When rheological models of polymer blends are used for inverse modeling, they can characterize polymer mixtures from rheological observations. This requires repeated evaluation of potentially expensive rheological models. We explored surrogate models based on Gaussian processes (GPSM) as a cheaper alternative for describing the rheology of polydisperse binary blends. We used the timedependent diffusion double reptation (TDDDR) model as the true model; it takes a 5dimensional input vector specifying the binary blend as input and yields a function called the relaxation spectrum as output. We used the TDDDR model to generate training data of different sizes [Formula: see text], via Latin hypercube sampling. The optimal values of the GPSM hyperparameters, assuming a separable covariance kernel, were obtained by maximum likelihood estimation. The GPSM interpolates the training data by design and offers reasonable predictions of relaxation spectra with uncertainty estimates. In general, the accuracy of GPSMs improves as the size of the training data [Formula: see text] increases, as does the cost for training and prediction. The optimal hyperparameters were found to be relatively insensitive to [Formula: see text]. Finally, we considered the inverse problem of inferring the structure of the polymer blend from a synthetic dataset generated using the truemore »
Identification of the 3D crystallographic orientation using 2D deformations
Polycrystalline materials consist of grains (crystals) oriented at different angles resulting in a heterogeneous and anisotropic mechanical behavior at that microlength scale. In this study, a novel method is proposed for the first time to determine the [Formula: see text] crystal orientations of grains in a [Formula: see text] domain, using solely [Formula: see text] deformation fields. The grain boundaries are assumed to be unknown and delineated from the reconstructed changes in the crystallographic orientation. Further, the constitutive equations that describe the mechanical behavior of the domain in [Formula: see text] under plane stress conditions are derived, assuming that the material is transversely isotropic in 3D. Finite element based algorithms are utilized to discretize the inverse problem. The inhouse written inverse problem solver is coupled with Matlabbased optimization scripts to solve for the mechanical property distributions. The performance of this method is tested at different noise levels with synthetic displacements that were used as measured data. The reconstructions deteriorate as the noise level is increased. This work presents a first milestone in the verification of this novel technology with synthetic data.
 Award ID(s):
 1663435
 Publication Date:
 NSFPAR ID:
 10327675
 Journal Name:
 The Journal of Strain Analysis for Engineering Design
 Page Range or eLocationID:
 030932472110431
 ISSN:
 03093247
 Sponsoring Org:
 National Science Foundation
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