publications | Brian Doran Giffin

2025

Exactly bit-reversible computational methods for memory-efficient adjoint sensitivity analysis of dissipative dynamic systems

Brian Doran Giffin

Jul 2025

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As interest in inverse problems continues to grow across a wide range of disciplines of science and engineering, the size and complexity of inverse problems of practical interest is also increasing. Inverse problems involving time-dependent dynamic systems with a large number of design parameters commonly employ the adjoint state method to compute design parameter sensitivities within a gradient-based optimization framework. For forward analyses entailing a large number of time steps (such as for transient dynamic systems), solution of the adjoint problem may incur excessive memory, I/O, or computational costs which cannot be entirely ameliorated through conventional solution checkpointing schemes, ultimately limiting scalability and efficiency in solving larger problems of emergent interest. To overcome these limitations, a systematic approach is proposed for the development of exactly “bit-reversible” computational methods, enabling prior time states to be rematerialized by reversing the steps of the forward analysis, thereby reducing the additional memory requirements and computational overheads associated with the adjoint state method. Within the proposed framework, a duplicate set of adjoint variables are introduced as ancillary data buffers which continuously accumulate roundoff bits due to finite-precision arithmetic during solution of the forward problem. Upon time-reversal of the forward problem accompanying the solution of the adjoint problem, the roundoff bits are restored to ensure that prior solution states are precisely rematerialized. Utilizing this approach, several foundational bit-reversible algorithms are devised, including a memory-efficient bit-reversible matrix multiplication/inversion algorithm, and exactly bit-reversible explicit time integrators. The developed algorithms are predicated on the use of fixed-precision arithmetic, and are implemented within a proof-of-concept open source library. The computational performance characteristics of the proposed methods are demonstrated through several benchmark problems with intended applications for inverse analysis of dissipative dynamic systems.
@conference{giffin_2025a, title = {Exactly bit-reversible computational methods for memory-efficient adjoint sensitivity analysis of dissipative dynamic systems}, author = {Giffin, Brian Doran}, url = {https://usnccm18.usacm.org}, journal = {18th U.S. National Congress on Computational Mechanics}, place = {Chicago, IL}, year = {2025}, month = jul, }
Fragility Analysis of Transmission Towers through Physics-Based Modeling of Tornado-Induced Wind and Debris Impact Loads

Himamshu Poudel, and Brian Doran Giffin

Feb 2025

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Wind-borne debris is a significant contributor to structural damage during high-intensity wind events, but existing methods for estimating debris impact loads on structures are relatively limited. These limitations stem from inherent uncertainties and lack of knowledge regarding the characterization of combined wind and debris loads, as well as a lack of computational modeling strategies for representing wind-borne debris impacts and their effects on structures. In the present study, a physics-based fluid-structure-debris modeling framework coupled with OpenSees is developed to investigate and quantify of the extent to which wind-borne debris impact contributes to structural damage and collapse. Specific focus is placed on assessing the risk of structural collapse of electrical transmission towers subjected to tornadic winds. Within the proposed modeling framework, flying debris is represented through discrete realizations of debris trajectories and impacts, with the nonlinear transient dynamic behavior of the structure of interest modeled using OpenSees. Collisions between debris and the structure are resolved through a penalty-based contact enforcement strategy. A parametric vortex model is used to represent the wind field and to determine wind pressures acting on both the structure and the debris. As a particular application of the proposed methodology, damage and collapse fragility curves were developed for a representative lattice transmission tower using quoFEM, incorporating variability with respect to relevant structural, wind field, and debris loading parameters. The study presents findings which quantitatively compare the estimated risk of collapse when debris impact is included/excluded in the analysis to assess its relative importance.
@conference{poudel_2025a, title = {Fragility Analysis of Transmission Towers through Physics-Based Modeling of Tornado-Induced Wind and Debris Impact Loads}, author = {Poudel, Himamshu and Giffin, Brian Doran}, url = {https://simcenter.designsafe-ci.org/nheri-computational-symposium/2025/agenda/session-abstracts/presenters-session-3a/}, journal = {NHERI Computational Symposium 2025}, place = {Anahiem, CA}, year = {2025}, month = feb, }

2024

Hyper-dimensional gap finite elements for the enforcement of interfacial constraints

