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Full-Field Material Calibration Using LS-OPTยฎ
Nielen Stander, Anirban Basudhar, Imtiaz Gandikota, Suri Bala Sophie Du Bois, Denis Kirpicev
H Keshtkar, A Patil, A Sheshadri, P Du Bois (Fiat Chrysler Automobiles)
German LS-DYNA Forum Bamberg, Germany
October 16, 2018
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Parameter Identification: Overview
โข New curve matching algorithm
Dynamic Time Warping
โข Digital Image Correlation
Nearest Neighbor Cluster: Reduce resources
โข Post-processing
Automated Contour History display (LS-PrePost) using Similarity Measure
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Material Calibration: Introduction
๐ง๐ง
๐๐(๐๐), ๐๐๏ฟฝ
Computed curve: ๐๐(๐๐, ๐ก๐ก)
Response Surface constructed for each interpolated matching point
Test results
Test curve ๐๐๏ฟฝ(๐ก๐ก)
Material parameters ๐๐
Prof. S. Kumar, Dr. H. Ghassemi-Armaki (Brown U.) Prof. F. Pourboghrat (OSU)
Experiment (single crystal micropillar)
Result FE model
Test
min๐๐
๏ฟฝ(๐๐๐๐ ๐๐ โ ๐๐๏ฟฝ๐๐)2๐๐
๐๐=1
Simulation
๐๐โ
Euclidean Distance
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Calibration: Computational challenges
Noise Failure model: GISSMO โ element erosion a discrete process
Hysteresis Material 125 โ Loading/Unloading (5 cases)
Partial Matching Failure model: GISSMO โ post-failure oscillation of coupon
Experimental and computational results can be difficult to compare
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โข DTW calculates the distance between two data sets, which may vary in time, via its corresponding warping path.
โข This path is the result of the minimum accumulated distance which is necessary to traverse all points in the curves.
โข The matching is end-to-end.
โข While the Euclidean distance measure is a strict one-to-one mapping, DTW also allows one-to-many mappings.
โข Mathematically, optimize the path:
๐ท๐ท๐ท๐ท๐ท๐ท(๐๐, ๐๐) =1๐๐
๐๐๐๐๐๐๐๐
๏ฟฝ ๐ฟ๐ฟ(๐ค๐ค๐๐)๐๐
๐๐=1
Sophie du Bois, Denis Kirpicev 2018
Addressing noise: Dynamic Time Warping
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Dynamic Time Warping: DTW mapping
Contour Mapping
โข Multi-point histories: Apply to multiple points (full field): ๐บ๐บ vs. force
โข Use DTW map to construct
test contours for comparison simulation experiment
Best fit DTW map
Poor fit DTW map
Sophie du Bois, Denis Kirpicev
Simulated GISSMO model: force-displacement curves for tensile test
DTW
dis
tanc
e
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Dynamic Time Warping: Partial curves
โข In DTW, red connectors are summed
โข Curve length difference artificially distorts mismatch
โข Truncation required
Partial curve pairs can distort the DTW result
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Example: GISSMO model
The GISSMO failure model requires special treatment for curve matching
Itera
tions
โข Parameters: 7, Material Model: GISSMO โ Uses discrete (element-by-element)
erosion
โข Curve Matching โ Dynamic Time Warping (DTW) โ Does not address partial curves โจ
Truncate Force history at failure
โข Optimization โ SRSM (fast local optimizer)
Shear: single case calibration history
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Calibration: GISSMO model
Tensile Notch
Shear Punch
In industry, the calibration of the GISSMO model typically involves multiple cases
Optimal match
Courtesy: FCA
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Digital Image Correlation
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Full field test result (4557 pts) from optical scan is mapped and tracked
DIC data: deformation states
Local deformation
๐ก๐ก = 0
Digital Image Correlation (DIC)
Alignment
Align and map optical data to the Finite Element model
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Digital Image Correlation: LS-OPT technologies (1)
โข Alignment in 3D of test to FE model. Least Squares solution:
๐ฟ๐ฟ1:Test pts (subset), ๐ฟ๐ฟ2: FE model pts, ๐ป๐ป: transform, ๏ฟฝฬ๏ฟฝ๐ : Isotropic scaling. Typically 3 or 4 points
โ Alternative: LS-PrePostยฎ to translate, rotate and scale test points.
