Asymptotic Theory of Viscoelastic Multilayer Thin Composite Plates

When designing products made of composite materials intended for use in difficult conditions of inhomogeneous deformations and temperatures, it is important to take into account viscoelastic, including spectral and dynamic, properties of the binder and fillers. The article considers dynamic characteristics (complex modulus, complex malleability, their real and imaginary parts, loss angle tangent) and spectral characteristics of relaxation and creep and their dependence on each other. The abovementioned characteristics were found for all known types of creep kernel and relaxation kernel. To find the spectral characteristics, one of the numerical methods of reversing the Laplace transformation was used - the method of quadrature formulas. Algorithms and computer programs have been compiled to implement this method.

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“…Where G t and J t are relaxation and creep functions, respectively [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Mathematical Formulations Of the Problem Accepted Assumptionsmentioning

confidence: 99%

“…Complex modulus and complex malleability, as the name implies, have real and imaginary parts: (14) Where the left side of the equality, by definition, is called the tangent of the loss angle…”

Section: Dynamic Characteristics Of Viscoelastic Materials and The Re...mentioning

confidence: 99%

Modeling of dynamic and spectral viscoelastic characteristics of composite materials

Valishin

Tinyaev²

2023

E3S Web of Conf.

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“…In [16], to calculate the viscoelasticity operators of composites, it was proposed to use the method of asymptotic averaging, and to invert these operators, a generalization of the approximation method by A.A. Ilyushin [17]. Various versions of the method for applying the averaging method for calculating the stress-strain state of thin viscoelastic structures were proposed in [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Finite element modeling of integral viscoelastic properties of textile composites

Dimitrienko

Yurin²,

Bogdanov³

et al. 2023

E3S Web of Conf.

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The problem of modeling the effective integral viscoelastic properties of unidirectional composite materials is considered. To calculate the integral properties of viscoelasticity, the Fourier transform and the inverse Fourier transform are used, as well as the method of asymptotic averaging for composites with steady polyharmonic vibrations, and a finite element algorithm for solving local problems of the viscoelasticity theory on the periodicity cell of the composite. To obtain the material constants, a method of approximation of the Fourier images of the relaxation and creep kernels is proposed, which makes it possible to avoid the numerical error of the inverse Fourier transform.

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“…Artificial neural networks (ANN) models are arguably the most popular machine learning technique due to their great performance in many fields and their ability to approximate very complex relations. Some of the most interesting opp5rtunities brought by AI to composite materials science and mechanics include discovery of unknown constitutive laws, acceleration of multiscale modeling, design optimisation, damage detection and quality control integrated with manufacturing processes, additive manufacturing, and analysis of process-structure-property-performance relationships [1][2][3][4][5][6][7][8][9]. However, despite the promising uses of AI in composite materials mechanics, new challenges and problems arise, like the high computational cost of high-quality data generation based on complex numerical simulations and mechanical models [1][2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Applying neural networks to analyse the properties and structure of composite materials

Valishin

Beriachvili²

2023

E3S Web of Conf.

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In this paper, we show how a simple convolutional neural network (CNN) can be trained to predict homogenised elastic properties of a composite material based on its representative volume element (RVE). We consider both 2D and 3D composites featuring two components with fixed isotropic elastic properties. The dataset used to train the neural network is obtained in two stages. The first stage is the generation of random RVEs and computation of their homogenised elastic properties using finite element analysis (FEA) with periodic boundary conditions (PBC) applied to them, and the second stage is the application of a data augmentation scheme to that dataset obtained in the first stage. For the 2D and 3D cases, we present two neural networks and show that they are able to estimate the values of homogenised elastic properties fairly accurately. At the same time, we confirm that the data generation stage is computationally very expensive and is a major challenge for machine learning based techniques in computational mechanics. Indeed, it is expensive even for “low resolution” RVEs such as those considered in our work, i.e. squares (2D case) or cubes (3D case) uniformly subdivided into 8x8 (2D case) or 8x8x8 (3D case) domains. We discuss the flaws and drawbacks as well as the possible developments and uses of this approach in multiscale modeling of composite materials.

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Asymptotic Theory of Viscoelastic Multilayer Thin Composite Plates

Cited by 9 publications

References 6 publications

Modeling of dynamic and spectral viscoelastic characteristics of composite materials

Modeling of dynamic and spectral viscoelastic characteristics of composite materials

Finite element modeling of integral viscoelastic properties of textile composites

Applying neural networks to analyse the properties and structure of composite materials

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