NUI Galway – UL Alliance First Annual ENGINEERING AND - ARAN ...

Development of a mixed-mode cohesive zone model for stent and cell
applications
Ó Máirtίn, É. 1,2 1, 2
, McGarry, P.
Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway,
e.omairtin1@nuigalway.ie
Abstract
Cohesive zone models have been commonly used to
simulate coating delamination from a substrate and
crack propagation in certain material types [1]. In this
study we develop a path-dependent cohesive zone
model (CZM). The CZM is then applied to two distinct
case studies: (i) mixed-mode cell debonding during
cyclic substrate stretching and (ii) mixed-mode
overclosure of a stent coating during stent deployment.
Unphysical mixed-mode behaviour is computed for
cohesive zone model formulations derived from an
interface potential function.
1. Introduction
In this study we present a potential-based, coupled
cohesive zone formulation which has been used to
describe many mixed-mode delamination processes. We
propose an alternative, path-dependent cohesive zone
model in an effort to simulate physically realistic mixedmode
behaviour at an interface.
2. Materials and Methods
A path-dependent CZM is developed whereby
interface tractions, Ti, are related to interface
separations, Ui, by
2
U
Ti AiU
i exp 1 exp U
where i= 1,2. Subscripts 1 and 2 refer to normal and
tangential directions respectively. The constants Ai
define the independent interface strengths in the 1 and 2
directions.
Simulations are also performed using a potentialbased
cohesive zone model whereby tractions are
derived from an interface potential function [2],
ø(U1,U2):
i
This requires the definition of n and t; the work of
normal and tangential interface separation, respectively.
Cohesive zone formulations are implemented by means
of UINTER user-defined subroutine in Abaqus ©
Ti U1
U 2 U
software.
,
3. Results
Repulsive normal tractions develop during mixedmode
cell separation following application of potentialbased
model. The cell is forced away from the substrate
at 0% substrate strain, preventing the formation of new
bonds (Figure1(a)).
2
69
Repulsive normal
forces
(a)
Application of the path-dependent model produces a
more realistic result where bond formation occurs at the
end of each strain cycle (Figure1(b)).
(a)
1
0.5
0
-0.5
0 1 2 3 4 5
Time (seconds)
Figure 1. Normal traction and separation results
following application of (a) potential-based CZM and
(b) path-dependent CZM at the cell-substrate interface
(b)
Application of the potential-based model produces
unrealistic coating overclosure and no coating buckling
occurs (Figure2(a)). Overclosure is prevented when
path-dependent model is used with significant buckling.
4. Discussion
Unrealistic repulsive tractions are computed for
mixed-mode cell separation when a potential-based
cohesive zone model is applied at a cell-substrate
interface.
Unrealistic mixed-mode coating overclosure is
computed when a potential-based model is applied at a
stent-coating interface. Implementation of a pathdependent
model leads to more physically realistic
mixed-mode behaviour.
8. References
[1] Y. Yan, F. Shang, “Cohesive zone modeling of interfacial
delamination in PZT thin films”, Int.J.Solids Struct,
Publisher, Location, 2009, 46(13), pp. 2739-2749.
[2] X. P.. Xu, A. Needleman, “Void nucleation by inclusion
debonding in a crystal matrix”, Modell. Simul. Mater. Sci.
Eng, 1994, 1(2), pp.111-132.
(b)
-1
0 1 2 3 4 5
Time (seconds)
Figure 2. Coating deformation after application of
(a) potential-based model and (b) path dependent
model at the stent-coating interface
1
0.5
0
-0.5