A data-driven approach to nonlinear elasticity

Nguyen, Lu Trong Khiem; Keip, Marc‐André

doi:10.1016/j.compstruc.2017.07.031

Cited by 142 publications

(91 citation statements)

References 32 publications

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“…The convergence properties of the fixed-point solver (13) have been investigated in [1]. The Data-Driven paradigm has been extended to dynamics [3], finite kinematics [34] and objective functions other than phase-space distance can be found in [2]. The well-posedness of Data-Driven problems and properties of convergence with respect to the data set have been investigated in [4].…”

Section: (12b)mentioning

confidence: 99%

Model-Free Data-Driven inelasticity

Eggersmann

Kirchdoerfer

Reese

et al. 2019

Computer Methods in Applied Mechanics and Engineering

220

140

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We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz [1] to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for the evolving material data sets: i) materials with memory, i. e., conditioning the material data set to the past history of deformation; ii) differential materials, i. e., conditioning the material data set to short histories of stress and strain; and iii) history variables, i. e., conditioning the material data set to ad hoc variables encoding partial information about the history of stress and strain. We also consider combinations of the three paradigms thereof and investigate their ability to represent the evolving data sets of different classes of inelastic materials, including viscoelasticity, viscoplasticity and plasticity. We present selected numerical examples that demonstrate the range and scope of Data-Driven inelasticity and the numerical performance of implementations thereof.

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Section: (12b)mentioning

confidence: 99%

Model-Free Data-Driven inelasticity

Eggersmann

Kirchdoerfer

Reese

et al. 2019

Computer Methods in Applied Mechanics and Engineering

220

140

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“…In these works, the material behavior is only described by data. The idea is to find the point in the data set which is closest to the constraint set given by kinematical relations, balance laws and boundary conditions (see also [46,47]).…”

Section: Machine Learning Methods As An Alternative To Materials Modelsmentioning

confidence: 99%

Application of artificial neural networks for the prediction of interface mechanics: a study on grain boundary constitutive behavior

Fernández

Rezaei

Mianroodi

et al. 2020

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

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The present work aims at the identification of the effective constitutive behavior of 5 aluminum grain boundaries (GB) for proportional loading by using machine learning (ML) techniques. The input for the ML approach is high accuracy data gathered in challenging molecular dynamics (MD) simulations at the atomic scale for varying temperatures and loading conditions. The effective traction-separation relation is recorded during the MD simulations. The raw MD data then serves for the training of an artificial neural network (ANN) as a surrogate model of the constitutive behavior at the grain boundary. Despite the extremely fluctuating nature of the MD data and its inhomogeneous distribution in the traction-separation space, the ANN surrogate trained on the raw MD data shows a very good agreement in the average behavior without any data-smoothing or pre-processing. Further, it is shown that the trained traction-separation ANN captures important physical properties and is able to predict traction values for given separations not contained in the training data. For example, MD simulations show a transition in traction-separation behaviour from pure sliding mode under shear load to combined GB sliding and decohesion with intermediate hardening regime at mixed load directions. These changes in GB behaviour are fully captured in the ANN predictions. Furthermore, by construction, the ANN surrogate is differentiable for arbitrary separation and also temperature, such that a thermo-mechanical tangent stiffness operator can always be evaluated. The trained ANN can then serve for large-scale FE simulation as an alternative to direct MD-FE coupling which is often infeasible in practical applications.

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“…The convergence properties of the fixed-point solver (13) have been investigated in [7]. The Data-Driven paradigm has been extended to dynamics [9], finite kinematics [13] and objective functions other than phase-space distance can be found in [8]. The well-posedness of Data-Driven problems and properties of convergence with respect to the data set have been investigated in [1].…”

Section: Data-driven Simulation Algorithmmentioning

confidence: 99%

Model-free data-driven methods in mechanics: material data identification and solvers

2019

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This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain-stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a nonconventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the datadriven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns.

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A data-driven approach to nonlinear elasticity

Cited by 142 publications

References 32 publications

Model-Free Data-Driven inelasticity

Model-Free Data-Driven inelasticity

Application of artificial neural networks for the prediction of interface mechanics: a study on grain boundary constitutive behavior

Model-free data-driven methods in mechanics: material data identification and solvers

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