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5. When a polymer is subjected to a constant stress it tends to creep due to its viscoelastic behaviour. Various mathematical models are available to predict this behaviour. One such model is the Kelvin Voight model which considers a polymer to behave as a Spring and dashpot in parallel E www which results in an ODE of the form 77 де σ = EE+nat Where σ is the applied stress, E is the modulus of the polymer, n is the viscosity of the polymer and t is the time. The analytical solution of this ODE is €(t) = (1-e Using the Euler method with an initial condition of zero strain at zero time, solve the ODE to predict the creep behaviour (strain vs time) of a polymer rod subjected to a constant stress of 10MPa and plot the solution vs the analytical solution to the equation for a period of time of 1 minute. Select a step size such that the average % error between the analytical and numerical solution is less than 5%. The parameters for the equations are as follows σ = 10MPa, E = 0.1MPa, n = 1Pa-s

5. When a polymer is subjected to a constant stress it tends to creep due to its viscoelastic behaviour. Various mathematical models are available to predict this behaviour. One such model is the Kelvin Voight model which considers a polymer to behave as a Spring and dashpot in parallel E www which results in an ODE of the form 77 де σ = EE+nat Where σ is the applied stress, E is the modulus of the polymer, n is the viscosity of the polymer and t is the time. The analytical solution of this ODE is €(t) = (1-e Using the Euler method with an initial condition of zero strain at zero time, solve the ODE to predict the creep behaviour (strain vs time) of a polymer rod subjected to a constant stress of 10MPa and plot the solution vs the analytical solution to the equation for a period of time of 1 minute. Select a step size such that the average % error between the analytical and numerical solution is less than 5%. The parameters for the equations are as follows σ = 10MPa, E = 0.1MPa, n = 1Pa-s

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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5. When a polymer is subjected to a constant stress it tends to creep due to its viscoelastic behaviour. Various mathematical models are available to predict this behaviour. One such model is the Kelvin Voight model which considers a polymer to behave as a Spring and dashpot in parallel E www which results in an ODE of the form 77 де σ = EE+nat Where σ is the applied stress, E is the modulus of the polymer, n is the viscosity of the polymer and t is the time. The analytical solution of this ODE is €(t) = (1-e Using the Euler method with an initial condition of zero strain at zero time, solve the ODE to predict the creep behaviour (strain vs time) of a polymer rod subjected to a constant stress of 10MPa and plot the solution vs the analytical solution to the equation for a period of time of 1 minute. Select a step size such that the average % error between the analytical and numerical solution is less than 5%. The parameters for the equations are as follows σ = 10MPa, E = 0.1MPa, n = 1Pa-s
Transcribed Image Text:5. When a polymer is subjected to a constant stress it tends to creep due to its viscoelastic behaviour. Various mathematical models are available to predict this behaviour. One such model is the Kelvin Voight model which considers a polymer to behave as a Spring and dashpot in parallel E www which results in an ODE of the form 77 де σ = EE+nat Where σ is the applied stress, E is the modulus of the polymer, n is the viscosity of the polymer and t is the time. The analytical solution of this ODE is €(t) = (1-e Using the Euler method with an initial condition of zero strain at zero time, solve the ODE to predict the creep behaviour (strain vs time) of a polymer rod subjected to a constant stress of 10MPa and plot the solution vs the analytical solution to the equation for a period of time of 1 minute. Select a step size such that the average % error between the analytical and numerical solution is less than 5%. The parameters for the equations are as follows σ = 10MPa, E = 0.1MPa, n = 1Pa-s
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