Three-Element Viscoelastic Models

three-element

k

1

1.5

solid

k

2

1.5

η

0.5

three-element

η

1

1.

liquid

η

2

2.5

k

1.5

y axes maxima

creep

2.

relaxation

3.

deformation

1.

This Demonstration plots ideal creep, stress-relaxation, and stress-strain curves of a viscoelastic solid or liquid represented by a three-element mechanical analog. The solid model comes in the form of either a spring and Maxwell element in parallel or a spring and a Kelvin–Voigt element in series, and the liquid is in the form of a dashpot and a Maxwell element in parallel or a dashpot and a Kelvin–Voigt element in series. The creep curve is generated for a unit-step stress, the relaxation curve for a unit-step strain, and the stress-strain curves for three constant strain rates (.5, 1.0, and 5.0 arbitrary time unit reciprocal). The Demonstration shows that the curves produced by each model's two versions, with the same spring constants and dashpots' viscosities, are quantitatively different, although they are qualitatively similar.