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[January 2006] Materials used in medical engineering applications operate in very demanding conditions. They generally need to be biocompatible, offer good wear-resistance properties but, sometimes, also need to have some specialised characteristics such as unusual structural properties (e.g.: shape-memory alloys, auxetic foams).
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Figure 1. Scaled rapid-prototyping
model of an auxetic foam sample
(real dimensions: 0.1 x 0.1 x 0.1 mm) |
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Auxetic foam materials (Figure 1) are commonly used in a variety of industrial applications (sound and shock absorption) and are very promising for novel applications in medical engineering. By actively controlling their microstructure through specific loading conditions they can allow/prevent fluid and solid particles flow in specific directions. Thanks to this useful characteristic, auxetic foams can be used as tuneable filters for filtration of biological fluids and/or process engineering.
Auxetic materials have the particular property to expand in all directions when stretched in one direction thus exhibiting a negative Poisson’s ratio. Similarly, a sample of auxetic material submitted to compression in one direction will contract in the other directions. This counter-intuitive behaviour is due to the structural properties. Other significant structural properties include increased shear stiffness, increased plane strain fracture toughness and increased indentation resistance.
There is therefore a real industrial need for understanding, developing and predicting the mechanical behaviour of auxetic materials. Predicting accurately the mechanical properties of auxetic materials is intractable with analytical methods and cannot only be performed by using computational mechanics simulations. In collaboration with Simpleware Ltd, FIRST Numerics developed a general methodology combining image processing, automatic generation of finite element mesh and non-linear finite element analyses to investigate the microstructural property of an industrial auxetic foam developed by DuPont.
High-resolution three-dimensional scan data of the auxetic foam sample were obtained from synchrotron scanning facilities at the Advanced Photon Source at Argonne National Laboratory, IL,USA (courtesy of Dr. Jerry Seidler, University of Washington, Seattle, USA), processed and automatically converted to a three-dimensional finite element mesh.
The total combined image processing and meshing time, including user interaction time, was less than ten minutes on a 2 GHz Pentium PC. The finite element mesh generated by the software module ScanFETM (Simpleware) consisted of very large number of elements ( about 620,000). Figure 2 presents an enlarged view of the finite element mesh which highlights the complex structural features of the auxetic foam.
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Figure 2. Zoom-in view of the
finite element mesh of the
auxetic foam sample |
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A non-linear finite element analysis was then performed using the software package ABAQUS to simulate the compaction regime. The finite element analysis simulating compression (16.5 % strain) of the auxetic foam took over 27 hours on a dual Intel Xeon processor PC cadenced at 2.8 Ghz.
The analysis demonstrated the negative Poisson’s ratio effect. The auxetic structure collapsed towards its centre resulting in a lateral contraction as the vertical displacement of the top of the cube progressed. Figure 3 displays the fringe plot of the maximal principal compressive strains at various stages of the analysis. The numerous branching substructures of the auxetic sample lead to complex load redistribution patterns which affect the global deformation of the whole structure.
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Figure 3. Maximal principal compressive strains (logarithmic strains) at various stages of the deformation of the auxetic foam sample (increment 0: beginning of the analysis / increment 86: end of the analysis) |
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The methodology which incorporates image processing, automatic meshing and non-linear finite element analyses has been shown to be very robust. Its main advantage is that arbitrary complex three-dimensional geometries can be meshed automatically and readily analysed.
Non-linear finite element analyses can therefore be a fast and practical tool to explore the structural properties of auxetic materials. Future studies should look at comparing quantitative data obtained from experimental, analytical and numerical analyses.
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