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Viscoelastic material inversion using Sierra-SD and ROL

Walsh, Timothy; Aquino, Wilkins; Ridzal, Denis; Kouri, Drew P.; Van Bloemen Waanders, Bart; Urbina, Angel U.

In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.

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TYPE SAND Report YEAR 2014
DOIOSTI

Optimality conditions for the numerical solution of optimization problems with PDE constraints: Theoretical framework and applications to parameter identification and optimal control problems

Valentin, Miguel A.; Ridzal, Denis

A theoretical framework for the numerical solution of partial differential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to efficiently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identification and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

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TYPE SAND Report YEAR 2014
DOIOSTI

Edge Remap for Solids

Love, Edward; Robinson, Allen C.; Ridzal, Denis

We review the edge element formulation for describing the kinematics of hyperelastic solids. This approach is used to frame the problem of remapping the inverse deformation gradient for Arbitrary Lagrangian-Eulerian (ALE) simulations of solid dynamics. For hyperelastic materials, the stress state is completely determined by the deformation gradient, so remapping this quantity effectively updates the stress state of the material. A method, inspired by the constrained transport remap in electromagnetics, is reviewed, according to which the zero-curl constraint on the inverse deformation gradient is implicitly satisfied. Open issues related to the accuracy of this approach are identified. An optimization-based approach is implemented to enforce positivity of the determinant of the deformation gradient. The efficacy of this approach is illustrated with numerical examples.

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TYPE SAND Report YEAR 2013
DOIOSTI

Designing Experiments Through Compressed Sensing

Young, Joseph G.; Ridzal, Denis

In the following paper, we discuss how to design an ensemble of experiments through the use of compressed sensing. Specifically, we show how to conduct a small number of physical experiments and then use compressed sensing to reconstruct a larger set of data. In order to accomplish this, we organize our results into four sections. We begin by extending the theory of compressed sensing to a finite product of Hilbert spaces. Then, we show how these results apply to experiment design. Next, we develop an efficient reconstruction algorithm that allows us to reconstruct experimental data projected onto a finite element basis. Finally, we verify our approach with two computational experiments.

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TYPE SAND Report YEAR 2013
DOIOSTI
Results 76–100 of 140
Results 76–100 of 140