Polymers and composites
Which statement about mechanical models of viscoelasticity is correct?
- AThe Maxwell model, a spring and dashpot in series, can represent stress relaxation under constant strain
- BThe Voigt model, a spring and dashpot in parallel, can describe stress relaxation under constant strain
- CThe Maxwell model can represent creep in which strain approaches a constant value under constant stress
Show answer and explanation
Answer: A. The Maxwell model, a spring and dashpot in series, can represent stress relaxation under constant strain
When a constant strain is applied to the Maxwell model (series), the spring stretches first and stress develops; then the dashpot slowly extends while the spring contracts, so the stress relaxes as σ = σ₀exp(−t/τ) (τ = η/E). In the Voigt (Kelvin–Voigt) model (parallel), the spring and dashpot always have the same strain, so the stress does not relax under constant strain. What the Voigt model represents is delayed elasticity (creep), in which strain approaches a constant value over time under constant stress. Under constant stress, the strain of the Maxwell model does not approach a constant value but keeps increasing in proportion to time. Real polymers are approximated by combinations such as the four-element model.