A neural network enhanced system for learning nonlinear constitutive law and failure initiation criterion of composites using indirectly measurable data

2020 ◽  
Vol 252 ◽  
pp. 112658 ◽  
Author(s):  
Xin Liu ◽  
Fei Tao ◽  
Wenbin Yu
Keyword(s):  
Neural Network ◽  
Constitutive Law ◽  
Failure Initiation ◽  
Nonlinear Constitutive Law

Prediction of Non-Linear Mechanical Behavior With Deep Neural Network: Application on Low Pressure Turbine Disc

2020 ◽  
Author(s):  
Yuan Jin ◽  
Weichen Li ◽  
Zheyi Yang ◽  
Olivier Jung
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Displacement Field ◽  
Deep Neural Network ◽  
Low Pressure ◽  
Constitutive Law ◽  
Design Parameters ◽  
Low Pressure Turbine ◽  
Turbine Disc ◽  
Nonlinear Constitutive Law

Abstract Thanks to the increase of computational capacity and the diversification of computational means, deep learning techniques have shown great successes in learning representations from data in the past decade. Following this trend, efforts have been made in the literature to apply Deep Neural Network (DNN) as surrogate model. Common practice consists in utilizing a single DNN to predict a certain physical property given input design parameters, and the DNN is trained by corresponding simulation results. However, most of the complex high-fidelity simulations involve nonlinear physical laws, e.g. elasto-plasticity, which cannot be explicitly depicted by the applied single DNN model. In the present work, static mechanical simulation with nonlinear constitutive law is addressed with a novel approach in a deep learning framework. We approximate the displacement and the nonlinear constitutive law by two deep neural networks. The first DNN acts as a prior on the unknown displacement field, while the second network aims at describing the nonlinear strain-stress relationship. The dependence of the strainstress relationship on the strain level is taken into consideration by taking the first order derivative with respect to spatial coordinates of the first DNN as an input of the second network. A new loss model combining the error in displacement field prediction and constitutive law description is proposed to train the two DNNs together. We demonstrate the effectiveness of the proposed framework on a low pressure turbine disc design problem.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

scholarly journals Application of the Generalized Nonlinear Constitutive Law to Hollow-Core Slabs

2021 ◽  
Author(s):  
Natalia Staszak ◽  
Tomasz Garbowski ◽  
Barbara Ksit
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Crack Opening ◽  
Constitutive Law ◽  
Fe Model ◽  
Hollow Core ◽  
Linear Finite Element ◽  
Deformation State ◽  
Non Linear ◽  
Nonlinear Constitutive Law

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. Preferably based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

Learning Nonlinear Constitutive Laws Using Neural Network Models Based on Indirectly Measurable Data

2020 ◽  
Vol 87 (8) ◽  
Author(s):  
Xin Liu ◽  
Fei Tao ◽  
Haodong Du ◽  
Wenbin Yu ◽  
Kailai Xu
Keyword(s):  
Neural Network ◽  
Damage Model ◽  
Network Models ◽  
Great Accuracy ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Ann Model ◽  
Neural Network Models ◽  
Plane Shear ◽  
Ann Models

Abstract Artificial neural network (ANN) models are used to learn the nonlinear constitutive laws based on indirectly measurable data. The real input and output of the ANN model are derived from indirect data using a mechanical system, which is composed of several subsystems including the ANN model. As the ANN model is coupled with other subsystems, the input of the ANN model needs to be determined during the training. This approach integrates measurable data, mechanics, and ANN models so that the ANN models can be trained without direct data which is usually not available from experiments. Two examples are provided as an illustration of the proposed approach. The first example uses two-dimensional (2D) finite element (FE) analysis to train an ANN model to learn the nonlinear in-plane shear constitutive law. The second example applies a continuum damage model to train an ANN model to learn the damage accumulation law. The results show that the trained ANN models achieve great accuracy based on the proposed approach.

scholarly journals Generalized Nonlinear Constitutive Law Applied to Steel Trapezoidal Sheet Plates

