PSI - Issue 15

Sharath Chavalla et al. / Procedia Structural Integrity 15 (2019) 8–15 Chavalla et al. / Structural Integrity Procedia 00 (2019) 000–000

12

5

T ( - ) / 2 = ( - ) / 2 F F E = C 1 1 t t t t

(7)

T -T 1    C F F F CF e e e t

Additionally, the elastic right Cauchy-Green tensor used. The complete material law is summarized as follows:

t with its transitional counterpart C e t is

Stress quantities



-1 2 ψ   F F S = C e t t e

-T

(8)

+ X = X X t z

(9)

E E

ψ

ψ





X =

X

2

,

-1

-T



t

t

F

F

(10)

t

t

t

z

C

β



t  

d

d

t

e

Y = CS - C X t and Y = C X t t t

(11)

b

C = 



2 1 (    λ Y D

2 (  λ

), Y C C = D

Y C D

)

Evolution equations:

(12)



t

t

t

t

t

μ

d

d

t

0,   λ sma 0,  

  λ

0 

,    M X D D k  

, where sma 

(13)

Kuhn-Tucker conditions:



sma

 

where the Mandel stress tensor := 2 ψ e e e M C C and the half height of hysteresis k , ψ e represents the elastic part of the Helmholtz free energy function. The superscript D indicates the deviatoric part of the respective measure.

, = E t   

0 1   z

z

Martensitic volume fraction:

(14)



The constitutive material parameters for the material model of NiTi alloy are fit to the experimental data provided by Ferdinand Auricchio, Robert L. Taylor (1997). 3.3. Carotid artery model For the stent deployment a realistic carotid artery model from clinical intervention is considered for the study. The carotid artery geometry is obtained from the medical reconstruction technique which was exported as the STL file format. The file when imported into the Rhinoceros 5 is in the form of a point cloud as shown in the Fig. 2a. In order to generate the NURBS model of the artery, a skeleton sketch comprising of circular cross-sections is constructed that encompasses the artery. Enough care is taken such that the cross-section of the model traces along the length and orientation around center line of the artery. In the final step a surface is wrapped over the skeleton sketch resulting in the artery as depicted in the Fig. 2c. The surface model of the artery is then exported as a text file with the GeoPde plugin Falco et al. (2011) in Rhinoceros 5. Using in-house Matlab codes the NURBS model is generated from the text file, which is further used for contact simulation between the stent and artery using IGA.