Abstract
Optimizing the geometry deformation characteristics in contact problems with random rough surfaces is an important component of improving product performance, such as assembly accuracy, sealing percolation, contact thermal resistance, and electrical resistance. Traditionally, the deformation is computed by numerically solving the partial differential equations that govern the contact problems. In the optimization process, the deformations under a variety of random rough surfaces need to be solved. It is computationally intensive and necessitates a surrogate model to approximate the numerical solutions. This study employs non-uniform rational B-splines (NURBS) to represent the geometries involved in the contact problem and proposes treating the NURBS control points as image pixels, treating the deformations of these points as image pixel values. Furthermore, an image generator-enhanced deep operator network (IGE-DeepONet) that leverages an image generator as a trunk net is proposed to predict the deformations and a concatenation-based information fusion mechanism between the trunk net and branch net of the DeepONet was developed to improve the prediction accuracy. Based on the contact problem between a smooth elastomer cube and a rigid cuboid with a random rough surface, it was demonstrated that the proposed IGE-DeepONet has smaller test error and reduced training time compared to the standalone image generator and the traditional DeepONet which uses a fully connected neural network as trunk net.
References
1.
Sun
, Q.
, Zhao
, B.
, Liu
, X.
, Mu
, X.
, and Zhang
, Y.
, 2019
, “Assembling Deviation Estimation Based on the Real Mating Status of Assembly
,” Comput.-Aided Des.
, 115
, pp. 244
–255
. 2.
Zeng
, W.
, and Rao
, Y.
, 2019
, “Modeling of Assembly Deviation With Considering the Actual Working Conditions
,” Int. J. Precis. Eng. Manuf.
, 20
(5
), pp. 791
–803
. 3.
Zhang
, F.
, Liu
, J.
, Ding
, X.
, and Yang
, Z.
, 2017
, “An Approach to Calculate Leak Channels and Leak Rates Between Metallic Sealing Surfaces
,” ASME J. Tribol.
, 139
(1
), p. 011708
. 4.
Yang
, Z.
, Liu
, J.
, Ding
, X.
, and Zhang
, F.
, 2019
, “The Effect of Anisotropy on the Percolation Threshold of Sealing Surfaces
,” ASME J. Tribol.
, 141
(2
), p. 022203
. 5.
Panagouli
, O. K.
, Margaronis
, K.
, and Tsotoulidou
, V.
, 2020
, “A Multiscale Model for Thermal Contact Conductance of Rough Surfaces Under Low Applied Pressure
,” Int. J. Solids Struct.
, 200–201
, pp. 106
–118
. 6.
Ren
, X.-J.
, Dai
, Y.-J.
, Gou
, J.-J.
, and Tao
, W.-Q.
, 2021
, “Numerical Study on Thermal Contact Resistance of 8-Harness Satin Woven Pierced Composite
,” Int. J. Therm. Sci.
, 159
, p. 106584
. 7.
Zhang
, S.
, Zhao
, X.
, Ye
, M.
, and He
, Y.
, 2019
, “Theoretical and Experimental Study on Electrical Contact Resistance of Metal Bolt Joints
,” IEEE Trans. Compon. Packag. Manuf. Technol.
, 9
(7
), pp. 1301
–1309
. 8.
Zhang
, C.
, and Ren
, W.
, 2021
, “Modeling of 3D Surface Morphologies for Predicting the Mechanical Contact Behaviors and Associated Electrical Contact Resistance
,” Tribol. Lett.
, 69
(1
), p. 20
. 9.
Greenwood
, J. A.
, and Williamson
, J. B. P.
, 1966
, “Contact of Nominally Flat Surfaces
,” Proc. R. Soc. Lond. Ser. Math. Phys. Sci.
, 295
(1442
), pp. 300
–319
. 10.
Persson
, B. N. J.
, 2001
, “Elastoplastic Contact Between Randomly Rough Surfaces
,” Phys. Rev. Lett.