Brian Doran Giffin

16th World Congress on Computational Mechanics, Jul 2024

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In the classical theory of two-body contact, a single shared contact interface is con- sidered between two continuum bodies, and is further discretized as such in the finite element setting. In general, however, the finite element mesh topology of two contacting bodies will be non-conforming at this shared interface, requiring the definition of a preferred or intermediate surface over which integral constraints may be evaluated. The specification of this interface is deemed to be somewhat arbitrary, but in practice the numerical solution of contact problems may exhibit sensitivity to the particular choice of intermediate surface. A further complication concerns the need to establish projective mappings between the discretized finite element sur- faces and the chosen intermediate surface, particularly for the sake of evaluating the contact gap function between pairs of points on each of the two bodies. In this work, a new methodology for the enforcement of contact constraints in the context of finite element analyses is proposed. The method entails an alternative representation of contact surface integrals by equivalently integrating over the interstitial – albeit degenerate gap volume between two contacting bodies. An auxiliary indicator field is defined on each body, and is used to represent the degenerate interstitial volume as a non-degenerate hyper-dimensional gap volume. Over this domain, the gradient of the continuously interpolated displacement field with respect to the indicator field yields the oriented displacement gap, which may be used in the for- mulation of contact inequality constraints. Discretization of the hyper-dimensional gap volume into conforming finite elements is explored, and is observed to offer several advantages over existing contact discretization methods: the proposed method does not require the computation of geometric intersections or projections; it exploits conventional Gaussian quadrature schemes to integrate the hyper-dimensional gap integrals with a sufficient degree of accuracy; and may be naturally and efficiently extended to represent contact between higher-order surfaces. The efficacy of the method is demonstrated on several benchmark problems. Continuing and future work is also discussed, with a focus on intended applications and extensions of the method.
@article{giffin_2024c, title = {Hyper-dimensional gap finite elements for the enforcement of interfacial constraints}, author = {Giffin, Brian Doran}, doi = {10.23967/wccm.2024.109}, url = {https://www.scipedia.com/public/Giffin_2024a}, journal = {16th World Congress on Computational Mechanics}, place = {Vancouver, Canada}, year = {2024}, month = jul, }
Model-Based Uncertainty in Predicting Damage to Near-Fault Reinforced Concrete Structures

Maha Kenawy, and Brian Doran Giffin

Jul 2024

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Earthquake-induced ground shaking near rupturing faults typically contains strong velocity pulses dictated by the fault rupture characteristics and seismic wave propagation patterns, and can cause significant damage to civil structures compared to ground shaking at locations further away from the fault. Therefore, modeling of the nonlinear, and especially degrading, behavior of near-fault structures with a high degree of fidelity is important for evaluating the structural demands in geographical regions proximate to active faults. Several alternative modeling strategies of varying fidelities exist for representing damage mechanisms in structures under dynamic earthquake loading, but it remains unclear the extent to which the specific choice of modeling strategy affects the estimated risks to near-fault structures. In this study, we examine the bias associated with the predicted seismic demands on near-fault reinforced concrete structures due to deficiencies in the modeling of the degrading behavior of the structural components. We test the use of three different modeling approaches which represent the deterioration of the structural components in different ways: (1) a lumped-plasticity frame model which cumulatively represents several damage mechanisms using nonlinear springs at the ends of the structural components, (2) a conventional distributed-plasticity frame model which represents the deterioration of the concrete and steel materials using uniaxial constitutive models, but is subject to numerical singularities, and (3) a regularized distributed-plasticity frame model recently developed by the authors which utilizes a nonlocal damage technique to overcome artificial strain singularities in representing the deterioration of the concrete and steel materials. We conduct a series of nonlinear dynamic analyses to predict the seismic demands imposed by representative ensembles of near-fault ground motions on structures located between 1 and 15 km away from the fault, and we compare the statistical distributions of the demands associated with each damage modeling approach. The findings of this study highlight the advantages and deficiencies of the different structural modeling strategies in the seismic analysis of degrading systems, and will aid in quantifying the modeling uncertainty associated with performance-based design of near-fault structures.
@conference{giffin_2024b, title = {Model-Based Uncertainty in Predicting Damage to Near-Fault Reinforced Concrete Structures}, author = {Kenawy, Maha and Giffin, Brian Doran}, journal = {Proceedings of the 18th World Conference on Earthquake Engineering}, place = {Milan, Italy}, year = {2024}, month = jul, }
A layered solid finite element formulation with interlaminar enhanced displacements for the modeling of laminated composite structures

