Biomedical Engineering – From Theory to Applications

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452 Biomedical Engineering – From Theory to Applications A comparison between classical implants and proposed modular implants based on shape memory alloys is presented: Traditional implants Proposed implants Big dimensions, configuration which results in the redundant bone callus Invasive surgical interventions in order to couple the implants Medium risk of postsurgical infections due to the surgical intervention Neutral from the point of view of the bio-stimulation bone restoration Require an important number of physical connections (holes) for implant fixation The fixation problems related to classical implants can cause pseudo arthritis 5. Theoretical and experimental studies for NiTi staples Small dimensions, completely adaptable to the fracture Minimal invasive surgical techniques are used for this types of implants – microincisions Minimal risk due to reduced area of surgical intervention Bio-stimulation properties for bone growth, reduced time for healing the fracture zone Small number and reduced dimensions for the fixation holes (in some cases the number of holes can be zero) Due to the constant pressure that the implants make the fracture fragments are well compacted, no micro-movements are allowed, avoiding in this way the pseudo arthritis 5.1 Decomposition of the elasticity matrix for Nitinol structure phases The form of the elasticity matrix contains the restrictions done by the symmetry theory of classical crystallography and it permits a simple geometrical interpretation of the relationship between stress and strain regardless of the degree on anisotropy. These restrictions are reflected in the invariant structures of the spectral decompositions. The spectral forms are determined by the symmetry groups, and are independent of the values of the elastic constants. In (Cowin & Mehrabadi, 1987, 1990) the eigenvalues and eigenvectors for anisotropic elasticity were determined. (Ting, 1987) has discussed the eigenvalue problem in connection with his study of the invariants of the elasticity tensor. The first spectral decomposition of the elasticity tensor was made in (Rychlewski & Zhang, 1989), using tensorial products. Then, (Sutcliffe, 1992) developed this method and they used it for different types of symmetries. A more simple method, using matrix 6x6 was used in (Theocaris & Philippidis, 1989) for the decomposition of the rigidity matrix of the transversal isotropic materials. In the case of the linear-elastic materials, the dependence between the deformation matrix components and the stress matrix components can be written as a linear dependence: 3 3 S (1) ij ijkl kl k1l1 This dependence can be written on the following form: where: S ( ) ( ) (2)
Orthopaedic Modular Implants Based on Shape Memory Alloys with: S = ε11 ε 22 ε 33 (ε)= 2 ε ; 23 2 ε 13 2 ε 12 (σ)= σ 11 σ 22 σ 33 2 σ 23 2 σ 13 2 σ 12 S1111 S1122 S1133 2S1123 2S1113 2S 1112 S S S 2S 2S 2S 2211 2222 2233 2223 2213 2212 S3311 S3322 S3333 2S3323 2S3313 2S3312 2S2311 2S2322 2S2333 2S2323 2S2313 2S2312 2S1311 2S1322 2S1333 2S1323 2S1313 2S 1312 2S1211 2S1222 2S1233 2S1223 2S1213 2S 1212 453 S ijkl =S jikl =S ijlk =S (5) klij Basically, SMA presents two well-defined crystallographic phases, i.e., austenite and martensite. Martensite is a phase that is easily deformed, reaching large strains (~8%), and in the absence of stress, is stable only at low temperatures; in addition, it can be induced by either stress or temperature. The kinematics associated with the martensitic phase transformation in a single crystal is described for a cubic to tetragonal and cubic to monoclinic transformation, and the lattice invariant strain by plastic slip is discussed (Patoor et al.,2006). When the martensitic transformation takes place, numerous physical properties are modified. During the transformation, a latent heat associated with the transformation is absorbed or released based on the transformation direction. The forward, austenite-tomartensite transformation is accompanied by the release of heat corresponding to a change in the transformation enthalpy (exothermic phase transformation). The reverse, martensiteto-austenite transformation is an endothermic phase transformation accompanied by absorption of thermal energy. For a given temperature, the amount of heat is proportional to the volume fraction of the transformed material. 5.2 Symmetry cases of Nitinol crystallographic phases We present the elasticity matrix for the crystallographic phases of Nitinol. For the trigonal crystallographic structure, the matrix [S] has the expression: C11 C12 C13 0 - 2C15 0 C C C 0 2C 0 12 11 13 15 C13 C13 C33 0 0 0 0 0 0 C44 0 2C 15 S= - 2C 2C 0 0 C 0 15 15 44 0 0 0 2C15 0 C11-C12 (3) (4) (6)
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BIOMEDICAL ENGINEERING - FROM THEOR
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VI Contents Chapter 9 Targeted Magn
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190 R* M M M M MR*M O O O O M O R*
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Biomedical Engineering – From Theory to Applications

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