DDP STAGE-I Presentation

7/29/2019 DDP STAGE-I Presentation

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Mechanics of FilamentNetwork

Tarun Meena(08D10048)


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Introduction Deformation of the cells are dictated by their

mechanical behavior under loading

Critical component which is governing the mechanicalbehavior is actin cytoskeleton

In this thesis filament network has been idealized as2-D network in Abaqus

Behavior of the Network is analyzed due to finitedisplacement in vertical direction

Effect of the variation in basic parameters like densityand length of the fiber has been discussed


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The F-Actin Network The cytoskeleton is a cellular scaffolding or skeleton for

cells.

The cytoskeleton is an organized network of three primary

protein filaments Microtube

Actin Filaments

Intermediate fibers


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Continued F-actin filament plays an important role in the

mechanical behavior of the network

Some Functions of the F-actin are as follows Provides mechanical strength to the cell Generate locomotion in cells

Links transmemberane proteins to cytoplasmic


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Cross linked F-actin Network In the cytoskeleton, the local microstructure and

connectivity of F-actin is controlled by actin bindingproteins.

The binding proteins control the organization of F-actin into mesh like gels, branched network etc.

Cross-links have a compliance that depends on their

detailed molecular structure and determines networkmechanical response.


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Existing ModelsDeformation of Cross-Linked Semiflexible Networks(F.C.Mackintosh,2003)

It is a simple model of cross-linked rods

It is assumed that the deformation field is affine(Strain isuniform)

Through the analysis it is found that network becomeincreasingly affine down to the smallest scale of thenetwork e.g. mesh size, cross link density etc.


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Continued Model was studied for dependence of the bulk shear

modulus on the Cross link density

Bending and Extension of the individual filament

Elasticity of Stiff polymer network

Model is about the elasticity of two-dimensional networkof rigid rods

Essential features of this model are Anisotropic elasticity of the rods

Random geometry of the network


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Continued Typical networks at high density and low density

The random network was generated by placing N line

like objects of equal length l and area L2

It was observed that shear modulus scales vary linearly

with filament compressional modulus and no. offilaments per unit area.


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ContinuedElasticity of Planar Network

In this model wool assembly was treated as a layered

system with fiber bending deflection In the model, only fiber axial deformation was

considered


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Continued It was observed in the model that effective stiffness of

planar random Filament Network increase with theincrease of arial density, which can be measured by thenumber of fibers per unit area

The model account for microscopic deformation offiber segments of all possible lengths and orientations

The constitutive relation is derived is as follows

Where,


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Modeling and analysisFinite Element Analysis

Powerful computational technique for approximate

solution to a variety of engineering problems This method is used to solve a modelling problem by

dividing the solution domain into discrete regions,these are the finite elements

Finite element modelling provides a simply costeffective way of monitoring and predicting situationsthat occurs in any sphere of engineering, medicine,aeronautics etc.


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ABAQUS Finite Modelling and analysis FEM packages such as ABAQUS is a very useful

program as it allows for the material, geometric, andboundary conditions to be set and adjusted asinformation becomes apparent

The result of model such as stress vs strain curves,

pressure displacement diagram has a short run overtime in ABAQUS


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Assumptions made in model In order to simplify and practically model the system

some assumption are taken, are as follows The fibers are straight and oriented in the same plane

The fibers are randomly distributed and of same lengths

Total Elasticity of the network is dependent on the elasticityof filaments

Effect of medium, in which fiber networks, is being assumed

negligible The fiber elasticity used is 2x10^11 N/mm^2 and possions ratio

to be 0.3 ,which are arbitrary properties of the fiber


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Random Network FormulationA 2-D Fiber network defined as a set of independently

short line segments are placed.

Fibers of same length and orientation has been place Network has been idealised as mixture of 2-D beam

element of diameter 1mm.

Any two intersection beams are joined at their

intersections. In the Network at y=0 hinge and roller boundary

conditions have been applied and at y=20mmdisplacement has been applied.


