Industrial Digital Twins based on the non-linear LATIN-PGD

Digital Twins, which tend to intervene over the entire life cycle of products from early design phase to predictive maintenance through optimization processes, are increasingly emerging as an essential component in the future of industries. To reduce the computational time reduced-order modeling (ROM) methods can be useful. However, the spread of ROM methods at an industrial level is currently hampered by the difficulty of introducing them into commercial finite element software, due to the strong intrusiveness of the associated algorithms, preventing from getting robust and reliable tools all integrated in a certified product. This work tries to circumvent this issue by introducing a weakly-invasive reformulation of the LATIN-PGD method which is intended to be directly embedded into Simcenter Samcef $$^{\hbox {TM}}$$ TM finite element software. The originality of this approach lies in the remarkably general way of doing, allowing PGD method to deal with not only a particular application but with all facilities already included in such softwares—any non-linearities, any element types, any boundary conditions...—and thus providing a new high-performance all-inclusive non-linear solver.

[1]  David Néron,et al.  A rational strategy for the resolution of parametrized problems in the PGD framework , 2013 .

[2]  O. C. Zienkiewicz,et al.  The Finite Element Method for Solid and Structural Mechanics , 2013 .

[3]  Fabien Casenave,et al.  A nonintrusive distributed reduced‐order modeling framework for nonlinear structural mechanics—Application to elastoviscoplastic computations , 2018, International Journal for Numerical Methods in Engineering.

[4]  Herman van der Auweraer,et al.  Digital Twins , 2020, SEMA SIMAI Springer Series.

[5]  Antonio Huerta,et al.  Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM , 2019, Comput. Phys. Commun..

[6]  Francisco Chinesta,et al.  Non-intrusive Sparse Subspace Learning for Parametrized Problems , 2019 .

[7]  Pierre Ladevèze,et al.  The Reference Point Method, a ``hyperreduction'' technique: Application to PGD-based nonlinear model reduction , 2017 .

[8]  P. Ladeveze,et al.  The Large Time Increment Method Applied to Cyclic Loadings , 1991 .

[9]  Dishi Liu,et al.  To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations - the "Plain Vanilla" Galerkin Case , 2013, SIAM J. Sci. Comput..

[10]  Michele Conti,et al.  A nonintrusive proper generalized decomposition scheme with application in biomechanics , 2018 .

[11]  N. Nguyen,et al.  An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .

[12]  M. Bhattacharyya,et al.  A LATIN-based model reduction approach for the simulation of cycling damage , 2018 .

[13]  Christian Rey,et al.  The finite element method in solid mechanics , 2014 .

[14]  David Néron,et al.  Time‐space PGD for the rapid solution of 3D nonlinear parametrized problems in the many‐query context , 2015 .

[15]  Pierre Ladevèze,et al.  A new approach in non‐linear mechanics: The large time increment method , 1990 .

[16]  David Néron,et al.  Integration of PGD-virtual charts into an engineering design process , 2016 .

[17]  Pierre-Alain Boucard,et al.  A parallel non-invasive mixed domain decomposition - Implementation and applications to mechanical assemblies , 2019, Finite Elements in Analysis and Design.

[18]  F. Chinesta,et al.  3 Proper generalized decomposition , 2020, Snapshot-Based Methods and Algorithms.

[19]  P. Ladevèze,et al.  Sur une famille d'algorithmes en mécanique des structures , 1985 .

[20]  D. Ryckelynck,et al.  A priori hyperreduction method: an adaptive approach , 2005 .

[21]  Francisco Chinesta,et al.  Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data , 2018, Archives of Computational Methods in Engineering.

[22]  Pierre Ladevèze,et al.  Separated Representations and PGD-Based Model Reduction , 2014 .

[23]  Edward H. Glaessgen,et al.  The Digital Twin Paradigm for Future NASA and U.S. Air Force Vehicles , 2012 .

[24]  Adrien Leygue,et al.  The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer , 2013 .

[25]  Christian Rey,et al.  Multi-fidelity bayesian optimization using model-order reduction for viscoplastic structures , 2020 .

[26]  K. Benkrid,et al.  Simulation of sheet cutting by the large time increment method , 1996 .

[27]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[28]  Y. Maday,et al.  A generalized empirical interpolation method : application of reduced basis techniques to data assimilation , 2013, 1512.00683.

[29]  Pierre Ladevèze,et al.  On reduced models in nonlinear solid mechanics , 2016 .

[30]  Pierre Ladevèze,et al.  Separated representations and PGD-based model reduction : fundamentals and applications , 2014 .

[31]  P. Ladevèze.  Nonlinear Computational Structural Mechanics: New Approaches and Non-Incremental Methods of Calculation , 1998 .

[32]  Pierre Ladevèze,et al.  PGD in linear and nonlinear Computational Solid Mechanics , 2014 .

[33]  Oddvar O. Bendiksen,et al.  Structures, Structural Dynamics and Materials Conference , 1998 .

[34]  P. Wriggers.  Nonlinear finite element analysis of solids and structures , 1998 .

[35]  Pierre Ladevèze,et al.  Nonlinear Computational Structural Mechanics , 1999 .

[36]  David Néron,et al.  A model reduction technique based on the PGD for elastic-viscoplastic computational analysis , 2013 .

[37]  S. P. van den Bosch,et al.  Model reduction methods , 1993 .

[38]  David Néron,et al.  A Study on the LATIN-PGD Method: Analysis of Some Variants in the Light of the Latest Developments , 2020, Archives of Computational Methods in Engineering.

[39]  Francisco Chinesta,et al.  A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition , 2018, Complex..