DeepBND: A machine learning approach to enhance multiscale solid mechanics
نویسندگان
چکیده
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity interest in a window observation. The entire problem setting encompasses solution local PDE and some averaging formula for such domain. There relatively standard methods literature to completely determine formulation except two choices: i) domain itself ii) boundary conditions. Hence, modelling errors governed quality these choices. choice relates degree representativeness microscale sample, i.e., it is essentially statistical characteristic. Naturally, its reliability higher as size observation becomes larger and/or number samples increases. On other hand, excepting few special cases there no automatic guideline handle ii). Although known that overall effect condition less important domain, computational cost simulate large several times might be prohibitive even small accuracy requirements. Here we introduce machine learning procedure select most suitable conditions multiscale problems, particularly those arising solid mechanics. We propose combination Reduced-Order Models Deep Neural Networks an offline phase, whilst online phase consists very same homogenisation plus one (cheap) evaluation trained model method allows implementation minimal changes existing codes use domains without losing accuracy, which reduces orders magnitude. A test accounting circular elliptical inclusions reported aiming at proving potentials DeepBND method.
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2023
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2023.111996