Brian Doran Giffin, and Miklos J. Zoller

International Journal for Numerical Methods in Engineering, Jul 2024

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Abstract Accurate modeling of layered composite structures often requires the use of detailed finite element models which can sufficiently resolve the kinematics and material behavior within each layer of the composite. However, individually discretizing each material layer into finite elements presents a prohibitive computational expensive given the large number of thin layers comprising some laminated composites. To address these challenges, an 8-node layered solid hexahedral finite element is formulated with the aim of striking an appropriate balance between efficiency and fidelity. The element is discretized into an arbitrary number of distinct material layers, and employs reduced in-plane integration within each layer. The chosen reduced integration scheme is supplemented by a novel physical stabilization approach which includes layerwise enhancements to mitigate various forms of locking phenomena. The proposed framework additionally supports the inclusion of interlaminar enhanced displacements to better represent the kinematics of general layered composite materials. The described element formulation has been implemented in the ParaDyn finite element code, and its efficacy for modeling laminated composite structures is demonstrated on a variety of verification problems.
@article{giffin_2024a, author = {Giffin, Brian Doran and Zoller, Miklos J.}, title = {A layered solid finite element formulation with interlaminar enhanced displacements for the modeling of laminated composite structures}, journal = {International Journal for Numerical Methods in Engineering}, volume = {125}, number = {23}, pages = {e7581}, keywords = {finite element method, interlaminar enhancements, laminated composites, layered solid element}, doi = {https://doi.org/10.1002/nme.7581}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7581}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.7581}, year = {2024}, }

2023

A smeared crack modeling framework accommodating multi-directional fracture at finite strains

Brian Doran Giffin, and Edward Zywicz

International Journal of Fracture, Jan 2023

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A generic smeared crack modeling framework predicated on the deformation gradient decomposition (DGD) approach is proposed for use in dynamic fracture problems at finite strains, accommodating failure along multiple mutually orthogonal fracture planes embedded within an independently defined bulk material model. Within this constitutive framework, the traction equilibrium conditions imposed at each failure surface are used to determine the associated crack displacements stored as internal state variables. In general, the enforcement of interfacial equilibrium entails the implicit solution of a non-linear system of equations within the constitutive update procedure. However, if inertial effects arising due to the relative motion of the fractured material are incorporated within the model, the traction equilibrium conditions are shown to give rise to corresponding dynamic equations of motion governing the time-evolution of the crack opening displacements. For dynamic problems, an explicit time-integration procedure is devised to efficiently update the material state, subject to a set of internal frictionless contact constraints to prevent material inversion. The efficacy of the proposed modeling framework is investigated through several benchmark dynamic fracture problems run within the explicit finite element code DYNA3D.
@article{giffin_2023, title = {A smeared crack modeling framework accommodating multi-directional fracture at finite strains}, author = {Giffin, Brian Doran and Zywicz, Edward}, doi = {10.1007/s10704-022-00665-9}, url = {https://doi.org/10.1007/s10704-022-00665-9}, journal = {International Journal of Fracture}, volume = {239}, issue = {1}, pages = {87-109}, place = {United States}, year = {2023}, month = jan, }

2022

BCLink User Documentation

Brian Doran Giffin

Sep 2022

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BCLink is a shared programming library providing general functionality to read temporally- and spatially-varying boundary condition data (contained in Exodus files) into MDG codes (ParaDyn and Diablo). This document is intended for prospective users of BCLink, presenting a summary of the available features of the library, including details regarding the input syntax with accompanying examples. The library’s capabilities are demonstrated through example problems run in ParaDyn, and using the BCRemap command line utility – a stand-alone preprocessing tool which leverages the native functionality provided by the BCLink library to remap surface data between dissimilar meshes.
@techreport{giffin_2022a, author = {Giffin, Brian Doran}, title = {BCLink User Documentation}, institution = {Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)}, doi = {10.2172/1889533}, url = {https://www.osti.gov/biblio/1889533}, place = {United States}, year = {2022}, month = sep, }
Elasto-Plastic Hourglass Control for Physically Stabilized Non-Linear Finite Elements with Reduced Integration

