In this paper, we investigate hyperelastic and viscoelastic model parameters using Global Sensitivity Analysis(GSA). These models are used to characterize the physical response of many soft-elastomers, which are used in a wide variety of smart material applications. Recent research has shown the effectiveness of using fractional-order calculus operators in modeling the viscoelastic response. The GSA is performed using parameter subset selection (PSS), which quantifies the relative parameter contributions to the linear and nonlinear, fractional-order viscoelastic models. Calibration has been performed to quantify the model parameter uncertainty; however, this analysis has led to questions regarding parameter sensitivity and whether or not the parameters can be uniquely identified given the available data. By performing GSA we can determine which parameters are most influential in the model, and fix non-influential parameters at a nominal value. The model calibration can then be performed to quantify the uncertainty of the influential parameters.
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Gaussian Process to Identify Hydrogel Constitutive Model
Unlike traditional structural materials, soft solids can often sustain very large deformation before failure, and many exhibit nonlinear viscoelastic behavior. Modeling nonlinear viscoelasticity is a challenging problem for a number of reasons. In particular, a large number of material parameters are needed to capture material response and validation of models can be hindered by limited amounts of experimental data available. We have developed a Gaussian Process (GP) approach to determine the material parameters of a constitutive model describing the mechanical behavior of a soft, viscoelastic PVA hydrogel. A large number of stress histories generated by the constitutive model constitute the training sets. The low-rank representations of stress histories by Singular Value Decomposition (SVD) are taken to be random variables which can be modeled via Gaussian Processes with respect to the material parameters of the constitutive model. We obtain optimal material parameters by minimizing an objective function over the input set. We find that there are many good sets of parameters. Further the process reveals relationships between the model parameters. Results so far show that GP has great potential in fitting constitutive models.
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- Award ID(s):
- 1903308
- NSF-PAR ID:
- 10329053
- Date Published:
- Journal Name:
- Challenges in Mechanics of Time Dependent Materials, Mechanics of Biological Systems and Materials & Micro-and Nanomechanics, Volume 2.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Dielectric elastomers are employed for a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many cases a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. Accurate estimation of the elastomer’s viscoelastic behavior to quantify parameter uncertainty motivates the use of Markov Chain Monte Carlo (MCMC) methods. Since MCMC is a sampling based method, requiring many model evaluations, efficient estimation of the fractional derivative operator is crucial. In this paper, we demonstrate the effectiveness of using quadrature techniques to approximate the Riemann–Liouville definition for fractional derivatives in the context of estimating the uncertainty of a nonlinear viscoelastic model. We also demonstrate the use of parameter subset selection techniques to isolate parameters that are identifiable in the sense that they are uniquely determined by measured data. For those identifiable parameters, we employ Bayesian inference to compute posterior distributions for parameters. Finally, we propagate parameter uncertainties through the models to compute prediction intervals for quantities of interest.
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Abstract Developing constitutive models that can describe a complex fluid’s response to an applied stimulus has been one of the critical pursuits of rheologists. The complexity of the models typically goes hand-in-hand with that of the observed behaviors and can quickly become prohibitive depending on the choice of materials and/or flow protocols. Therefore, reducing the number of fitting parameters by seeking compact representations of those constitutive models can obviate extra experimentation to confine the parameter space. To this end, fractional derivatives in which the differential response of matter accepts non-integer orders have shown promise. Here, we develop neural networks that are informed by a series of different fractional constitutive models. These fractional rheology-informed neural networks (RhINNs) are then used to recover the relevant parameters (fractional derivative orders) of three fractional viscoelastic constitutive models, i.e., fractional Maxwell, Kelvin-Voigt, and Zener models. We find that for all three studied models, RhINNs recover the observed behavior accurately, although in some cases, the fractional derivative order is recovered with significant deviations from what is known as ground truth. This suggests that extra fractional elements are redundant when the material response is relatively simple. Therefore, choosing a fractional constitutive model for a given material response is contingent upon the response complexity, as fractional elements embody a wide range of transient material behaviors.
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A finite strain nonlinear viscoelastic constitutive model is used to study the uniaxial tension behaviour of chemical polyampholyte (PA) gel. This PA gel is cross-linked by chemical and physical bonds. Our constitutive model attempts to capture the time and strain dependent breaking and healing kinetics of physical bonds. We compare model prediction by uniaxial tension, cyclic and relaxation tests. Material parameters in our model are obtained by least squares optimization. These parameters gave fits that are in good agreement with the experiments.more » « less
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Polymer networks consisting of a mixture of chemical and physical cross-links are known to exhibit complex time-dependent behaviour due to the kinetics of bond association and dissociation. In this article, we highlight and compare two recent physically based constitutive models that describe the nonlinear viscoelastic behaviour of such transient networks. These two models are developed independently by two groups of researchers using different mathematical formulations. Here, we show that this difference can be attributed to different viewpoints: Lagrangian versus Eulerian. We establish the equivalence of the two models under the special situation where chains obey Gaussian statistics and steady-state bond dynamics. We provide experimental data demonstrating that both models can accurately predict the time-dependent uniaxial behaviour of a poly(vinylalcohol) dual cross-link hydrogel. We review the advantages and disadvantages of both approaches in applications and close by discussing a list of open challenges and questions regarding the mathematical modelling of soft, viscoelastic networks.more » « less
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Accepted Manuscript1.0
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