You have been given two samples of a biological scaffold that have been treated with two...

 

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You have been given two samples of a biological scaffold that have been treated with two different methods to increase hyaluronan (HA) content. From preliminary testing, you know that treatment had no effect on collagen or elastin content and that Young's modulus E = E1 = E2 = 150 MPa. You are asked to determine which sample has more HA. Instead of running an HA assay, you decided to perform a creep test and model the HA-augmented scaffold using the Kelvin-Voight model. The governing equation for the Kelvin-Voight model is (as given in class): de Equation 11 where o is stress, E is Young's modulus of the elastic spring component, & is strain, n is the viscosity coefficient of the dashpot, and is strain rate. By applying the initial conditions that o = 0, E = 0 at t=0 0 = 0o =3 MPa att > 0 the equation above can be solved to get: σ = EE + n= dt 8(t) = (1 - exp(-t)) Equation 2 This equation relates strain & to time t, using initial stress go, Young's modulus E, and the viscosity coefficient n. Solve the ODE (Equation 1) by applying the initial condition that o = 0, E = 0 at t = 0 000 = 3 MPa at t > 0 to get Equation 2 e(t) = (1 - exp(-t)) Show your derivation to get extra credit (all or nothing). (10 points) You have been given two samples of a biological scaffold that have been treated with two different methods to increase hyaluronan (HA) content. From preliminary testing, you know that treatment had no effect on collagen or elastin content and that Young's modulus E = E1 = E2 = 150 MPa. You are asked to determine which sample has more HA. Instead of running an HA assay, you decided to perform a creep test and model the HA-augmented scaffold using the Kelvin-Voight model. The governing equation for the Kelvin-Voight model is (as given in class): de Equation 11 where o is stress, E is Young's modulus of the elastic spring component, & is strain, n is the viscosity coefficient of the dashpot, and is strain rate. By applying the initial conditions that o = 0, E = 0 at t=0 0 = 0o =3 MPa att > 0 the equation above can be solved to get: σ = EE + n= dt 8(t) = (1 - exp(-t)) Equation 2 This equation relates strain & to time t, using initial stress go, Young's modulus E, and the viscosity coefficient n. Solve the ODE (Equation 1) by applying the initial condition that o = 0, E = 0 at t = 0 000 = 3 MPa at t > 0 to get Equation 2 e(t) = (1 - exp(-t)) Show your derivation to get extra credit (all or nothing). (10 points)

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To solve the differential equation Equation 1 and obtain Equation 2 ... View the full answer