## Material Properties

#### Why doesn’t my Harmonic analysis with a visco-elastic material show any phase lag with a pre-stressed static structural analysis?

• FAQ
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This behavior is a limitation with the linear perturbation method. Viscoelasticity can be modeled either in the time or frequency domain. In the time domain, we have a (real) stiffness that changes as a function of applied stress and time. In the frequency domain (harmonic), we have complex stiffness (storage and loss moduli) that is a function of frequency. Now, when we use linear perturbation, we start off in the time domain (static is a special case where time doesnâ€™t change). We construct a tangent stiffness matrix based on the deformed shape and stress from the â€˜base stateâ€™, but this constructed tangent stiffness matrix is a real matrix. There is no provision to develop a complex stiffness (i.e., imaginary stiffness matrix) from time-domain results. If you have no linear perturbation (regular harmonic), we construct complex stiffness from viscoelastic data (based on undeformed shape). However, once you use linear perturbation, you are limited to using a real stiffness matrix only. That is why you lose the phase lag â€“ namely, you no longer have the imaginary stiffness term present. A way around this is to use damping instead of harmonic viscoelasticity. This can be achieved with TB,ELASTIC and TB,SDAMP. The drawbacks are that (a) you donâ€™t get viscoelastic behavior in your base static/transient analysis and (b) since we use damping [C] instead of imaginary stiffness [Kâ€™], stress and strain will be in-phase. However, by substituting the imaginary [Kâ€™] with [C], you get the phase lag based on input excitation compared with output response.