A scale-dependent numerical approach is developed through combining the finite element (FE)-based averaging process with the Monte Carlo method to determine the desired size of a characteristic volume element (CVE) for a random magnetoactive composite (MAC) under applied magnetic field and large deformations. Spatially random distribution of identically magnetic inclusions inside a soft homogeneous matrix is considered to find the appropriate size of the characteristic volume element. Monte Carlo method is used to generate ensembles of a randomly distributed magnetoactive composite to be applied in the homogenization study. The ensemble is utilized as a statistical volume element (SVE) in a scale-dependent numerical algorithm to search the desired characteristic volume element size. Results of this study can be used to investigate effective behavior and multiscale modeling of randomly particulate magnetoactive composites.

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