โข Map: Test โ FE mesh: โ Exact Nearest Neighbor (bin tree) search and
element interpolation (107 โ 107 pts). (Practice: ~ 106)
โข Optimization: Minimize Similarity Measure:
min๐ฅ๐ฅ
๏ฟฝ ๐ท๐ท๐ท๐ท๐ท๐ท(๐๐, ๐๐)๐๐
๐๐๐๐๐๐๐๐๐๐๐๐
๐๐=1
min๐ป๐ป,๏ฟฝฬ๏ฟฝ๐
๏ฟฝฬ๏ฟฝ๐ ๐ฟ๐ฟ1๐ป๐ป โ ๐ฟ๐ฟ2
Align Test points
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Validation of a Synthetic Problem
๐๐โ ๐๐โ
Start 4.0 0.9
PCM 0.502 0.501
DF 0.500 0.500
DTW 0.497 0.499
Exact 0.500 0.500
๐๐๐ฅ๐ฅ๐ฅ๐ฅ ๐๐๐ฆ๐ฆ๐ฆ๐ฆ Forc
e
Test pts & nodes coincide
Material 24 with Hockett-Sherby flow curve extrapolation
๐๐ ๐๐๐๐ = ๐ด๐ด โ ๐ต๐ต๐๐โ๐๐๐๐๐๐๐๐๐๐
โข ๐๐ and ๐๐ are variables
Full-field deformation
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Distance vs. parameters
Partial Curve Mapping Discrete Frรฉchet Dynamic Time Warping
Different similarity measures compared
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Example 1: DIC Validation: Punch example Calibrate GISSMO material properties using strains/transverse displacement
DIC data
Courtesy: FCA
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๐ข๐ข๐ง๐ง
๐๐1
๐๐2
Example 1: DIC Validation: Punch example
Computed Test Difference
The calibration was done using a Force-Displacement similarity match (GISSMO)
Courtesy: FCA
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Digital Image Correlation: Nearest Neighbor Cluster 4557 points 1063 points
โข Accuracy and cost โข Nearest Neighbor Clustering
โ Pre-processing feature โ Reduce resources for large point set
(~106) โข Storage space โข CPU time: mapping is done at each
time step (vanishing nodes/points) โ Nodal 1-to-1 map โ Can also apply a proximity tolerance for
removing outlier points โข Algorithm (๐๐ = ๐๐)
โ Nearest node to each point โ reduced node set.
โ Prune reduced node set โ nearest points โ 1-to-1 map
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Digital Image Correlation: Nearest Neighbor Cluster
โข Accuracy and cost โข Nearest Neighbor Clustering
โ Pre-processing feature โ Reduce resources for large point set
(~106) โข Storage space โข CPU time: mapping is done at each
time step (vanishing nodes/points) โ Nodal 1-to-1 map โ Can also apply a proximity tolerance for
removing outlier points โข Algorithm (๐๐ = ๐๐)
โ Nearest node to each point โ reduced node set.
โ Prune reduced node set โ nearest points โ 1-to-1 map
๐๐. ๐๐ ร ๐๐๐๐๐๐ points ๐๐๐๐๐๐๐๐ points = ๐๐. ๐๐๐
Enlarged
DIC Test points (full set)
Nearest test points
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Example 2: Tensile test
Computed
DIC Test points
๐๐๐ฆ๐ฆ๐ฆ๐ฆ Nearest test points
DIC
๐๐๐ฅ๐ฅ๐ฅ๐ฅ FE model
The contour comparison uses Dynamic Time Warping: ๐๐. ๐๐ ร ๐๐๐๐๐๐ DIC points
โข Reduces 380,000 DIC points to 7275 points with nodal neighbors
โข Reduces extraction time from 2 hours โ 6 minutes
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LS-OPT DIC calibration feature summary (v6.0)
โข DIC Interfaces: โ gom/ARAMIS
โข v6 CSV โข v7 XML
โ Fixed Format (LS-PrePost) โ Free Format (LS-OPT/GenEx parser)
โข LS-DYNA interface โ Multi-point histories (d3plot) โ Entities
โข Nodal โข Shell โข Solid
โ Exact nearest neighbor point mapping (~107 pts). Test pt โ FE pt
โข Curve similarity methods โ Euclidean, Frรฉchet, DTW, PCM
โข Filtering โ Online filtering (SAE, Ave)
โข GUI โ Test pre-view โ Test alignment
โ Strain fringe plot (LS-PrePost) โข Simulation โข Experiment โข Error
DTW
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Outlook
โข General feature: Improved pre-viewing/pre-processing of experimental data.
Interactive filtering and truncation of test results
โข Partial DTW-based curve mapping
DTW-LCS method
โข Further speedup
Multiple similarity responses typically have the same mapping