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Research Papers

Triple Shape Memory Polymers: Constitutive Modeling and Numerical Simulation

[+] Author and Article Information
S. Moon

Department of Mechanical Engineering,
Northeastern University,
Boston, MA 02115

I. J. Rao

Department of Mechanical Engineering,
New Jersey Institute of Technology,
Newark, NJ 07012
e-mail: raoi@njit.edu

S. A. Chester

Department of Mechanical Engineering,
New Jersey Institute of Technology,
Newark, NJ 07012

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 11, 2016; final manuscript received April 11, 2016; published online May 9, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(7), 071008 (May 09, 2016) (18 pages) Paper No: JAM-16-1138; doi: 10.1115/1.4033380 History: Received March 11, 2016; Revised April 11, 2016

Recently, triple shape memory polymers (TSMPs) have been discovered; these materials can be programmed to switch between three distinct shapes. Previously, we introduced a model to describe the mechanical behavior of TSMPs; however, the earlier study was limited in scope to simple cases of uniaxial deformation. In this work, we build upon our prior work, and develop robust numerical methods and constitutive equations to model complex mechanical behavior of TSMPs in inhomogeneous deformations and loading conditions using a framework based on the theory of multiple natural configurations. The model has been calibrated to uniaxial experiments. In addition, the model has been implemented as a user material subroutine (UMAT) in the finite element package abaqus. To demonstrate the applicability of the developed constitutive model, we have numerically simulated two cases of three-dimensional bodies undergoing triple-shape cycles; triple-shape recovery response of a complex TSMP geometry and the triple-shape recovery response of a stent when it is inserted in an artery modeled as a compliant elastomeric tube.

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Figures

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Fig. 1

Schematic illustration of the triple shape effect in TSMPs in a typical triple shape memory creation process. (c)—Second temporary shape, (b)—first temporary shape and (a)—permanent shape).

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Fig. 2

Schematic of a stress versus stretch curve of a TSMP for the deformation cycle illustrated in Fig. 1

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Fig. 3

Natural configurations associated with the amorphous and the crystalline phase

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Fig. 4

Schematic associated with the circular shear geometry

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Fig. 5

Plot of stretch versus time for uniaxial extension with crystallization taking place at constant stress, time is in seconds. *indicates experimental data (Zotzmann et al. [22]).

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Fig. 6

Plot of time versus applied moment for circular shear geometry. (a) During crystallization, moment is kept constant. (b) During crystallization, shear is kept constant.

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Fig. 7

Plot of shear versus time for circular shear geometry. (a) During crystallization, moment is kept constant (___r = 1,….. r = 1.2_._._.,r = 1.5). (b) During crystallization, shear is kept constant (___r = 1, _._._., r = 1.2,…..r = 1.5).

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Fig. 8

Plot of moment versus shear for circular shear geometry. (a) During crystallization, moment is kept constant (___r = 1,…..r = 1.2_._._.,r = 1.5). (b) During crystallization, shear is kept constant (___r = 1, _._._., r = 1.2,…..r = 1.5).

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Fig. 9

Comparison of the stress versus stretch plot for a single element simulation in abaqus to analytical solution using matlab, * represents the data from abaqus

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Fig. 10

(a) One-fourth symmetry finite element mesh for the 3D geometry. All the nodes on the “M” symmetry plane were prescribed symmetry in the three-direction, all the nodes on the symmetry plane “N” were prescribed symmetry in the one-direction. (b) Side view of the geometry. (c) Complete mirrored geometry.

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Fig. 11

Numerically predicted thermomechanical triple shape-recovery cycle showing maximum principal logarithmic strain for the TSMP body; for clarity, the body has been mirrored along relevant symmetry planes. (c) Second temporary shape. (b) First temporary shape. (a) Permanent shape.

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Fig. 12

(a) One-fourth symmetry finite element mesh for the stent geometry, (b) complete mirrored geometry of the stent. All the nodes on the symmetry plane “ABCD” were prescribed symmetry in the one-direction, all the nodes on the symmetry plane “EFGH” were prescribed symmetry in the two-direction, and all the nodes on the front surface were prescribed symmetry in the three-direction.

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Fig. 13

Numerically predicted thermomechanical shape-recovery cycle for the TSMP stent; for clarity the mesh has been mirrored along relevant symmetry planes to show the full stent and artery. (c) Second temporary shape of the stent. (b) First temporary shape (shape recovery of the stent inside the artery with temperature.). (a) Permanent shape (final shape recovery of the stent inside the artery with temperature).

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Fig. 14

Predictions from the numerical simulation for the outer diameter of a TSMP stent at different temperatures during the thermomechanical cycle of fixation and recovery of the stent in an artery (1–7 show different steps in the fixation and recovery cycle)

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