2021 ◽  
Author(s):  
Natalia Staszak ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Degrees Of Freedom ◽  
Nonlinear Finite Element ◽  
Constitutive Law ◽  
Shell Structures ◽  
Nonlinear Material ◽  
Nonlinear Finite Element Method ◽  
Nonlinear Materials ◽  
Nonlinear Constitutive Law

In the paper, a modified nonlinear finite element method for analysis of trapezoidal plates geometrically reduced to shallow-shell Reissner-Mindlin formulation is presented. Due to the method proposed the complex plate cross-section and nonlinear materials may be modelled and no implementation of advanced constitutive law via user subroutines is needed. The generalized nonlinear constitutive law is used to update the stiffness of the plate element. The method enables modeling of complicated cross-sections, such as steel trapezoidal sheets, metal facing sandwich panels or reinforced concrete. Additionally, for those geometrically complex sections an advanced nonlinear material may be adopted. To verify the proposed method, a selected trapezoidal sheets were modeled in a commercial software as full 3D shell structures. By comparing displacements and forces, it was shown that both models behave almost identically, however, the simplified model has about 300-400 times less degrees of freedom, thus it is much more efficient.

A neural network framework for mechanical behavior of unsaturated soils

2003 ◽  
Vol 40 (3) ◽  
pp. 684-693 ◽  
Author(s):  
Ghassem Habibagahi ◽  
Alireza Bamdad
Keyword(s):  
Neural Network ◽  
Mechanical Behavior ◽  
Unsaturated Soils ◽  
Axial Strain ◽  
Volumetric Strain ◽  
Constitutive Law ◽  
Soil Conditions ◽  
Neural Network Approach ◽  
Network Simulations ◽  
Multilayer Perceptron Network

In this paper, a neural network approach is used to describe the mechanical behavior of unsaturated soils. A sequential architecture was chosen for the network, that is, a multilayer perceptron network with feedback capability. The input layer consisted of nine neurons, where six of them represented the initial soil conditions and the remaining three neurons were continuously updated for each increment of axial strain based on outputs from the previous increment. The output layer consisted of three neurons representing values of deviatoric stress, volumetric strain, and change in suction at the end of each increment. Next, a database was developed from triaxial test results available in the literature. The database was used to train and test the network. Neural network simulations were compared with experimental results. The comparison indicates the good performance of the proposed network for predicting the mechanical behavior of unsaturated soils. Moreover, the trained network was employed to simulate other stress paths not present in the database to model the so-called "collapse phenomena." The results were promising.Key words: unsaturated soil, neural network, stress–strain, collapse, modeling, constitutive law.

Some aspects of application of artificial neural network for numerical modeling in civil engineering

2013 ◽  
Vol 61 (1) ◽  
pp. 39-50 ◽  
Author(s):  
M. Lefik
Keyword(s):  
Neural Network ◽  
Inverse Problem ◽  
Artificial Neural Network ◽  
Finite Element ◽  
Civil Engineering ◽  
Constitutive Law ◽  
Finite Element Code ◽  
Hybrid Finite Element ◽  
Artificial Neural ◽  
Theoretical Results

Abstract In order to obtain reliable results of computations in civil engineering, the numerical procedures that are used at the stage of design should be calibrated by comparison of the theoretical results with an observed behavior of previously modeled and then executed structures. The hybrid Finite Element code with an Artificial Neural Network inserted as a representation of a constitutive law, offers a possibility to adjust not only parameters of the constitutive relationships but also its qualitative form. Because of this, the representation of constitutive law by the ANN is presented in this paper. The constitutive data should be calibrated to fit well the observable values, measured in experiments. If the constitutive law is expressed by ANN, the inverse problem can be reduce to a training of the ANN inserted into the Finite Element code. An example of a solution of the inverse problem in calibration of constitutive law is presented. An identification of parameters of flow of pollutant in soils is described as another example of application of ANN in engineering

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