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Continued For different value of displacements the corresponding

reaction force has been calculated

Model of the Network with vertical displacement andsupport condition


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Continued The model is analyzed using static linear analysis

procedure

The reaction is obtained on the upper surface of thenetwork are summed up to the total reaction force, RF2in y-direction

Elastic modulus of elasticity can be calculated as

followsEc = (RF2/A)/(disp/L)


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Results and DiscussionComparison of Beam element B21 and B23 B23 is an Euler-Bernoulli beam, a 2 node cubic beam in

plane

It does not allow transverse shear deformation i.e. planesections initially normal remain plane While B21 beam is a Timoshenko beam and they allow

transverse shear deformation, a 2 node linear beam inplane

The model is analyzed for both the beam elements forcomparison purpose The comparative plot of Force-Displacement for both of

the beam elements is as follows


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Continued


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Continued From the plot it can be seen that results are almost

same i.e.

But as in the model we are considering fiber which isslender, i.e. the beams cross-sectional dimensionsshould be small compared to typical distances alongits axis, that comply with the B23 beam element

Therefore, it would be more suitable to use B23 beamelement than B21 in modelling


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Effect of variation in density on the

elasticity of the network To study the effect of variation in density, we created

two models of different density of fibers under sameloading condition

We keep length of the fiber and orientation same

Low density Network and its deformed shape


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Continued Relatively High Density network and its deformed

shape

The Stress-Strain curve for both of the network is asfollows


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Continued


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Continued Elasticity for Low Density network=6.81E+10 N/mm2

Elasticity for High Density Network=1.20E+11 N/mm2

It can be clearly seen that the Elasticity of the networkincreases with increase in the density of the Network

which comply the power law E= C(-ref) (R.Y. Kwon, 2008)where is the volume(density), validating the aboveresult.


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Effect of variation in Fiber length

on Elasticity of the network To study the effect of variation in length two different

models of different fiber length of 10mm and15mm,keeping the orientation same has been created

In the model orientation of fibers and loadingcondition has been kept same

Network and its deformed shape for fiber length of10mm


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ContinuedNetwork and its deformed shape for fiber length of15mm

The plot for displacement Vs Force is as follow for both ofthe Model


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Continued


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Continue Elasticity in the case of fiber of 10mm length is found

to be 6.81E+10 N/mm2

and in the case of network of fibers of 15 mm length isfound to be 1E+11 N/mm2

The result suggests that Length of the fiber plays asignificant role in the morphology of the network

structure or the linear elasticity.


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References (n.d.). Retrieved from Wikipedia: http://en.wikipedia.org/wiki/Cytoskeleton

ABAQUS CAE documentation. (n.d.). Retrieved fromhttp://abaqus.civil.uwa.edu.au:2080/v6.9/

Abed, G. (2010). COMPUTATIONAL MECHANICS TOWARDS IMPROVED

UNDERSTANDING OF THE BIOMECHANICS OF MYOCARDIALINFARCTION.

David A. Head, A. J. (2003). Deformation of Cross-Linked SemiflexiblePolymer Networks. PHYSICAL REVIEW LETTERS, 91 (10), 108102.

F. C. MacKintosh, J. K. (1995). Elasticity of Semiflexible Biopolymer

Networks. P. A. Janmey, 75 (24). Frey, J. W. (2008). Elasticity of Stiff Polymer Networks.

G. A. Buxton, N. C. (2009). Actin dynamics and the elasticity of cytoskeletalnetworks. eXPRESS Polymer Letters Vol.3, No.9 , 579-587.

Gardel, M. L. (2004). Elasticity of F-actin Networks.


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Jeffrey S. Palmer, M. C. (2008). Constitutive modeling of the stressstrainbehavior of F-actin filament networks.Actabiomaterialia, 4, 597612.

Jonathan Stricker, T. F. (2010). Mechanics of the F-actin cytoskeleton.Journal of Biomechanics, 43, 914.

Madenci, E. (2005). The Finite Element Method and Applications in EngineeringUsing ANSYS(1st ed.). Springer.

Margaret L. Gardel, *. K. (2008). Mechanical Response of Cytoskeletal Networks.In M. L. Gardel,METHODS IN CELL BIOLOGY(Vol. 89, pp. 487-519).

R.Y. Kwon, A. L. (2008). A microstructurally informed model for the mechanicalresponse of three-dimensional actin networks. Computer Methods inBiomechanics and Biomedical Engineering, 11 (4), 407418.

Risler, T. (2011). Cytoskeleton and Cell Motility.

X.-F. Wu, Y. A. (2005). Elasticity of planar fiber networks.JOURNAL OF APPLIEDPHYSICS, 98, 093501.


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Thank You

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