As known, the weight of structures is one of the principle concerns in transport engineering. In this relation, the multilayered structural materials with their high strength-to-weight and stiffness-to-weight ratios are excellent for application in transport engineering. However, delamination is one of the momentous disadvantages of multilayered structural members. Therefore, a multilayered delaminated beam structure exhibiting linear relaxation behavior is studied in this paper. The beam under consideration is statically undetermined. The angle of rotation of the cross-section located near the beam left-hand end is fixed in order to generate conditions for relaxation of stresses. There is a delamination crack in the beam. The time-dependent problem of the energy release rate (ERR) for the delamination crack is solved. For this purpose, an analysis that takes into account the relaxation of stresses is developed by considering the compliance of the beam. An alternative approach is used for verification. The effect of the beam static indeterminacy on the ERR is assessed.

1.
N. A.
Dolgov
, “
Determination of stresses in a two-layer coating
”,
Strength of Materials
37
, pp.
422
431
(
2005
).
2.
N. A.
Dolgov
, “
Analytical methods to determine the stress state in the substrate–coating system under mechanical loads
”,
Strength of Materials
48
, pp.
658
667
(
2016
).
3.
J. S.
Kim
,
K. W.
Paik
and
S. H.
Oh
, “
The multilayer-modified Stoney’s formula for laminated polymer composites on a silicon substrate
”,
J. Appl. Phys.
86
(
10
),
5474
(
1999
).
4.
J-H.
Yu
,
S.
Guo
and
D. A.
Gillard
, “
Bimaterial curvature measurements for the CTE of adhesives: optimization, modeling, and stability
”,
J. Adhes. Sci. Technol.
17
, pp.
149
164
(
2003
).
5.
V. A.
Greenhut
,
principles and methods of metal-ceramic bonding for PM applications
,
International Journal of Powder Metallurgy
47
, pp.
57
76
(
2011
).
6.
C. H.
Hsueh
,
W. H.
Tuan
and
W. C. J.
Wei
, “
Analyses of steady-state interface fracture of elastic multilayered beams under four-point bending
”,
Scripta Mater.
60
, pp.
721
724
(
2009
).
7.
J.
Malzbender
, “
Mechanical and thermal stresses in multilayered materials
”,
J. Appl. Phys.
95
(
4
),
1780
(
2003
).
8.
J.
Hutchinson
and
Z.
Suo
, “
Mixed mode cracking in layered materials
”,
Adv. Appl. Mech.
29
, pp.
63
191
(
1991
).
9.
V. I.
Rizov
, “
Longitudinal fracture analysis of inhomogeneous beams with continuously changing radius of cross-section along the beam length
”,
Strength, Fracture and Complexity
13
(
1
), pp.
31
43
(
2020
).
10.
V. I.
Rizov
, “
Longitudinal vertical crack analysis in beam with relaxation stresses
”,
World Journal of Engineering
18
(
3
), pp.
452
457
(
2021
).
11.
N. E.
Dowling
,
Mechanical Behaviour of Materials
(
Person
,
2003
).
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