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A plastic which behaves in accordance with a Kelvin-Voigt model is subjected to the stress history plot as shown in Figure 1, with σ1 = 20 MPa and t₁ = 200 s. Assuming that the Boltzmann Superposition Principle applies, calculate the strain in the material: (i) after 150 seconds (ii) after 250 seconds Data: spring constant (ε) = 20 GPa viscosity of the dashpot (n) = 1000 GPa.s. The Kelvin model: ɛ(t) = ½- (1 − e¯/), - where the symbols have their usual meanings. Stress, σ, (MPa) 25 0120 15 10 10 5 0 0 100 200 300 Time (s) Figure 1: Stress history plot

A plastic which behaves in accordance with a Kelvin-Voigt model is subjected to the stress history plot as shown in Figure 1, with σ1 = 20 MPa and t₁ = 200 s. Assuming that the Boltzmann Superposition Principle applies, calculate the strain in the material: (i) after 150 seconds (ii) after 250 seconds Data: spring constant (ε) = 20 GPa viscosity of the dashpot (n) = 1000 GPa.s. The Kelvin model: ɛ(t) = ½- (1 − e¯/), - where the symbols have their usual meanings. Stress, σ, (MPa) 25 0120 15 10 10 5 0 0 100 200 300 Time (s) Figure 1: Stress history plot

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A plastic which behaves in accordance with a Kelvin-Voigt model is subjected to the stress history plot as shown in Figure 1, with σ1 = 20 MPa and t₁ = 200 s. Assuming that the Boltzmann Superposition Principle applies, calculate the strain in the material: (i) after 150 seconds (ii) after 250 seconds Data: spring constant (ε) = 20 GPa viscosity of the dashpot (n) = 1000 GPa.s. The Kelvin model: ɛ(t) = ½- (1 − e¯/), - where the symbols have their usual meanings. Stress, σ, (MPa) 25 0120 15 10 10 5 0 0 100 200 300 Time (s) Figure 1: Stress history plot
Transcribed Image Text:A plastic which behaves in accordance with a Kelvin-Voigt model is subjected to the stress history plot as shown in Figure 1, with σ1 = 20 MPa and t₁ = 200 s. Assuming that the Boltzmann Superposition Principle applies, calculate the strain in the material: (i) after 150 seconds (ii) after 250 seconds Data: spring constant (ε) = 20 GPa viscosity of the dashpot (n) = 1000 GPa.s. The Kelvin model: ɛ(t) = ½- (1 − e¯/), - where the symbols have their usual meanings. Stress, σ, (MPa) 25 0120 15 10 10 5 0 0 100 200 300 Time (s) Figure 1: Stress history plot
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