1
July 16, 2026
5.
6.
7.
1.
2.
3.
4.
8.
9.
11.
12.
13.
10.
14.
(Major Poisson ratio)
(Shear Modulus)
(poisson effect value)
Theoretical Calculations of Material Properties
f: fiber, m: matris, c:kompozit, Vf : Fiber volumetric ratio, , Vm: Matrix volumetric ratio =1-Vf , ρ: density
(density of composite)
(modulus of elasticity in direction of fiber -1)
(E2: modulus of elasticity in the direction 2 ,
If p* is neglected)
(E2: modulus of elasticity in the direction 2 ,
If p* is not neglected)
(load rate coming to fiber in direction 1)
(composite strength in direction 1)
(Critical Fiber Volume fraction )
(minimum fiber Volume fraction)
(isotropic material property)
(normal stress in fiber direction)
Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor
2
July 16, 2026
at any instant
constrained in direction 1:
Temperature Differences for an orthotropic lamina
at strength limit
Free state:
CTE- coefficient of thermal expansion
(in direction 1)
(in direction 2)
THERMAL EQUATIONS
17
18
19
20
15
16
Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor
3
July 16, 2026
off -axis
Torsional Tube
45o
Iosipescu
(Rijitlik Modülü)
(Shear Strength)
Some Experimental Measurements
21
22
23
Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor
4
July 16, 2026
Transformation and Hooke’s Equations (For Stress and Strain Calculations)
32
33
34
35
θ: fiber orientation angle
θ’: straingage angle
local
stresses
Global
stresses
Local
strains
Global
strains
Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor
24
25
26
27
28
29
30
31
36
5
July 16, 2026
Maximum Stress Criterion
Maximum Strain Criterion
Tsai-Hill
Hoffman
Mises-Hencky
Hoffman Criterion
Tsai-Wu Criterion
Yield and Fracture Criteria in Composites (No Damage Inequalities)
37
Tsai-Hill Criterion
39
38
40
Modified Tsai-Hill Criterion
41
42
ult: Ultimate, C: Comporession , T: Tension
: Tensile strength in direction 1
: Tensile strength in direction 2
:Shear Strength
Semboller için Örnek Açıklama
Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor
6
July 16, 2026
Stifness Matrices [A], [B], [D] in CLT
43
44
45
Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor
7
July 16, 2026
Homogenization in Laminated Composites
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
65
64
66
67
68
69
70
71
72
Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor
Strengt Limits in the Zor Model
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
Formula Sheet for Mechanics of Composite Materials-Lecture Notes / Mehmet Zor
July 16, 2026