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End date: 2024 × Start date: 2020 × Has files: Yes × Subject: Homogenization ×

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Now showing 1 - 5 of 5
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    Intrinsic modulus and strain coefficients in dilute composites with a Neo-Hookean elastic matrix
    (Amsterdam : Elsevier, 2022) Ivaneyko, Dmytro; Domurath, Jan; Heinrich, Gert; Saphiannikova, Marina
    A finite element modelling of dilute elastomer composites based on a Neo-Hookean elastic matrix and rigid spherical particles embedded within the matrix was performed. In particular, the deformation field in vicinity of a sphere was simulated and numerical homogenization has been used to obtain the effective modulus of the composite μeff for different applied extension and compression ratios. At small deformations the well-known Smallwood result for the composite is reproduced: μeff=(1+[μ]φ)μ0 with the intrinsic modulus [μ]=2.500. Here φ is the volume fraction of particles and μ0 is the modulus of the matrix solid. However at larger deformations higher values of the intrinsic modulus [μ] are obtained, which increase quadratically with the applied true strain. The homogenization procedure allowed to extract the intrinsic strain coefficients which are mirrored around the undeformed state for principle extension and compression axes. Utilizing the simulation results, stress and strain modifications of the Neo-Hookean strain energy function for dilute composites are proposed.
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    Prediction of Short Fiber Composite Properties by an Artificial Neural Network Trained on an RVE Database
    (Basel : MDPI, 2021) Breuer, Kevin; Stommel, Markus
    In this study, an artificial neural network is designed and trained to predict the elastic properties of short fiber reinforced plastics. The results of finite element simulations of three-dimensional representative volume elements are used as a data basis for the neural network. The fiber volume fraction, fiber length, matrix-phase properties, and fiber orientation are varied so that the neural network can be used within a very wide range of parameters. A comparison of the predictions of the neural network with additional finite element simulations shows that the stiffnesses of short fiber reinforced plastics can be predicted very well by the neural network. The average prediction accuracy is equal or better than by a two-step homogenization using the classical method of Mori and Tanaka. Moreover, it is shown that the training of the neural network on an extended data set works well and that particularly calculation-intensive data points can be avoided without loss of prediction quality.
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    Statistical Analysis of Mechanical Stressing in Short Fiber Reinforced Composites by Means of Statistical and Representative Volume Elements
    (Basel : MDPI, 2021) Breuer, Kevin; Spickenheuer, Axel; Stommel, Markus
    Analyzing representative volume elements with the finite element method is one method to calculate the local stress at the microscale of short fiber reinforced plastics. It can be shown with Monte-Carlo simulations that the stress distribution depends on the local arrangement of the fibers and is therefore unique for each fiber constellation. In this contribution the stress distribution and the effective composite properties are examined as a function of the considered volume of the representative volume elements. Moreover, the influence of locally varying fiber volume fraction is examined, using statistical volume elements. The results show that the average stress probability distribution is independent of the number of fibers and independent of local fluctuation of the fiber volume fraction. Furthermore, it is derived from the stress distributions that the statistical deviation of the effective composite properties should not be neglected in the case of injection molded components. A finite element analysis indicates that the macroscopic stresses and strains on component level are significantly influenced by local, statistical fluctuation of the composite properties.
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    Precompact probability spaces in applied stochastic homogenization
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Heida, Martin
    We provide precompactness and metrizability of the probability space Ω for random measures and random coefficients such as they widely appear in stochastic homogenization and are typically given from data. We show that these properties are enough to implement the convenient two-scale formalism by Zhikov and Piatnitsky (2006). To further demonstrate the benefits of our approach we provide some useful trace and extension operators for Sobolev functions on Ω, which seem not known in literature. On the way we close some minor gaps in the Sobolev theory on Ω which seemingly have not been proven up to date.
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    Stochastic homogenization on perforated domains II -- Application to nonlinear elasticity models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Heida, Martin
    Based on a recent work that exposed the lack of uniformly bounded W1,p → W1,p extension operators on randomly perforated domains, we study stochastic homogenization of nonlinear elasticity on such structures using instead the extension operators constructed in [11]. We thereby introduce two-scale convergence methods on such random domains under the intrinsic loss of regularity and prove some generally useful calculus theorems on the probability space Ω, e.g. abstract Gauss theorems.