, 87
(11
), p. 116101
. 11.
Hu
, Y.
, Barber
, G. C.
, and Zhu
, D.
, 1999
, “Numerical Analysis for the Elastic Contact of Real Rough Surfaces
,” Tribol. Trans.
, 42
(3
), pp. 443
–452
. 12.
Pei
, L.
, Hyun
, S.
, Molinari
, J. F.
, and Robbins
, M. O.
, 2005
, “Finite Element Modeling of Elasto-Plastic Contact Between Rough Surfaces
,” J. Mech. Phys. Solids
, 53
(11
), pp. 2385
–2409
. 13.
Hu
, H.
, Batou
, A.
, and Ouyang
, H.
, 2022
, “An Isogeometric Analysis Based Method for Frictional Elastic Contact Problems With Randomly Rough Surfaces
,” Comput. Methods Appl. Mech. Eng.
, 394
, p. 114865
. 14.
Hughes
, T. J. R.
, Cottrell
, J. A.
, and Bazilevs
, Y.
, 2005
, “Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement
,” Comput. Methods Appl. Mech. Eng.
, 194
(39
), pp. 4135
–4195
. 15.
Cottrell
, J. A.
, Hughes
, T. J. R.
, and Bazilevs
, Y.
, 2009
, Isogeometric Analysis: Toward Integration of CAD and FEA
, John Wiley & Sons
, Hoboken, NJ
.16.
Piegl
, L.
, and Tiller
, W.
, 1997
, The NURBS Book
, Springer Berlin Heidelberg
, Berlin, Heidelberg
.17.
Alizadeh
, R.
, Allen
, J. K.
, and Mistree
, F.
, 2020
, “Managing Computational Complexity Using Surrogate Models: A Critical Review
,” Res. Eng. Des.
, 31
(3
), pp. 275
–298
. 18.
Herrmann
, L.
, and Kollmannsberger
, S.
, 2024
, “Deep Learning in Computational Mechanics: A Review
,” Comput. Mech.
, 74
(2
), pp. 281
–331
. 19.
Guo
, H.
, Zhuang
, X.
, Fu
, X.
, Zhu
, Y.
, and Rabczuk
, T.
, 2023
, “Physics-Informed Deep Learning for Three-Dimensional Transient Heat Transfer Analysis of Functionally Graded Materials
,” Comput. Mech.
, 72
(3
), pp. 513
–524
. 20.
Jiang
, Z.
, Jiang
, J.
, Yao
, Q.
, and Yang
, G.
, 2023
, “A Neural Network-Based PDE Solving Algorithm With High Precision
,” Sci. Rep.
, 13
(1
), p. 4479
. 21.
Bai
, J.
, Rabczuk
, T.
, Gupta
, A.
, Alzubaidi
, L.
, and Gu
, Y.
, 2023
, “A Physics-Informed Neural Network Technique Based on a Modified Loss Function for Computational 2D and 3D Solid Mechanics
,” Comput. Mech.
, 71
(3
), pp. 543
–562
. 22.
Zhu
, Q.
, Zhao
, Z.
, and Yan
, J.
, 2023
, “Physics-Informed Machine Learning for Surrogate Modeling of Wind Pressure and Optimization of Pressure Sensor Placement
,” Comput. Mech.
, 71
(3
), pp. 481
–491
. 23.
Taghizadeh
, M.
, Nabian
, M. A.
, and Alemazkoor
, N.
, 2024
, “Multi-Fidelity Physics-Informed Generative Adversarial Network for Solving Partial Differential Equations
,” ASME J. Comput. Inf. Sci. Eng.
, 24
(11
), p. 111003
. 24.
Faroughi
, S. A.
, Pawar
, N. M.
, Fernandes
, C.
, Raissi
, M.
, Das
, S.
, Kalantari
, N. K.
, and Kourosh Mahjour
, S.
