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TECHNICAL PAPERS: Other

Computational Studies of Shape Memory Alloy Behavior in Biomedical Applications

[+] Author and Article Information
Lorenza Petrini

Dipartimento di Meccanica Strutturale, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italypetrini@unipv.it

Francesco Migliavacca, Gabriele Dubini

Laboratory of Biological Structure Mechanics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Paolo Massarotti

Dipartimento di Meccanica Strutturale, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy; and Laboratory of Biological Structure Mechanics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Silvia Schievano

Ferdinando Auricchio

Dipartimento di Meccanica Strutturale, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy; Istituto di Matematica Applicata e Tecnologie Informatiche, CNR, Via Ferrata 1, 27100 Pavia, Italy

The use of the small deformation theory can be justified if one considers that in many biomedical applications large displacements but small strains are induced.

J Biomech Eng 127(4), 716-725 (Jan 24, 2005) (10 pages) doi:10.1115/1.1934203 History: Received June 21, 2004; Revised January 24, 2005

Background: Nowadays, shape memory alloys (SMAs) and in particular Ni–Ti alloys are commonly used in bioengineering applications as they join important qualities as resistance to corrosion, biocompatibility, fatigue resistance, MR compatibility, kink resistance with two unique thermo-mechanical behaviors: the shape memory effect and the pseudoelastic effect. They allow Ni–Ti devices to undergo large mechanically induced deformations and then to recover the original shape by thermal loading or simply by mechanical unloading. Method of approach: A numerical model is developed to catch the most significant SMA macroscopic thermo-mechanical properties and is implemented into a commercial finite element code to simulate the behavior of biomedical devices. Results: The comparison between experimental and numerical response of an intravascular coronary stent allows to verify the model suitability to describe pseudo-elasticity. The numerical study of a spinal vertebrae spacer, where the effects of different geometries and material characteristic temperatures are investigated, allows to verify the model suitability to describe shape memory effect. Conclusion: the results presented show the importance of computational studies in designing and optimizing new biomedical devices.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 5

CAD model of the Ni–Ti stent simulated

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Figure 6

Boundary conditions of the stent model: the highlighted points, belonging to the line tangent to the lower plane, are restrained to move along direction 1

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Figure 7

Three-dimensional CAD model of the spinal vertebrae spacer. Due to the symmetry only one fourth of the device is simulated. The mesh of the spacer and the boundary conditions are reported in the lower panel.

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Figure 8

Results from the sensitivity analysis of the spacer model A: comparison between the displacement histories of a central node (upper panel) and the Von Mises stresses at the end of the loading path (lower panel) of three different meshes with 1530, 3336, and 5702 elements, respectively

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Figure 9

Comparison between experimental results from the crush test and computational curve by the FEM analysis

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Figure 10

Numerical simulation: deformed (black) and undeformed (blue) configuration in a prospective view at the end of the loading step. In the lower panel the Von Mises stresses are depicted at the end of the loading step.

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Figure 11

SMA1 Spacer A: central node vertical displacement in mm at different steps and some deformed configurations (black color in the inset). The corresponding Von Mises contour maps of the deformed configurations are reported as well.

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Figure 12

SMA2 Spacer A, B, and C: central node vertical displacement in mm at different steps

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Figure 1

Pseudo-elastic effect (T=Af). (1) Elastic deformation of austenite; (2) austenite to single-variant martensite transformation (upper plateau); (3) elastic deformation of single-variant martensite; (4) elastic strain recovery; (5) transformation strain recovery by unloading (lower plateau). E=elastic modulus; h=transformation phase tangent modulus; ϵL=maximum transformation strain; s0=initial mean value of the mechanical hysteresis in the uniaxial tensile test; R=half of the mechanical hysteresis loop amplitude in the uniaxial tensile test; sAS=value of the stress deviatoric component inducing A→S transformation.

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Figure 2

Shape memory effect (T=Mf). (1) Elastic deformation of multi-variant martensite; (2) multi-variant to single-variant martensite transformation; (3) elastic deformation of single-variant martensite; (4) elastic strain recovery; (5) transformation strain recovery by thermal loading. E=elastic modulus; h=transformation phase tangent modulus; ϵL=maximum transformation strain; s0=initial mean value of the mechanical hysteresis in the uniaxial tensile test; R=half of the mechanical hysteresis loop amplitude in the uniaxial tensile test; sMS=value of the stress deviatoric component inducing M→S transformation; ΔT=temperature increment above Af inducing inverse transformation.

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Figure 3

Stress deviatoric component inducing transformation-temperature relation. sMS=value of the stress deviatoric component inducing M→S transformation at temperature T⩽Mf; sAS=value of the stress deviatoric component inducing A→S transformation at temperature T=Af.

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Figure 4

Experimental instrumentation: thermostatic fluid circuit with the MTS SYNERGIE 200H electromechanical machine. A sketch of the circuit is shown.

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