Brian Doran Giffin

Jun 2022

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A physically stabilized hourglass control scheme is proposed for low-order finite elements with reduced integration, specialized to the case of elasto-plastic material behavior. Conventional hourglass stabilization techniques necessitate an ad hoc reduction of the element’s stabilization stiffness parameters to prevent artificially stiff behavior under large plastic deformations. In contrast, the proposed approach circumvents this difficultly by instead enabling plastic deformation in the element’s hourglass modes. The method employs an elasto-plastic model order reduction strategy over a given finite element domain to effect a non-linear form of hourglass stabilization, bearing similarity to a resultant plasticity model. Specifically, a mixed discretization of the element’s hourglass stress/strain fields is established within a co-rotational frame, and supplemented by a stabilizing plastic strain field to characterize the plastic deformations associated with the hourglass modes. An Lp measure of the hourglass stress field is integrated over the element domain to obtain an element-averaged representation of the stabilizing effective stress. By exploiting the mixed representation of the hourglass stress field, the resulting integrals can be efficiently evaluated without recourse to quadrature. The chosen effective stress measure is then used to generalize an element-based yield criterion, which is designed to inherit the same yield stress and hardening parameters from the constitutive model associated with the element’s single integration point. Within this framework, a generalization of the classical radial return algorithm for continuum plasticity is proposed to facilitate a convenient and computationally efficient evolution of the stabilizing plastic strains. The method is formulated to satisfy an element-averaged dissipation inequality, and the resulting stabilization scheme is demonstrated to exhibit energetic consistency. The proposed technique is applied to low-order hexahedral elements, and may be viewed as an elasto-plastic extension of the physically stabilized element formulation introduced by Puso (2000). The efficacy and computational efficiency of the method are explored through a variety of large deformation elasto-plastic problems in explicit dynamics, and compared against conventional hourglass stabilization approaches. References: Puso, M.A. (2000), A highly efficient enhanced assumed strain physically stabilized hexahedral element. Int. J. Numer. Meth. Engng., 49: 1029-1064. https://doi.org/10.1002/1097-0207(20001120)49:8<1029::AID-NME990>3.0.CO;2-3
@conference{giffin_2022b, title = {Elasto-Plastic Hourglass Control for Physically Stabilized Non-Linear Finite Elements with Reduced Integration}, author = {Giffin, Brian Doran}, url = {https://www.emi-conference.org/sites/emi-conference.org/2022/files/inline-files/EMI%202022%20Book%20of%20Abstracts.pdf}, journal = {Engineering Mechanics Institute 2022 Conference}, place = {Baltimore, Maryland}, year = {2022}, month = jun, }

2021

A Smeared Crack Modeling Framework Accomodating Multi-directional Fracture at Finite Strains

Brian Doran Giffin

Jun 2021

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@conference{giffin_2021,
  title = {A Smeared Crack Modeling Framework Accomodating Multi-directional Fracture at Finite Strains},
  author = {Giffin, Brian Doran},
  url = {https://2020.emi-conference.org},
  journal = {Engineering Mechanics Institute Conference 2021},
  place = {(virtual)},
  year = {2021},
  month = jun,
}

2020

Shell Element Material Model Verification Problems for DYNA3D: Part II

Brian Doran Giffin

Sep 2020

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A suite of supplementary shell element material model verification tests were developed for the explicit finite element program DYNA3D, in continuation of the work performed in LLNL-TR-792469 (Shell Element Material Model Verification Problems for DYNA3D). The testing procedure developed in the preceding report is extended, and used to verify all remaining untested shell model features and inputs. A collection of 78 feature-specific verification tests are proposed, some of which are applicable to multiple material models, though many are specialized to a particular model. The collective suite of tests cover all 27 currently available material models in DYNA3D. In the course of developing the proposed test suite, 24 separate shell model-related issues were identified and have subsequently been resolved.
@techreport{giffin_2020, author = {Giffin, Brian Doran}, title = {Shell Element Material Model Verification Problems for DYNA3D: Part II}, institution = {Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)}, doi = {10.2172/1668518}, url = {https://www.osti.gov/biblio/1668518}, place = {United States}, year = {2020}, month = sep, }

2019

A stable, efficient, locking free hexahedral element for problems in non-linear dynamics

