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Title: Adaptive reduction of constitutive model-form error using a posteriori error estimation techniques

Journal Article · · Computer Methods in Applied Mechanics and Engineering
ORCiD logo [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
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In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energy norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. As a result, the algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000; NA0003525
OSTI ID:
1455219
Alternate ID(s):
OSTI ID: 1575936
Report Number(s):
SAND-2018-6265J; 664255
Journal Information:
Computer Methods in Applied Mechanics and Engineering, Vol. 340; ISSN 0045-7825
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

References (34)

In Situ Neutron Diffraction Study of the Influence of Microstructure on the Mechanical Response of Additively Manufactured 304L Stainless Steel journal October 2017
Three-dimensional finite element analysis of temperatures and stresses in wide-band laser surface melting processing journal August 2010
Thermomechanical Modeling of Additive Manufacturing Large Parts journal October 2014
An Integrated Approach to Additive Manufacturing Simulations Using Physics Based, Coupled Multiscale Process Modeling journal October 2014
Multiscale Modeling of Powder Bed–Based Additive Manufacturing journal July 2016
Simulation and experimental comparison of the thermo-mechanical history and 3D microstructure evolution of 304L stainless steel tubes manufactured using LENS journal December 2017
A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys journal September 1993
On the accuracy of self-consistent elasticity formulations for directionally solidified polycrystal aggregates journal February 2005
A finite strain elastic–viscoplastic self-consistent model for polycrystalline materials journal April 2010
Determination of the size of the representative volume element for random composites: statistical and numerical approach journal June 2003
Direct numerical simulations in solid mechanics for understanding the macroscale effects of microscale material variability journal April 2015
Texture control during laser deposition of nickel-based superalloy journal September 2012
Effect of build geometry on the β-grain structure and texture in additive manufacture of Ti6Al4V by selective electron beam melting journal October 2013
Microstructural and texture development in direct laser fabricated IN718 journal March 2014
Site specific control of crystallographic grain orientation through electron beam additive manufacturing journal November 2014
Origin of grain orientation during solidification of an aluminum alloy journal August 2016
Self-consistent elastic properties for transversely isotropic polycrystals journal December 1998
Texture of welded joints of 316L stainless steel, multi-scale orientation analysis of a weld metal deposit journal January 2000
Effect of heat input on the microstructure, residual stresses and corrosion resistance of 304L austenitic stainless steel weldments journal July 2014
Quantifying the Impact of Material-Model Error on Macroscale Quantities-of-Interest Using Multiscale a Posteriori Error-Estimation Techniques journal January 2016
Hierarchical modeling of heterogeneous bodies journal December 1996
Estimation of Local Modeling Error and Goal-Oriented Adaptive Modeling of Heterogeneous Materials journal October 2000
Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials journal September 2001
Modeling error and adaptivity in nonlinear continuum mechanics journal October 2001
Modeling and discretization errors in hyperelasto-(visco-)plasticity with a view to hierarchical modeling journal December 2004
Adaptive computational meso–macro-scale modeling of elastic composites journal January 2006
Adaptive Bridging of Scales in Continuum Modeling Based on Error Control journal January 2008
Multi-scale goal-oriented adaptive modeling of random heterogeneous materials journal August 2006
A finite element multiscale capability for nonlinear quasistatic stress analysis journal April 2005
The Closest Elastic Tensor of Arbitrary Symmetry to an Elasticity Tensor of Lower Symmetry journal October 2006
Monocrystal-Polycrystal Elastic Constants of a Stainless Steel journal September 1984
Effect of 3D grain structure representation in polycrystal simulations journal October 2012
Hierarchical modeling of heterogeneous solids journal April 1999
Adaptive hierarchical modeling of heterogeneous structures journal September 1999

Cited By (1)

Modeling mechanical behavior of an additively manufactured metal structure with local texture variations: a study on model form error journal January 2019

Figures / Tables (24)

Figure 1(p. 2)figure Figure 1
Algorithm 1(p. 7)figure Algorithm 1
Figure 2(p. 9)figure Figure 2
Figure 3(p. 10)figure Figure 3
Figure 4(p. 11)figure Figure 4
Figure 5(p. 12)figure Figure 5
Figure 6(p. 12)figure Figure 6
Table 1(p. 12)table Table 1
Figure 7(p. 13)figure Figure 7
Figure 8(p. 14)figure Figure 8
Figure 9(p. 14)figure Figure 9
Figure 10(p. 15)figure Figure 10
Figure 11(p. 16)figure Figure 11
Figure 12(p. 16)figure Figure 12
Figure 13(p. 16)figure Figure 13
Figure 14(p. 17)figure Figure 14
Table 2(p. 17)table Table 2
Figure 15(p. 18)figure Figure 15
Figure C.16(p. 21)figure Figure C.16
Figure C.17(p. 21)figure Figure C.17
Figure D.18(p. 22)figure Figure D.18
Table C.3(p. 22)table Table C.3
Figure D.19(p. 23)figure Figure D.19
Table D.4(p. 23)table Table D.4

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42 ENGINEERING
a posteriori error estimation
Uncertainty quantification
Model-form error
Model adaptivity