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.

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.

In the present work, the magneto-mechanical coupling in magneto-active elastomers is investigated from two different modeling perspectives: a micro-continuum and a particle–interaction approach. Since both strategies differ significantly in their basic assumptions and the resolution of the problem under investigation, they are introduced in a concise manner and their capabilities are illustrated by means of representative examples. To motivate the application of these strategies within a hybrid multiscale framework for magneto-active elastomers, their interchangeability is then examined in a systematic comparison of the model predictions with regard to the magneto-deformation of chain-like helical structures in an elastomer surrounding. The presented results show a remarkable agreement of both modeling approaches and help to provide an improved understanding of the interactions in magneto-active elastomers with chain-like microstructures.

In this contribution, particle‐matrix interactions in magneto‐active elastomers are analyzed with regard to the resulting mechanical deformations. By comparing experimental observations with the results of finite element simulations, a fully coupled continuum model for magneto‐active elastomers is validated with the help of real data. The model under consideration permits the investigation of magneto‐active elastomers with arbitrary particle distances, shapes and volume fractions as well as magnetic and mechanical properties of the individual constituents. Our results show a very good agreement of experiments and numerical simulations ‐ the deformation behavior of the system under consideration is captured by the model qualitatively as well as quantitatively.