A transient finite element analysis of linear viscoelastic material model. (English) Zbl 0774.73074
Most of the existing models of material behavior are not suitable to describe the wave propagation in soil/rock materials. The real damping in the soil is related to the local material properties and is also strain dependent. The Rayleigh-type damping, Kelvin-Voigt material, hysteretic damping, special rheological materials are still not realistic or may cause computational difficulties.
In the paper the convolutional form of the stress-strain relationship was reduced to a set of differential operators using the Padé approximation method. It was generalized to non-scalar waves and implemented for transient finite element analysis. The resultant differential operators were incorporated into the governing motion equation. The Newmark method was applied as a time marching scheme. One- and two-dimensional wave propagation problem was solved, and the results were compared with the theory.
In the paper practicians can find numerous plots which exhibit various properties of the approach: phase velocity, group velocity, internal friction, attenuation factor, attenuation error, stress, versus some parameters. Good accuracy is a significant feature of the method applied. Comparison to some other approaches could be interesting. However, it has not been carried on.
In the paper the convolutional form of the stress-strain relationship was reduced to a set of differential operators using the Padé approximation method. It was generalized to non-scalar waves and implemented for transient finite element analysis. The resultant differential operators were incorporated into the governing motion equation. The Newmark method was applied as a time marching scheme. One- and two-dimensional wave propagation problem was solved, and the results were compared with the theory.
In the paper practicians can find numerous plots which exhibit various properties of the approach: phase velocity, group velocity, internal friction, attenuation factor, attenuation error, stress, versus some parameters. Good accuracy is a significant feature of the method applied. Comparison to some other approaches could be interesting. However, it has not been carried on.
Reviewer: Cz.I.Bajer (Warszawa)
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74L10 | Soil and rock mechanics |
| 74J10 | Bulk waves in solid mechanics |
| 74Hxx | Dynamical problems in solid mechanics |
Keywords:
damping; stress-strain relationship; Padé approximation; differential operators; Newmark method; time marching scheme; phase velocity; group velocity; attenuationReferences:
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