Relaxation of a Maxwell Element

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This Demonstration aids in visualization of the roles of the two components of a Maxwell element in its response to a unit step stress. It depicts the relaxation curve resulting from changes in the relative magnitudes of the elastic component's modulus (represented by a spring) and the dissipating component's viscosity (represented by a dashpot). It also displays the element's relaxation time and the ratio between and the characteristic observation time (represented by the plot's time scale) referred to here as the Deborah number .

Contributed by: Mark D. Normand and Micha Peleg (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: a relaxation curve with a short relaxation time and small Deborah number

Snapshot 2: a relaxation curve with a longer relaxation time and larger Deborah number

Snapshot 3: a relaxation curve with a still longer relaxation time and even larger Deborah number

Snapshot 4: apparent elastic response of an element with a very long relaxation time

Snapshot 5: apparent viscous response of an element with a very short relaxation time

This Demonstration calculates and plots the stress relaxation curve of a Maxwell element subjected to a unit step stress described by the equation where is the dissipating stress at time , is the elastic component's modulus and the viscosity. The element's relaxation time, , is the ratio , here with arbitrary time units. The Deborah number, , is represented here by the ratio , where is the maximum value of the plot's time axis. The values of the parameters , , and are entered with sliders. An ideogram of the Maxwell element (a spring-dashpot in series combination) is displayed above the plot. Also shown are the stress relaxation equation and the current calculated numeric values of and .

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