, 2024
, “Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics
,” ASME J. Comput. Inf. Sci. Eng.
, 24
(4
), p. 040802
. 25.
Bhaduri
, A.
, Ramachandra
, N.
, Krishnan Ravi
, S.
, Luan
, L.
, Pandita
, P.
, Balaprakash
, P.
, Anitescu
, M.
, Sun
, C.
, and Wang
, L.
, 2024
, “Efficient Mapping Between Void Shapes and Stress Fields Using Deep Convolutional Neural Networks With Sparse Data
,” ASME J. Comput. Inf. Sci. Eng.
, 24
(5
), p. 051008
. 26.
Chen
, J.
, Pierce
, J.
, Williams
, G.
, Simpson
, T. W.
, Meisel
, N.
, Prabha Narra
, S.
, and McComb
, C.
, 2024
, “Accelerating Thermal Simulations in Additive Manufacturing by Training Physics-Informed Neural Networks With Randomly Synthesized Data
,” ASME J. Comput. Inf. Sci. Eng.
, 24
(1
), p. 011004
. 27.
Zhu
, T.
, Zheng
, Q.
, and Lu
, Y.
, 2024
, “Physics-Informed Fully Convolutional Networks for Forward Prediction of Temperature Field and Inverse Estimation of Thermal Diffusivity
,” ASME J. Comput. Inf. Sci. Eng.
, 24
(11
), p. 111004
. 28.
Raissi
, M.
, Perdikaris
, P.
, and Karniadakis
, G. E.
, 2019
, “Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations
,” J. Comput. Phys.
, 378
, pp. 686
–707
. 29.
Haghighat
, E.
, Raissi
, M.
, Moure
, A.
, Gomez
, H.
, and Juanes
, R.
, 2021
, “A Physics-Informed Deep Learning Framework for Inversion and Surrogate Modeling in Solid Mechanics
,” Comput. Methods Appl. Mech. Eng.
, 379
, p. 113741
. 30.
Gao
, H.
, Sun
, L.
, and Wang
, J.-X.
, 2021
, “PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain
,” J. Comput. Phys.
, 428
, p. 110079
. 31.
Janssen
, J. A.
, Haikal
, G.
, DeCarlo
, E. C.
, Hartnett
, M. J.
, and Kirby
, M. L.
, 2024
, “A Physics-Informed General Convolutional Network for the Computational Modeling of Materials With Damage
,” ASME J. Comput. Inf. Sci. Eng.
, 24
(11
), p. 111002
. 32.
Lu
, L.
, Jin
, P.
, Pang
, G.
, Zhang
, Z.
, and Karniadakis
, G. E.
, 2021
, “Learning Nonlinear Operators Via DeepONet Based on the Universal Approximation Theorem of Operators
,” Nat. Mach. Intell.
, 3
(3
), pp. 218
–229
. 33.
Wang
, S.
, Wang
, H.
, and Perdikaris
, P.
, 2021
, “Learning the Solution Operator of Parametric Partial Differential Equations With Physics-Informed DeepONets
,” Sci. Adv.
, 7
(40
), p. eabi8605
. 34.
Lagaris
, I. E.
, Likas
, A.
, and Fotiadis
, D. I.
, 1998
, “Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
,” IEEE Trans. Neural Netw.
, 9
(5
), pp. 987
–1000
. 35.
Mezzadri
, F.
, Gasick
, J.
, and Qian
, X.
, 2023
, “A Framework for Physics-Informed Deep Learning Over Freeform Domains
,” Comput.-Aided Des.
, 160
, p. 103520
. 36.
Chen
, T.
, and Chen
, H.
, 1995
, “Universal Approximation to Nonlinear Operators by Neural Networks With Arbitrary Activation Functions and Its Application to Dynamical Systems
,” IEEE Trans. Neural Netw.
, 6
(4
), pp. 911
–917
. 37.
Zhang
, J.
, Zhang
, S.
