Maxwell Material

A Maxwell material is a viscoelastic material having the properties both of elasticity and viscosity. It is named for James Clerk Maxwell who proposed the model in 1867. In a Maxwell material, stress σ, strain ε and their rates of change with respect to time t are governed by equations of the form:
\frac {1} {E} \frac {d\sigma} {dt} + \frac {\sigma} {c} = \frac {d\epsilon} {dt}
or, more elegantly:
\frac {\sigma} {c} + \frac {\dot {\sigma}} {E}= \dot {\epsilon}
where E is a modulus of elasticity and c a "viscosity". The equation can be applied either to the shear stress or to the uniform tension in a material. In the former case, the viscosity corresponds to that for a Newtonian fluid. In the latter case, it has a slightly different meaning relating stress and rate of strain.

 

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