Mechanics Section: 876486

Mechanics Section

• Stiffness- The magnitude of resistance to deformation when an object is subjected to external forces (either in tension or compression). The greater the resistance to deformation the greater is the stiffness of material. Different materials exhibit different stiffness ranges.

• Elastic modulus- This refers to the ratio of stress (applied on a body of an object) to the produced strain within the elastic region (the elastic region is the portion where material regains its original length when the stress causing the strain is released).

• In mechanical property, is mostly defined as response obtained from mechanical loading in a material; often depends on the material structural property while in structural property, this is the inherent characteristics present in a material and is often independent of mechanical property (Bilandzic and Stenvers, 2011)

• We know that from Hooke’s law:

F= ke where e= extension and k= stiffness of material

From the definition of elastic modulus above, E= Г/έ only for isotropic materials But έ=e/L such that e=έ/L…..(i)

From F=ke ; e= F/k …..(ii) Equating the two equations: έ/L= F/k έ=FL/k…(iii)

Alternatively, from the definition of elastic modulus: E= Г/έ

And we also note that : Г=F/A

Therefore, E= F/A/έ=F/Aέ

Which implies that : F= AέE

And from Hooke’s law: F=Ke

Equating these two equations: eK= AέE

Hence K= AEέ/e….(iv)

Equations (iv) and (iii) should be equivalent as far as relations between k and E is concerned hence: K= AEέ/e or έ=FL/K

• (a) The maximum stress Гmax= Fmax/A From the given figure, Fmax= 6.5N

Now, cross sectional area of an elliptical solid/surface is given by: A= πab where a=semi-minor axis radius and b=semi-major axis of radius

a= 0.75/2 and b= 2/2=1

A= 3.142 x0.75/2x 1= 1.17825mm² Гmax= 6.5/1.17825×10^-6 = 5.517MPa  

• Maximum strain, έ=e/L= 1.2/8= 0.15
• Linear regression elastic modulus

• For this case, we consider the limit state fixed at 2% for Toe region in most biomaterials

2% offset

• It is imperative to report both since the toe region indicates the correction factor that is due to material set up alignment. Normally, there will be experimental error attributable to the set up for example slipping of jaws. Therefore, this parameter is normally used to make corrections based on these circumstances (Kirkbride, Townsend, Bruinsma, Barnett, Blobe, 2008)

• (a) Compression cycle

(b) –cartilage

-collagen

-Ligament

(c)(i) Collagen

• Proteoglycan

• Chondrocytes

• Anisotropy refers to the tendency of a material exhibiting different physical behaviors along different orientations (Schäfer and Radmacher, 2005). In other words, the term is used to describe the material behavior to have different properties in different directions such that if tests are conducted laterally and transversely in the same material, different results are obtained. For example, the strength characteristics of such a material will often vary from direction to direction. In one direction, it may be stronger and in the other direction it becomes weaker. A good example is wood; based on the grain orientations, it is easier to split wood along the grains but not across the grains.

• Poisson’s ratio normally describes a material such that the length is increased while girth decreases in a pure tension force application. Therefore, a Poisson’s ratio of 0.5 indicates that the material is perfectly incompressible and elastic (Fictiv.com, 2018 and Yamamoto and Nakamura, 2017). In other words, in Poisson’s ration, as the length is increased by a factor say 2, the girth decreases by the same factor while volume of material remains constant. The reverse is normally true; in compression tests, the girth will increase while the length decreases. Therefore, Poisson’s ratio indicates the extent in which change in length affects the girth of a material.

• It will stay the same since there is neither addition nor extraction of material. Besides, volume changes are often influenced by either thermal expansion or contraction. Temperatures remain constant. The parameters that are likely to change are the length and diameter and this occurs in equal proportion (Bilandzic, Wang , Ahmed , Luwor , Zhu, Findlay, 2014).

• This is false. Most biological material exhibit anisotropic properties.

• Viscoelasticity refers to the material behavior phenomenon such that stress regime occur over a given time period. The term is composed of two words: Viscosity and elasticity. The former is normally linked with fluidic systems and it describes the resistance to flow of fluids while the latter is normally used in solids such that it describes the tendency of a material to regain its shape after stress causing the strain is released. Therefore, in viscoelasticity, the elastic and viscous behaviors are combined and spread on a timescale. The common characteristics exhibited include stress relaxation and creep (Wang, Naruse, Stamenovic, Fredberg, Mijailovich, Tolic-Norrelykke, Polte, Mannix and Ingber, 2001).

