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The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Barnett, Joshua L.; Kalashnikova, Irina; Mota, Alejandro M.

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

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Demonstration of the ACE (Arctic Coastal Erosion) model at Drew Point, AK during a permafrost bluff block collapse event in summer 2018

Frederick, Jennifer M.; Eymold, William K.; Mota, Alejandro M.; Kalashnikova, Irina; Jones, Benjamin M.; Flanary, Chris F.; Jones, Craig J.; Thomas, Matthew A.; Bristol, Emily M.; Choens, Robert C.; Jones Ward, Melissa K.; Kasper, Jeremy L.; Brown, Eloise J.; McClelland, James W.; Bull, Diana L.

Abstract not provided.

An Adaptive Framework for Extreme Deformation and Failure in Solids

Mota, Alejandro M.; Plews, Julia A.; Talamini, Brandon T.; Avery, Rock A.

Recent developments at Sandia in meshfree methods have delivered improved robustness in solid mechanics problems that prove difficult for traditional Lagrangian, mesh-based finite elements. Nevertheless, there remains a limitation in accurately predicting very large material deformations. It seems robust meshfree discretizations and integration schemes are necessary, but not sufficient, to close this capability gap. This state of affairs directly impacts current and future LEPs, whose simulation needs are not well met for extremely large deformation problems. We propose to use a new numerical framework, the Optimal Transportation Meshfree (OTM) method enhanced by meshfree adaptivity, as we believe that a combination of both will provide a novel way to close this capability gap.

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An error estimation driven adaptive tetrahedral workflow for full engineering models

Foulk, James W.; Granzow, Brian N.; Mota, Alejandro M.; Ibanez-Granados, Daniel A.

Tetrahedral finite element workflows have the potential to drastically reduce time to solution for computational solid mechanics simulations when compared to traditional hexahedral finite element analogues. A recently developed, higher-order composite tetrahedral element has shown promise in the space of incompressible computational plasticity. Mesh adaptivity has the potential to increase solution accuracy and increase solution robustness. In this work, we demonstrate an initial strategy to perform conformal mesh adaptivity for this higher-order composite tetrahedral element using well-established mesh modification operations for linear tetrahedra. We propose potential extensions to improve this initial strategy in terms of robustness and accuracy.

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Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics

Computational Mechanics

Alleman, Coleman A.; Foulk, James W.; Mota, Alejandro M.; Lim, Hojun L.; Littlewood, David J.

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.

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Corrigendum to “The Schwarz alternating method in solid mechanics” [Comput. Methods Appl. Mech. Engrg. 319 (2017) 19–51]

Computer Methods in Applied Mechanics and Engineering

Mota, Alejandro M.; tezaur, tezaur; Alleman, Coleman A.

This corrigendum clarifies the conditions under which the proof of convergence of Theorem 1 from the original article is valid. We erroneously stated as one of the conditions for the Schwarz alternating method to converge that the energy functional be strictly convex for the solid mechanics problem. Finally, we have relaxed that assumption and changed the corresponding parts of the text. None of the results or other parts of the original article are affected.

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Developing strong concurrent multiphysics multiscale coupling to understand the impact of microstructural mechanisms on the structural scale

Foulk, James W.; Alleman, Coleman A.; Mota, Alejandro M.; Lim, Hojun L.; Littlewood, David J.; Bergel, Guy L.; Popova, Evdokia P.; Montes de Oca Zapiain, David M.

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multi- scale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J 2 plas- ticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. Beyond cases studies in concurrent multiscale, we explore progress in crystal plastic- ity through modular designs, solution methodologies, model verification, and extensions to Sierra/SM and manycore applications. Advances in conformal microstructures having both hexahedral and tetrahedral workflows in Sculpt and Cubit are highlighted. A structure-property case study in two-phase metallic composites applies the Materials Knowledge System to local metrics for void evolution. Discussion includes lessons learned, future work, and a summary of funded efforts and proposed work. Finally, an appendix illustrates the need for two-way coupling through a single degree of freedom.

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Ductile failure X-prize

Boyce, Brad B.; Foulk, James W.; Littlewood, David J.; Mota, Alejandro M.; Ostien, Jakob O.; Silling, Stewart A.; Spencer, Benjamin S.; Wellman, Gerald W.; Bishop, Joseph E.; Brown, Arthur B.; Córdova, Theresa E.; Cox, James C.; Crenshaw, Thomas B.; Dion, Kristin D.; Emery, John M.

Fracture or tearing of ductile metals is a pervasive engineering concern, yet accurate prediction of the critical conditions of fracture remains elusive. Sandia National Laboratories has been developing and implementing several new modeling methodologies to address problems in fracture, including both new physical models and new numerical schemes. The present study provides a double-blind quantitative assessment of several computational capabilities including tearing parameters embedded in a conventional finite element code, localization elements, extended finite elements (XFEM), and peridynamics. For this assessment, each of four teams reported blind predictions for three challenge problems spanning crack initiation and crack propagation. After predictions had been reported, the predictions were compared to experimentally observed behavior. The metal alloys for these three problems were aluminum alloy 2024-T3 and precipitation hardened stainless steel PH13-8Mo H950. The predictive accuracies of the various methods are demonstrated, and the potential sources of error are discussed.

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Quantifying the debonding of inclusions through tomography and computational homology

Foulk, James W.; Jin, Huiqing J.; Lu, Wei-Yang L.; Mota, Alejandro M.

This report describes a Laboratory Directed Research and Development (LDRD) project to use of synchrotron-radiation computed tomography (SRCT) data to determine the conditions and mechanisms that lead to void nucleation in rolled alloys. The Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory (LBNL) has provided SRCT data of a few specimens of 7075-T7351 aluminum plate (widely used for aerospace applications) stretched to failure, loaded in directions perpendicular and parallel to the rolling direction. The resolution of SRCT data is 900nm, which allows elucidation of the mechanisms governing void growth and coalescence. This resolution is not fine enough, however, for nucleation. We propose the use statistics and image processing techniques to obtain sub-resolution scale information from these data, and thus determine where in the specimen and when during the loading program nucleation occurs and the mechanisms that lead to it. Quantitative analysis of the tomography data, however, leads to the conclusion that the reconstruction process compromises the information obtained from the scans. Alternate, more powerful reconstruction algorithms are needed to address this problem, but those fall beyond the scope of this project.

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103 Results
103 Results