The development and validation of a numerical integration method for non-linear viscoelastic modeling

PloS One
Nicole L RamoKevin L Troyer

Abstract

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue's mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients ...Continue Reading

References

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Citations

Mar 6, 2019·Journal of Biomechanical Engineering·Nicole L RamoChristian Puttlitz
Dec 22, 2019·Bioengineering·Wenqiang Liu, Zhijie Wang
Aug 6, 2021·Journal of Biomechanical Engineering·Wenqiang LiuZhijie Wang
Dec 14, 2021·PloS One·Victoria SpartacusCarolyn J Sparrey

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