Weakly-invasive LATIN-PGD for solving time-dependent non-linear parametrized problems in solid mechanics

Scanff, Ronan; Néron, David; Barabinot, Philippe; Cugnon, Frédéric; Delsemme, Jean-Pierre

doi:10.1016/j.cma.2022.114999

Cited by 10 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper focuses on the implementation-and the difficulties associated with-of the LATIN-PGD method in an industrial finite element software. Fundamentals as convergence and robustness studies will be presented in companion paper [27]. At the present time, what has been done fits into the framework of moderate displacements, outside instability zones.…”

Section: Introductionmentioning

confidence: 94%

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

Barabinot

Scanff

Néron

et al. 2021

Adv. Model. and Simul. in Eng. Sci.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 94%

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

Barabinot

Scanff

Néron

et al. 2021

Adv. Model. and Simul. in Eng. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since the bottleneck of FE 2 lies in computing lower-scale models, a popular approach to reduce computational effort is to substitute the original FE micromodels with either structure-preserving reduced-order models [15][16][17][18][19][20][21] or purely data-driven surrogates [22][23][24][25][26][27] trained offline. More recently, Recurrent Neural Networks (RNN) have become the model of choice especially for strain path-dependent materials, with a large body of literature dedicated to their use and tuning to different applications [28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Machine learning of evolving physics-based material models for multiscale solid mechanics

Rocha¹,

Kerfriden²,

Meer³

2023

Preprint

View full text Add to dashboard Cite

In this work we present a hybrid physics-based and data-driven learning approach to construct surrogate models for concurrent multiscale simulations of complex material behavior. We start from robust but inflexible physics-based constitutive models and increase their expressivity by allowing a subset of their material parameters to change in time according to an evolution operator learned from data. This leads to a flexible hybrid model combining a data-driven encoder and a physics-based decoder. Apart from introducing physics-motivated bias to the resulting surrogate, the internal variables of the decoder act as a memory mechanism that allows path dependency to arise naturally. We demonstrate the capabilities of the approach by combining an FNN encoder with several plasticity decoders and training the model to reproduce the macroscopic behavior of fiber-reinforced composites. The hybrid models are able to provide reasonable predictions of unloading/reloading behavior while being trained exclusively on monotonic data. Furthermore, in contrast to traditional surrogates mapping strains to stresses, the specific architecture of the hybrid model allows for lossless dimensionality reduction and straightforward enforcement of frame invariance by using strain invariants as the feature space of the encoder.

show abstract

Semi-reduced order stochastic finite element methods for solving contact problems with uncertainties

Zheng

Nackenhorst

2023

Comput Mech

View full text Add to dashboard Cite

This paper develops two-step methods for solving contact problems with uncertainties. In the first step, we propose stochastic Lagrangian multiplier/penalty methods to compute a set of reduced basis. In the stochastic Lagrangian multiplier method, the stochastic solution is represented as a sum of products of a set of random variables and deterministic vectors. In the stochastic penalty method, the problem is divided into the solutions of non-contact and possible contact nodes, which are represented as sums of the products of two different sets of random variables and deterministic vectors, respectively. The original problems are then transformed into deterministic finite element equations and one-dimensional (corresponding to stochastic Lagrangian multiplier method)/two-dimensional (corresponding to stochastic penalty method) stochastic algebraic equations. The deterministic finite element equations are solved by existing numerical techniques, and the one-/two-dimensional stochastic algebraic equations are solved by a sampling method. Since the computational cost for solving stochastic algebraic equations does not increase dramatically as the stochastic dimension increases, the proposed methods avoid the curse of dimensionality in high-dimensional problems. Based on the reduced basis, we propose semi-reduced order Lagrangian multiplier/penalty equations with two components in the second step. One component is a reduced order equation obtained by smooth solutions of the reduced basis and the other is the full order equation for the nonsmooth solutions. A significant amount of computational cost is saved since the sizes of the semi-reduced order equations are usually small. Numerical examples of up to 100 dimensions demonstrate the good performance of the proposed methods.

show abstract

Weakly-invasive LATIN-PGD for solving time-dependent non-linear parametrized problems in solid mechanics

Cited by 10 publications

References 34 publications

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

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

Machine learning of evolving physics-based material models for multiscale solid mechanics

Semi-reduced order stochastic finite element methods for solving contact problems with uncertainties

Contact Info

Product

Resources

About