• –Cartilage -Bone

Normally they exhibit a decreasing percentage recovery with increasing duration of tensile loading. At different time cycles, the recorded percent recovery often deviates with a certain margin.

MATERIAL TESTING METHODS SECTION

• -The nonlinear behavior exhibited by most materials would often impede concrete evaluation (Wang, Liu, Gao and Xu, 2011).

-Difficulty in maintaining visibility during tests as the materials lack stability unlike in engineering materials where most of them are solidly stable. There will be handling challenges from specimen preparation to finally acquiring the results.

-Variation in results is too wide for the same specimen under test. Due to the stability challenges, results obtainable from the same specimen under similar testing conditions may greatly vary.

-Besides, there is a challenge of deviating from the reality of biological structures. However, modern methods are integrating the aspect of ensuring that the testing environment mimics the physiological realities of these biological materials.

• –By redesigning the test equipment to accommodate these challenges For example, in compression testing of the skin, it is to be confined in a fluid-filled chamber where porosity is still allowed. The efficacy of results, in this case, is expected to improve tremendously.

• Reviewing the experimental methodology. For example, for cartilage, the common method used is indentation. This should be extended further such that there are more in-situ testing modes so that it becomes more physiological.

16. (a) Tensile and cyclic loading tests

Why? It is a viscoelastic and non-linearly behaving material such that tensile testing only may not yield sufficient results;

-Due to its complex structure, the tests required must be in tandem with the structural components hence incorporation of immerging technology for real-time tests in all directions (A, K. and A, L. 2016 and Wang, Tolić-Nørrelykke, Chen, Mijailovich, Butler, Fredberg and Stamenović, 2002)

-Also test must be performed in all directions possible as the material is also anisotropic, that is, it exhibits different properties for different orientations or directions in the material structure.

-Additionally compression tests may also be included as the real environment constitutes these load structures.

(b) –Strength of fibres (tensile)

– Strain values (within elastic region)

• A three-point bending since it purely gives the true picture of mechanical behavior of the whole bone. Besides, the structural property of mid-diaphysis is also tested (Fish, 2000)

• Atomic Force microscopy which is an instrument for nanoscale scanning such that it reveals the atomic structural composition during force applications. Hence producing finer details that were previously invisible; it also measures different force combinations.

STRUCTURE FUNCTIONS RELATIONSHIPS AT MULTIPLE SCALES SECTION

Greater is experienced towards the middle of the structure while stress levels are greater at the outer skirt of the structure (Hawkins, 2001). 

• In B2, there is uniform strain field exhibited when Ribose is added while in A2, strain field is boosted to higher levels when Ribose is added

Checking control on B2, strain field is non-uniform along the parallel fibres (J. D., U. and H.T. G, W., 2018).

• (a) They mostly boots resistance to deformation and improving load bearing characteristics

(b) However, in some structures due to different structural components, proteoglycans may not necessarily play a significant role (Lewis, Gray, Blount, MacConell, Wiater, Bilezilkjian, 2000)

• A single fibril has a homogenous structure than the whole tendon which is composed of heterogeneous structure hence less linear elasticity (Kasza, Nakamura, Hu, Kollmannsberger, Bonakdar, Fabry, Stossel, Wang and Weitz, 2009)

• (a) Exhibits similar behaviors with mechanical circumferential lamella bone having a slightly greater strength (Mujika, 2007).

(b) 0^o (at the highest strain obtainable)

(c) 90⁰ (lowest strain obtainable)

(d) Collagen

-Skin

1-Bone

3-Ligament

26) Extra Question (1)

ANSWERS:

• –Compression loading -Torsional loading -Tensile loading

– Shear loading

(b)

• They are often distributed circumferentially in the meniscus of the knee joint. The orientation ensures that the collagen fibers are able to resist various loading cycles both in radial and proximodistal orientations.

FEEDBACK

• Slightly challenging and thought-provoking

• Fair

• Long

• Number 7

• Number 24

• True

• Exam was great

Biblography

A, K. and A, L. (2016). Mechanical Behaviour of Skin: A Review. Journal of Material Science & Engineering, 5(4).