, and Lin
, G.
, 2022
, MultiAuto-DeepONet: A Multi-Resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problems,” Preprint arXiv: 2204.03193. 38.
Wu
, K.
, Yan
, X.-B.
, Jin
, S.
, and Ma
, Z.
, 2024
, “Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONets
,” Comput. Methods Appl. Mech. Eng.
, 418
, p. 116531
. 39.
Oommen
, V.
, Shukla
, K.
, Goswami
, S.
, Dingreville
, R.
, and Karniadakis
, G. E.
, 2022
, “Learning Two-Phase Microstructure Evolution Using Neural Operators and Autoencoder Architectures
,” Npj Comput. Mater.
, 8
(1
), pp. 1
–13
. 40.
He
, J.
, Koric
, S.
, Kushwaha
, S.
, Park
, J.
, Abueidda
, D.
, and Jasiuk
, I.
, 2023
, “Novel DeepONet Architecture to Predict Stresses in Elastoplastic Structures With Variable Complex Geometries and Loads
,” Comput. Methods Appl. Mech. Eng.
, 415
, p. 116277
. 41.
Diakogiannis
, F. I.
, Waldner
, F.
, Caccetta
, P.
, and Wu
, C.
, 2020
, “ResUNet-a: A Deep Learning Framework for Semantic Segmentation of Remotely Sensed Data
,” ISPRS J. Photogramm. Remote Sens.
, 162
, pp. 94
–114
. 42.
Schwing
, A. G.
, and Urtasun
, R.
, 2015
, Fully Connected Deep Structured Networks,” Preprint arXiv: 1503.02351. 43.
Sahin
, T.
, von Danwitz
, M.
, and Popp
, A.
, 2024
, “Solving Forward and Inverse Problems of Contact Mechanics Using Physics-Informed Neural Networks
,” Adv. Model. Simul. Eng. Sci.
, 11
(1
), p. 11
. 44.
Goodfellow
, I.
, Pouget-Abadie
, J.
, Mirza
, M.
, Xu
, B.
, Warde-Farley
, D.
, Ozair
, S.
, Courville
, A.
, and Bengio
, Y.
, 2014
, “Generative Adversarial Nets,” Advances in Neural Information Processing Systems
, Z.
Ghahramani
, M.
Welling
, C.
Cortes
, N.
Lawrence
, and K. Q.
Weinberger
, eds., Curran Associates, Inc.
, Montreal, QC, Canada
, pp. 2672
–2680
.45.
Pérez-Ràfols
, F.
, and Almqvist
, A.
, 2019
, “Generating Randomly Rough Surfaces With Given Height Probability Distribution and Power Spectrum
,” Tribol. Int.
, 131
, pp. 591
–604
. 46.
Lockyer
, P. S.
, 2007
, Controlling the Interpolation of NURBS Curves and Surfaces
, University of Birmingham
, Edgbaston, Birmingham, UK
.47.
LeCun
, Y.
, and Bengio
, Y.
, 1998
, “Convolutional Networks for Images, Speech, and Time Series,” The Handbook of Brain Theory and Neural Networks
, M. A.
Arbib
, ed., MIT Press
, Cambridge, MA
, pp. 255
–258
.48.
Kingma
, D. P.
, and Ba
, J.
, 2017
, “Adam: A Method for Stochastic Optimization,” Preprint arXiv: 1412.6980. 49.
Bradbury
, J.
, Frostig
, R.
, Hawkins
, P.
, Johnson
, M. J.
, Leary
, C.
, Maclaurin
, D.
, Necula
, G.
, et al, 2018
, “JAX: Composable Transformations of Python+ NumPy Programs.”50.
Tan
, L.
, and Chen
, L.
, 2022
, “Enhanced DeepONet for Modeling Partial Differential Operators Considering Multiple Input Functions,” Preprint arXiv: 2202.08942. Copyright © 2025 by ASME
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