Brian Doran Giffin

Jun 2019

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A new fully integrated 8-node hexahedral solid finite element is proposed for general use in non-linear quasi-static and dynamic problems. The element formulation is derived from a mixed/enhanced assumed strain principle, where the chosen enhancements for alleviating volumetric and shear locking are treated separately, leading to in- creased computational efficiency, as well as improved stability of the element in quasi-static problems. Nonetheless, for use in highly dynamic problems (such as impact), supplementary stabilization of the element is required. To this end, a novel stabilization strategy is proposed which avoids the use of non-physical parameters, and preserves the locking-free behavior of the element. An efficient implementation of the element is developed for the non-linear finite element code DYNA3D, and a number of example problems are shown to demonstrate the superior accuracy and stability of the element for problems involving highly dynamic processes. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
@conference{giffin_2019c, title = {A stable, efficient, locking free hexahedral element for problems in non-linear dynamics}, author = {Giffin, Brian Doran}, url = {https://2020.emi-conference.org/sites/emi-conference.org/2020/files/inline-files/2019-emi-conference-book-abstracts.pdf}, journal = {Engineering Mechanics Institute 2019 Conference}, place = {Pasadena, California}, year = {2019}, month = jun, }
Shell Element Material Model Verification Problems for DYNA3D

Brian Doran Giffin

Sep 2019

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A suite of shell element material model verification tests were developed for the explicit finite element program DYNA3D. Each test consists of a single quadrilateral shell element, whose nodal displacements and rotations have been prescribed such that the deformation of the material is fully controlled throughout the analysis. At one of the element’s integration points, the numerically computed stress, through-thickness strain, and equivalent plastic strain are compared against closed-form reference solutions that are derived to be consistent with the theory of finite deformation elasto-plasticity. A collection of 31 feature-specific verification tests are proposed, each of which may be used to verify all models which share in common the tested feature of interest. For each material model, a subset of these tests are selected and used to verify the correct behavior of all features of the model. The collective suite of tests cover 26 of the 27 currently available material models in DYNA3D. In the course of developing the proposed test suite, 18 implementation bugs were identified and have subsequently been resolved.
@techreport{giffin_2019b, author = {Giffin, Brian Doran}, title = {Shell Element Material Model Verification Problems for DYNA3D}, institution = {Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)}, doi = {10.2172/1569660}, url = {https://www.osti.gov/biblio/1569660}, place = {United States}, year = {2019}, month = sep, }
Verification Problems for Parameterized Load Curves in DYNA3D

Brian Doran Giffin

Jan 2019

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Two verification problems are presented which test a set of newly implemented load curve features in the explicit finite element program DYNA3D. Each test consists of a single element, with the velocity of each node specified via a different load curve type. The first test covers initialization and run-time execution of these new features, while the second test covers redefinition of load curves upon restart. The proposed problems may be easily extended to test additional load curve features.
@techreport{giffin_2019a, author = {Giffin, Brian Doran}, title = {Verification Problems for Parameterized Load Curves in DYNA3D}, institution = {Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)}, doi = {10.2172/1499983}, url = {https://www.osti.gov/biblio/1499983}, place = {United States}, year = {2019}, month = jan, }

2018

Partitioned Polytopal Finite-Element Methods for Nonlinear Solid Mechanics

Brian Doran Giffin

Jan 2018

ProQuest

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This work presents a novel polytopal finite-element framework that addresses the collective issues of discretization sensitivity and mesh generation for computational solid mechanics problems. The use of arbitrary polygonal and polyhedral shapes in place of canonical isoparametric elements seeks to remediate issues pertaining to meshing and mesh quality (particularly for irregularly shaped elements), while maintaining many of the desirable features of a traditional finite element method. A general class of partitioned element methods (PEM) is proposed and analyzed, constituting a family of approaches for constructing piecewise polynomial approximations to harmonic shape functions on arbitrary polytopes. Such methods require a geometric partition of each element, and under certain conditions will directly yield integration consistency. Two partitioned element methods are explored in detail, including a novel approach herein referred to as the discontinuous Galerkin partitioned-element method (DG-PEM). An implementational framework for the DG-PEM is presented, along with a discussion of its associated numerical challenges. The numerical precision of the PEM is explored via classical patch tests and single element tests for a representative sampling of polygonal element shapes. Solution sensitivity with respect to element shape is examined for a handful of problems, including a mesh convergence study in the nearly incompressible regime. Finally, the efficacy of the DG-PEM is assessed for a number of benchmark problems involving large deformations and nonlinear material behavior.
@phdthesis{giffin_2018, author = {Giffin, Brian Doran}, year = {2018}, title = {Partitioned Polytopal Finite-Element Methods for Nonlinear Solid Mechanics}, journal = {ProQuest Dissertations and Theses}, pages = {148}, note = {ProQuest}, keywords = {Applied sciences; Physical sciences; Element; Mechanics; Nonlinear; PEM; Partitioned; Polytopal; Computational physics; Applied mathematics; 0346:Mechanics; 0216:Computational physics; 0364:Applied Mathematics}, isbn = {978-0-438-28961-1}, language = {English}, url = {http://argo.library.okstate.edu/login?url=https://www.proquest.com/dissertations-theses/partitioned-polytopal-finite-element-methods/docview/2091485390/se-2}, }