Bilandzic M, Stenvers KL. (2011). Betaglycan: a multifunctional accessory. Mol Cell Endocrinol

339:180–9.

Bilandzic M, Wang Y, Ahmed N, Luwor RB, Zhu HJ, Findlay JK, et al. (2014). Betaglycan blocks metastatic behaviors in human granulosa cell tumors by suppressing NFkappaB-mediated induction of MMP2. Cancer Lett 354:107–14.

Boivin WA, Shackleford M, Hoek AV, Zhao H, Hackett TL, Knight DA, et al.(2012). Granzyme B cleaves decorin, biglycan and soluble betaglycan, releasing active transforming growth factor-β1. PLoS One 7:e33163.

Fictiv.com. (2018). Engineering Fundamentals Refresh: Strength vs Stiffness vs Hardness |

Fictiv – Hardware Guide. [online] Available at: https://www.fictiv.com/hwg/design/engineering-fundamentals-refresh-strength-vs-stiffness-vs-hardness [Accessed 27 Nov. 2018].

Fish R. (2000). Sinovial joints, PhD Thesis. Department of Biological Sciences, University of Manchester, Kingston, Canada. Available at: http://www.teachingbiomed.man.ac.uk/student_ projects/2000/mmmr7rjf/articula.htm 5. Akeson WH, Woo SL-Y, Amiel D,

Hawkins D. (2001). Tissue mechanics. Human performance laboratory, University of California, Davis. Lecture available at: http://dahweb.engr.ucdavis.edu/dahweb/126site/126site.

1. D., U. and H.T. G, W. (2018). The effect of mechanical stress on soft and hard tissue repair; a review. [online] Available at: https://www.jprasurg.com/article/0007-1226(88)90049-5/pdf [Accessed 28 Nov. 2018].

Kasza, K., Nakamura, F., Hu, S., Kollmannsberger, P., Bonakdar, N., Fabry, B., Stossel, T., Wang, N. and Weitz, D. (2009). Filamin A Is Essential for Active Cell Stiffening but not Passive Stiffening under External Force. Biophysical Journal, 96(10), pp.4326-4335.

Kirkbride KC, Townsend TA, Bruinsma MW, Barnett JV, Blobe GC. (2008). Bone morphogenetic proteins signal through the transforming growth factor-β type III receptor. J Biol Chem 283:7628–37.

Lewis KA, Gray PC, Blount AL, MacConell LA, Wiater E, Bilezilkjian LM, et al. (2000). Betaglycan binds inhibin and can mediate functional antagonism of activin signalling. Nature 404:411–4.

Mujika, F. (2007). On the effect of shear and local deformation in three-point bending tests. Polymer Testing, 26(7), pp.869-877.

Schäfer, A. and Radmacher, M. (2005). Influence of myosin II activity on stiffness of fibroblast cells. Acta Biomaterialia, 1(3), pp.273-280.

Wang, N., Naruse, K., Stamenovic, D., Fredberg, J., Mijailovich, S., Tolic-Norrelykke, I., Polte, T., Mannix, R. and Ingber, D. (2001). Mechanical behavior in living cells consistent with the tensegrity model. Proceedings of the National Academy of Sciences, 98(14), pp.7765-7770.

Wang, N., Tolić-Nørrelykke, I., Chen, J., Mijailovich, S., Butler, J., Fredberg, J. and Stamenović, D. (2002). Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells. American Journal of Physiology-Cell Physiology, 282(3), pp.C606-C616.

Wang, Y., Liu, H., Gao, L. and Xu, B. (2011). Test the Mechanical Properties of Articular Cartilage using Digital Image Correlation Technology. [online] Available at: https://ac.els-cdn.com/S1878029611006670/1-s2.0-S1878029611006670-main.pdf?_tid=94844327-05fb-4e5b-a561-ca7e225e03b1&acdnat=1543405123_bc00f6c8aed6e8f148c71b30bf8ef3a3 [Accessed 28 Nov. 2018].

Yamamoto, N. and Nakamura, S. (2017). Relationships between the tensile strength and diameter of collagen fibrils isolated from mouse tail tendons. Journal of Biomechanical Science and Engineering, 12(3), pp.16-00511-16-00511.