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Herein, we investigate the structure-property relationships of soft magnetorheological elastomers (MREs) filled with remanently magnetizable particles. The study is motivated from experimental results which indicate a large difference between the magnetization loops of soft MREs filled with NdFeB particles and the loops of such particles embedded in a comparatively stiff matrix, e.g. an epoxy resin. We present a microscale model for MREs based on a general continuum formulation of the magnetomechanical boundary value problem which is valid for finite strains. In particular, we develop an energetically consistent constitutive model for the hysteretic magnetization behavior of the magnetically hard particles. The microstructure is discretized and the problem is solved numerically in terms of a coupled nonlinear finite element approach. Since the local magnetic and mechanical fields are resolved explicitly inside the heterogeneous microstructure of the MRE, our model also accounts for interactions of particles close to each other. In order to connect the microscopic fields to effective macroscopic quantities of the MRE, a suitable computational homogenization scheme is used. Based on this modeling approach, it is demonstrated that the observable macroscopic behavior of the considered MREs results from the rotation of the embedded particles. Furthermore, the performed numerical simulations indicate that the reversion of the sample’s magnetization occurs due to a combination of particle rotations and internal domain conversion processes. All of our simulation results obtained for such materials are in a good qualitative agreement with the experiments.

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Herein, an artificial neural network (ANN)-based approach for the efficient automated modeling and simulation of isotropic hyperelastic solids is presented. Starting from a large data set comprising deformations and corresponding stresses, a simple, physically based reduction of the problem’s dimensionality is performed in a data processing step. More specifically, three deformation type invariants serve as the input instead of the deformation tensor itself. In the same way, three corresponding stress coefficients replace the stress tensor in the output layer. These initially unknown values are calculated from a linear least square optimization problem for each data tuple. Using the reduced data set, an ANN-based constitutive model is trained by using standard machine learning methods. Furthermore, in order to ensure thermodynamic consistency, the previously trained network is modified by constructing a pseudo-potential within an integration step and a subsequent derivation which leads to a further ANN-based model. In the second part of this work, the proposed method is exemplarily used for the description of a highly nonlinear Ogden type material. Thereby, the necessary data set is collected from virtual experiments of discs with holes in pure plane stress modes, where influences of different loading types and specimen geometries on the resulting data sets are investigated. Afterwards, the collected data are used for the ANN training within the reduced data space, whereby an excellent approximation quality could be achieved with only one hidden layer comprising a low number of neurons. Finally, the application of the trained constitutive ANN for the simulation of two three-dimensional samples is shown. Thereby, a rather high accuracy could be achieved, although the occurring stresses are fully three-dimensional whereas the training data are taken from pure two-dimensional plane stress states.

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Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. AbstractHerein, we present a numerical convergence study of the Cahn-Hilliard phase-field model within an isogeometric finite element analysis framework. Using a manufactured solution, a mixed formulation of the Cahn-Hilliard equation and the direct discretisation of the weak form, which requires a C 1 -continuous approximation, are compared in terms of convergence rates. For approximations that are higher than second-order in space, the direct discretisation is found to be superior. Suboptimal convergence rates occur when splines of order p = 2 are used. This is validated with a priori error estimates for linear problems. The convergence analysis is completed with an investigation of the temporal discretisation. Second-order accuracy is found for the generalised-α method. This ensures the functionality of an adaptive time stepping scheme which is required for the efficient numerical solution of the Cahn-Hilliard equation. The isogeometric finite element framework is eventually validated by two numerical examples of spinodal decomposition.

In the literature, different theoretical models have been proposed to describe the properties of systems which consist of magnetizable particles that are embedded into an elastomer matrix. It is well known that such magneto-sensitive elastomers display a strong magneto-mechanical coupling when subjected to an external magnetic field. Nevertheless, the predictions of available models often vary significantly since they are based on different assumptions and approximations. Up to now the actual accuracy and the limits of applicability are widely unknown. In the present work, we compare the results of a microscale continuum and a dipolar mean field approach with regard to their predictions for the magnetostrictive response of magneto-sensitive elastomers and reveal some fundamental relations between the relevant quantities in both theories. It turns out that there is a very good agreement between both modeling strategies, especially for entirely random microstructures. In contrast, a comparison of the finite-element results with a modified approach, which-similar to the continuum model-is based on calculations with discrete particle distributions, reveals clear deviations. Our systematic analysis of the differences shows to what extent the dipolar mean field approach is superior to other dipole models.