Flat, Cross-Ply Laminates
,”
Compos. Struct.
0263-8223,
4
, pp.
361
381
.
9.
Yin
,
W. L.
,
Sallam
,
S.
, and
Simitses
,
G. J.
, 1986, “
Ultimate Axial Load Capacity of a Delaminated Beam-Plate
,”
AIAA J.
0001-1452,
34
, pp.
123
128
.
10.
Daniel
,
I. M.
, and
Ishai
,
O.
, 1994,
Engineering Mechanics of Composite Materials
,
Oxford University Press
,
New York
.
11.
Wadee
,
M. A.
, and
Blackmore
,
A.
, 2001, “
Delamination From Localized Instabilities in Compression Sandwich Panels
,”
J. Mech. Phys. Solids
0022-5096,
49
, pp.
1281
1299
.
12.
Wadee
,
M. A.
, 2002, “
Localized Buckling in Sandwich Struts With Pre-Existing Delaminations and Geometrical Imperfections
,”
J. Mech. Phys. Solids
0022-5096,
50
, pp.
1767
1787
.
13.
Frostig
,
Y.
, and
Thomsen
,
O. T.
, 2005, “
Non-Linear Behavior of Delamination Unidirectional Sandwich Panels With Partial Contact and a Transversely Flexible Core
,”
Int. J. Non-Linear Mech.
0020-7462,
40
, pp.
633
651
.
14.
Aviles
,
F.
, and
Carlsson
,
L. A.
, 2005, “
Elastic Foundation Analysis of Local Face Buckling in Debonded Sandwich Columns
,”
Mech. Mater.
0167-6636,
37
, pp.
1026
1034
.
15.
Hutchinson
,
J. W.
, and
Suo
,
Z.
, 1992, “
Mixed Mode Cracking in Layered Materials
,”
Adv. Appl. Mech.
0065-2156,
29
, pp.
63
191
.
16.
Jensen
,
H. M.
, and
Sheinman
,
I.
, 2002, “
Numerical Analysis of Buckling-Driven Delamination
,”
Int. J. Solids Struct.
0020-7683,
39
, pp.
3373
3386
.
17.
Bažant
,
Z. P.
,
Zhou
,
Y.
, and
Daniel
,
I. M.
, 2006, “
Size Effect on Strength of Laminate-Foam Sandwich Plates
,”
ASME J. Eng. Mater. Technol.
0094-4289,
128
, pp.
366
374
.
18.
Bayldon
,
J.
,
Bažant
,
Z. P.
,
Daniel
,
I. M.
, and
Yu
,
Q.
, 2006, “
Size Effect on Compressive Strength of Laminate-Foam Sandwich Plates
,”
ASME J. Eng. Mater. Technol.
0094-4289,
128
, pp.
169
174
.
19.
Bažant
,
Z. P.
, and
Planas
,
J.
, 1998,
Fracture and Size Effect in Concrete and Other Quasibrittle Materials
,
CRC Press
,
Boca Raton
.
20.
Remmers
,
J. J. C.
, and
de Borst
,
R.
, 2001, “
Delamination Buckling of Fibre-Metal Laminates
,”
Compos. Sci. Technol.
0266-3538,
61
, pp.
2207
2213
.
21.
Han
,
T.
,
Ural
,
A.
,
Chen
,
C.
,
Zehnder
,
A. T.
,
Ingraffea
,
A. R.
, and
Billington
,
S. L.
, 2002, “
Delamination Buckling and Propagation Analysis of Honeycomb Panels Using a Cohesive Element Approach
,”
Int. J. Fract.
0376-9429,
115
, pp.
101
123
.
22.
Gdoutos
,
E. E.
,
Daniel
,
I. M.
, and
Wang
,
K.-A.
, 2003, “
Compression Facing Wrinkling of Composite Sandwich Structures
,”
Mech. Mater.
0167-6636,
35
, pp.
511
522
.
23.
Vadakke
,
V.
, and
Carlsson
,
L. A.
, 2004, “
Experimental Investigation of Compression Failure of Sandwich Speciments With Face/Core Debond
,”
Composites, Part B
1359-8368,
35
, pp.
583
590
.
24.
Bažant
,
Z. P.
, 2004, “
Scaling Theory for Quasibrittle Structural Failure
,”
Proc. Natl. Acad. Sci. U.S.A.
0027-8424,
101
, pp.
13400
13407
.
25.
Tvergaard
,
V.
, and
Needleman
,
A.
, 1980, “
On the Localization of Buckling Patterns
,”
ASME J. Appl. Mech.
0021-8936,
47
, pp.
613
619
.
26.
Vonach
,
W. K.
, and
Rammerstorfer
,
F. G.
, 2000, “
The Effects of In-Plane Core Stiffness on the Wrinkling Behavior of Thick Sandwiches
,”
Acta Mater.
1359-6454,
141
, pp.
1
10
.
27.
Bažant
,
Z. P.
, and
Oh
,
B.-H.
, 1983, “
Crack Band Theory for Fracture of Concrete
,”
Mater. Struct.
1359-5997,
16
, pp.
155
177
.
28.
Suo
,
Z.
,
Bao
,
G.
, and
Fan
,
B.
, 1992, “
Delamination R-Curve Phenomena Due to Damage
,”
J. Mech. Phys. Solids
0022-5096,
40
, pp.
1
16
.
29.
Bao
,
G.
, and
Suo
,
Z.
, 1992, “
Remarks on Crack-Bridging Concepts
,”
Appl. Mech. Rev.
0003-6900,
45
, pp.
355
366
.
30.
Massabó
,
R.
, and
Cox
,
B. N.
, 1999, “
Concepts for Bridged Mode II Delamination Cracks
,”
J. Mech. Phys. Solids
0022-5096,
47
(
6
), pp.
1265
1300
.
31.
Bažant
,
Z. P.
, and
Yavari
,
A.
, 2004, “
Is the Cause of Size Effect on Structural Strength Fractal or Energetic-Stastical
,”
Eng. Fract. Mech.
0013-7944,
72
, pp.
1
31
.
32.
Bažant
,
Z. P.
, 1997, “
Scaling of Quasi-Brittle Fracture: Asymptotic Analysis
,”
Int. J. Fract.
0376-9429,
83
, pp.
19
40
.
33.
Bažant
,
Z. P.
, and
Beghini
,
A.
, 2005, “
Which Formulation Allows Using a Constant Shear Modulus for Small-Strain Buckling of Soft-Core Sandwich Structures
,”
ASME J. Appl. Mech.
0021-8936,
72
, pp.
785
787
.
34.
Bažant
,
Z. P.
, and
Beghini
,
A.
, 2006, “
Stability and Finite Strain of Homogenized Structures Soft in Shear: Sandwich or Fiber Composites, and Layered Bodies
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
1571
1593
.
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