Biomedical Engineering – From Theory to Applications

Orthopaedic Modular Implants Based on Shape Memory Alloys
The matrix of eigenvectors is:
X 1/ 3 1/
6 1/ 2 0 0 0
1/ 3 1/ 6 1/
2 0 0 0
1/ 3 2/ 6 0 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
b. In the case of monoclinic crystallographic structure:
The eigenvalues are:
S 1
λ =
C +C + C +C +4C
C C C 0 0 C
11
C12 C13 12
C22 C23 13
C23 C33 0
0
0
0
16
C
26
C 36
0 0 0 C44 C45 0
0 0 0 C C 0
45 55
C16 C26 C36 0 0 C66
2 2
4 44 55 44 55 45
2
; 2 2
λ 5= C 44+C55-C 44+C 55 +4C45
2
and λ 1,λ 2,λ 3,λ4are the roots of the equation:
455
(13)
(14)
1
(15)
4 3 2
λ -I1λ +I2λ-I3λ+I 4=0
(16)
where Ik is the sum of the diagonal minors of k degree obtained by cutting the fourth and
the fifth columns and rows in matrix [S].
c. In the case of orthorhombic crystallographic structure:
The eigenvalues are:
S and λ 1,λ 2,λ3are the roots of the equation:
C11 C12 C13 0 0 0
C12 C22 C23 0 0 0
C13 C23 C33 0 0 0
0 0 0 C44 0 0
0 0 0 0 C55 0
0 0 0 0 0 C
66
(17)
λ 4=C 44;
λ 5=C 55;
λ 6=C 66
(18)
3 ' 2 ' '
λ -I1λ +I2λ-I 3=0
(19)