Kelvin Model-Viscoelastic Behaviour Of Muscles

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M.Sc. Bioengineering 2011-2012 Musculosketetal biomechanics assignment ALTOKA ERATO (PAC:11266318) Option V (Kelvin model) The aim of this assignment is to describe the general viscoelastic behaviour of muscles (soft tissues) when they subsist mechanical compression. To achieve that we will use the Kelvin model (standard linear solid model).This model simulates the two different reactions of the muscle,viscous and elastic,respectively by dashpots and springs . To be more precise,it consists of two systems in parallel:a) a spring and b)another spring with a dashpot in series.  The spring represents the elastic components of the muscle and obeys Hook’s law : F=k*x but in terms of stress the equation turns into : σ=Ε*ε where σ: applied stress, E:Young's Modulus of the material ε: strain.  The dashpot represents the viscous components of the muscle and is expressed in differential form by Newton’s law for straight,parallel and uniform flow: σ=η* where η: viscosity and :change of rate of strain (velocity). The important equations that are used in this model are:  F=F1+F0 where F0=k0*u and F1=η1*u1=k1*u1’  u=u1+u1’ After long calculations we finally take the differential equation of motion for a standard linear solid: The equation contains F, df/dt ,u ,du/dt functions as well as k0,k1,η constants and is impossible to solve as they are all unknown. For that reason we will use the experimental data from Bobsbooms given paper that will help understand how our functions are supposed to behave during the experiment and thus be able to extract some data and some important initial and boundary conditions, necessary for our model to work. From the Bobsbooms paper ‘Passive transverse mechanical properties of skeletal muscle in compression’ we are supposed to take the ramp and hold data (u versus t graph) and fit it in our model,expecting that our F versus t
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