2017

Improved Partitioned Element Method for Constructing Higher Order Shape Functions on Arbitrary Polyhedra

Brian Doran Giffin, and Mark Rashid

Jul 2017

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We present an improved reformulation of the "partitioned element method” (PEM): a finite-element-like method in which shape functions are defined on arbitrary polygonal and polyhedral element domains. The method proceeds by partitioning an element into quadrature cells, and allowing the element’s shape functions to vary according to a local polynomial defined within each of these cells, resulting in piece-wise polynomial shape functions which are discontinuous at quadrature cell boundaries. The polynomial coefficients defined in each cell are obtained by minimizing a quadratic functional which penalizes discontinuities in the shape functions (and their gradients) across all cell interfaces. Unlike the original method (presented in [1]) which is restricted to piece-wise linear approximants, the present formulation admits polynomials of arbitrary degree, leading directly to higher-order completeness of the shape functions, and improved convergence properties. Numerical results for two- and three-dimensional solid mechanics problems are presented, demonstrating the method’s ability to overcome issues pertaining to non-convex elements, geometric degeneracies, and certain forms of element locking phenomena – particularly, those concerning thin elements. References: [1] Rashid M, Sadri A. The partitioned element method in computational solid mechanics. Computer Methods in Applied Mechanics and Engineering 2012; 237–240: 152–165.
@conference{giffin_2017, title = {Improved Partitioned Element Method for Constructing Higher Order Shape Functions on Arbitrary Polyhedra}, author = {Giffin, Brian Doran and Rashid, Mark}, url = {http://14.usnccm.org/sites/default/files/ABSTRACTS%20M-Z.pdf}, journal = {14th U.S. National Congress on Computational Mechanics}, place = {Montreal, Quebec, Canada}, year = {2017}, month = jul, }

2015

Verification Tests for Sierra/SM’s Reproducing Kernal Particle Method

Brian Doran Giffin

Sep 2015

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@techreport{giffin_2015,
  author = {Giffin, Brian Doran},
  title = {Verification Tests for Sierra/SM's Reproducing Kernal Particle Method},
  institution = {Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)},
  doi = {10.2172/1411850},
  url = {https://www.osti.gov/biblio/1411850},
  place = {United States},
  year = {2015},
  month = sep,
}

2014

Applied Poromechanics for Hydraulic Fracture Simulation

Brian Doran Giffin

Dec 2014

Bib PDF

@mastersthesis{giffin_2014,
  author = {Giffin, Brian Doran},
  title = {Applied Poromechanics for Hydraulic Fracture Simulation},
  address = {Davis, CA},
  school = {University of California, Davis},
  type = {MS project report},
  place = {United States},
  year = {2014},
  month = dec,
}

2013

Verification of a Convergent Meshless Method in Sierra Solid Mechanics

Joseph E. Bishop, Brian Doran Giffin, and John Pott

Aug 2013

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Standard finite-element discretizations in solid mechanics consist of basis functions defined on simple element shapes such as hexahedra. While the use of these standard element shapes is expedient for computational software development, their use in the modeling of extreme deformation processes, such as fracture, pervasive failure, and penetration, is too limiting. Furthermore, the amount of effort required to create hexahedral meshes on geometrically complex shapes is time consuming and thus costly. Several other discretization methods exist for modeling extreme deformation processes, e.g. the nodally integrated Reproducing Kernel Particle Method (RKPM). The primary goal of this project is to implement existing and new RKPM technology into Sierra Solid Mechanics for the modeling of extreme deformation processes including fracture and fragmentation.
@conference{giffin_2013, author = {Bishop, Joseph E. and Giffin, Brian Doran and Pott, John}, title = {Verification of a Convergent Meshless Method in Sierra Solid Mechanics}, url = {https://www.osti.gov/biblio/1664749}, place = {United States}, organization = {Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)}, year = {2013}, month = aug, }