Thermodynamically consistent machine-learned internal state variable approach for data-driven modeling of path-dependent materials

He, Xiaolong; Chen, Jiun‐Shyan

doi:10.1016/j.cma.2022.115348

Cited by 32 publications

(28 citation statements)

References 59 publications

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“…Thus, internal state variables are needed for the training process. Another physically informed approach to dissipative materials, which has the advantage of requiring only stresses and strains for training, is shown in [35]. Thereby, the internal state variables capturing the path-dependency are inferred automatically from the hidden state of recurrent neural networks (RNNs).…”

Section: Overview On Data-based Constitutive Modelingmentioning

confidence: 99%

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

et al. 2023

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Herein, we present a new data-driven multiscale framework called FE$${}^\textrm{ANN}$$ ANN which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous data mining process. Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. Thereby, we restrict ourselves to finite strain hyperelasticity problems for now. By using a set of problem specific invariants as the input of the ANN and the Helmholtz free energy density as the output, several physical principles, e. g., objectivity, material symmetry, compatibility with the balance of angular momentum and thermodynamic consistency are fulfilled a priori. The necessary data for the training of the ANN-based surrogate model, i. e., macroscopic deformations and corresponding stresses, are collected via computational homogenization of representative volume elements (RVEs). Thereby, the core feature of the approach is given by a completely autonomous mining of the required data set within an overall loop. In each iteration of the loop, new data are generated by gathering the macroscopic deformation states from the macroscopic finite element simulation and a subsequently sorting by using the anisotropy class of the considered material. Finally, all unknown deformations are prescribed in the RVE simulation to get the corresponding stresses and thus to extend the data set. The proposed framework consequently allows to reduce the number of time-consuming microscale simulations to a minimum. It is exemplarily applied to several descriptive examples, where a fiber reinforced composite with a highly nonlinear Ogden-type behavior of the individual components is considered. Thereby, a rather high accuracy could be proved by a validation of the approach.

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Section: Overview On Data-based Constitutive Modelingmentioning

confidence: 99%

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

et al. 2023

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“…Figure 9 shows a possible implementation of this idea, which is similar to He and Chen. 49 Therein, at each time step, the RNN cell, which is an LSTM as shown in Figure 5 here, takes the new strain as argument as well as the time increment in case of viscous behavior and produces a new vector-valued output n h, which carries the history information and is initialized with 0 h = 0 c = 0. Subsequently, these values are fed into an FNN and are reduced…”

Section: 22mentioning

confidence: 99%

“…A similar approach tailored for the modeling of inelasticity is shown in the work. 49 In contrast to the former model, internal state variables capturing the path-dependency are inferred automatically from the hidden state of an RNN. Thus, this method has the advantage of requiring only stresses and strains for training.…”

Section: Introductionmentioning

confidence: 99%

A comparative study on different neural network architectures to model inelasticity

Rosenkranz

Kalina

Brummund

et al. 2023

Numerical Meth Engineering

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The mathematical formulation of constitutive models to describe the path‐dependent, that is, inelastic, behavior of materials is a challenging task and has been a focus in mechanics research for several decades. There have been increased efforts to facilitate or automate this task through data‐driven techniques, impelled in particular by the recent revival of neural networks (NNs) in computational mechanics. However, it seems questionable to simply not consider fundamental findings of constitutive modeling originating from the last decades research within NN‐based approaches. Herein, we propose a comparative study on different feedforward and recurrent neural network architectures to model 1D small strain inelasticity. Within this study, we divide the models into three basic classes: black box NNs, NNs enforcing physics in a weak form, and NNs enforcing physics in a strong form. Thereby, the first class of networks can learn constitutive relations from data while the underlying physics are completely ignored, whereas the latter two are constructed such that they can account for fundamental physics, where special attention is paid to the second law of thermodynamics in this work. Conventional linear and nonlinear viscoelastic as well as elastoplastic models are used for training data generation and, later on, as reference. After training with random walk time sequences containing information on stress, strain, and—for some models—internal variables, the NN‐based models are compared to the reference solution, whereby interpolation and extrapolation are considered. Besides the quality of the stress prediction, the related free energy and dissipation rate are analyzed to evaluate the models. Overall, the presented study enables a clear recording of the advantages and disadvantages of different NN architectures to model inelasticity and gives guidance on how to train and apply these models.

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“…However, its application to elastoplastic material modeling remains challenging due to difficulties in defining a material database to characterize path-dependent material behaviors. Meanwhile, machine learning techniques have been applied to construct surrogate models of constitutive laws, including Gaussian process modeling (Bostanabad et al 2018;Chen et al 2018) and artificial neural networks, such as feedforward neural networks (Ghaboussi et al 1991; He and Chen 2022) have been developed. Recently, coupling of neural networks with finite element methods and meshfree methods for modeling material damage and strain localization phenomena have also been investigated (Tao et al 2022;Baek et al 2022).…”

Section: Introductionmentioning

confidence: 99%

LS-DYNA Machine Learning–Based Multiscale Method for Nonlinear Modeling of Short Fiber–Reinforced Composites

Wei

et al. 2023

J. Eng. Mech.

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Short-fiber-reinforced composites (SFRC) are high-performance engineering materials for lightweight structural applications in the automotive and electronics industries. Typically, SFRC structures are manufactured by injection molding, which induces heterogeneous microstructures, and the resulting nonlinear anisotropic behaviors are challenging to predict by conventional micromechanical analyses. In this work, we present a machine learning-based multiscale method by integrating injection molding-induced microstructures, material homogenization, and Deep Material Network (DMN) in the finite element simulation software LS-DYNA for structural analysis of SFRC. DMN is a physics-embedded machine learning model that learns the microscale material morphologies hidden in representative volume elements of composites through offline training. By coupling DMN with finite elements, we have developed a highly accurate and efficient data-driven approach, which predicts nonlinear behaviors of composite materials and structures at a computational speed orders-of-magnitude faster than the high-fidelity direct numerical simulation. To model industrial-scale SFRC products, transfer learning is utilized to generate a unified DMN database, which effectively captures the effects of injection molding-induced fiber orientations and volume fractions on the overall composite properties. Numerical examples are presented to demonstrate the promising performance of this LS-DYNA machine learning-based multiscale method for SFRC modeling.

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Thermodynamically consistent machine-learned internal state variable approach for data-driven modeling of path-dependent materials

Cited by 32 publications

References 59 publications

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

A comparative study on different neural network architectures to model inelasticity

LS-DYNA Machine Learning–Based Multiscale Method for Nonlinear Modeling of Short Fiber–Reinforced Composites

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