Viscoelastic Material

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Constitutive Law

This MPM material is a small-strain, linear viscoelastic material with time-dependent shear modulus, G(t), and a time-independent bulk modulus, K. The time-dependen shear modulus is give by a sum of n exponentials:

      [math]\displaystyle{ G(t) = G_0 + \sum_{i=1}^n G_i e^{-t/\tau_i} }[/math]

Here G0 is the long-time shear modulus and the short-time shear modulus is the sum:

      [math]\displaystyle{ G(0) = \sum_{i=0}^n G_i }[/math]

Material Properties

Property Description Units Default
K Time-independent bulk modulus MPa none
ntaus The number of relaxation times. This property is only need in XML files and must come before any Gk or tauk properties. In scripted files, the number is automatically determined from the number of relaxation times you provide. MPa none
G0 The long term (or fully-relaxed) shear modulus MPa 0
Gk The shear modulus for the next relaxation time. Enter multiple Gk properties to have multiple relaxation times. MPa none
tauk The the next relaxation time. Enter multiple tauk properties to have multiple relaxation times. sec none
alpha Time-independent bulk modulus ppm/K 40
(other) Properties common to all materials varies varies

The total number of Gk and tauk properies must be equal. In XML files, that total number must match the supplied ntaus property.

History Variables

None

Examples