Summary
We present a modification of the multiscale finite element method (MsFEM) for modeling of heterogeneous viscoelastic materials and an enhancement of this method by the adaptive generation of both meshes, ie, a macroscale coarse one and a microscale fine one. The fine mesh refinements are performed independently within coarse elements adjusting the microscale discretization to the microstructure, whereas the coarse mesh adaptation optimizes the macroscale approximation. Besides the coupling of the hp‐adaptive finite element method with the MsFEM we propose a modification of the MsFEM to accommodate for the analysis of transient nonlinear problems. We illustrate the efficiency and accuracy of the new approach for a number of benchmark examples, including the modeling of functionally graded material, and demonstrate the potential of our improvement for upscaling nonperiodic and nonlinear composites.
In this paper, we present an enhanced framework for the synthetic asphalt concrete (AC) microstructure generation for the numerical analysis purposes. It is based on the Voronoi tessellation concept with some necessary extensions that allow for the reliable generation of the aggregate particles of the given size distribution. The synthetic microstructure generation allows for faster numerical modeling of the novel materials. It can partially replace the X-ray computed tomography approach, which is frequently used in such analysis. Our framework is a kind of compilation of the known techniques with the enhancements applied to expedite the microstructure modeling process. Therefore, the generated microstructure is used in the numerical upscaling to model the macroscale asphalt concrete properties. We restrict ourselves (in this paper only) to the 2D elastic computations. We also assume the perfect bonding between these two materials and the static load for the sake of simplicity. The upscaling is performed by the multiscale finite element method (MsFEM). A short recapitulation of the MsFEM foundations as well as the numerical test comparing the overkill mesh solution with the upscaled one is provided in the paper. The test results confirm that the whole presented methodology can serve as a fast and reliable tool for the tests on novel asphalt mixtures and other heterogeneous materials. It can reduce the cost of the design process substituting some of the laboratory experiments, giving the opportunity to test the developed constitutive models and expedite the numerical analysis itself.
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