Snapshot 1: creep curve under unit stress with

and

Snapshot 2: stress relaxation curve at unit strain with

and

Snapshot 3: stress relaxation curve at unit strain with

and

A four-element mechanical analog is one of eight different ("nondegenerate") arrangements of two springs and two dashpots. It behaves like a viscoelastic solid if the arrangement cannot be separated because of one or two springs in series, and like a viscoelastic liquid if the arrangement can be separated into two parts by the disengagement of one or two dashpots. For convenience, the solid model is presented as two Kelvin–Voigt elements in series for creep, and as a Kelvin–Voigt and a Maxwell element in parallel for stress relaxation. The liquid model is presented as a Kelvin–Voigt and a Maxwell element in series for creep, and as two Maxwell elements in parallel for relaxation. The corresponding creep curve equations are:

for the solid and

for the liquid model, and for the stress relaxation,

for the solid and

for the liquid models, respectively, where

is the strain,

is the stress,

and

are the spring constants in arbitrary stress units, and

and

are the dashpots' viscosities in units of arbitrary stress × time [1, 2].

In this Demonstration, you can choose the plot type, creep, or stress relaxation by clicking the corresponding setter bar, and you can select the magnitudes of

,

,

, and

with sliders. The program calculates and plots the corresponding curves for the viscoelastic solid and liquid. You can also vary the time and maxima of the plots for the strain and stress axes for improved resolution.

[1] D. R. Bland,

*The Theory of Linear Viscoelasticity*, New York: Pergamon Press, 1960.

[2] W. N. Findley, J. S. Lai, and K. Onaran,

*Creep and Relaxation of Nonlinear Viscoelastic Materials*, New York: North-Holland Publishing Company, 1976.