Machine-Learning assisted understanding of RVE-size dependent uncertainties and corresponding hierarchy of properties

Kurzfassung

Materials discovery and development processes are the two forefronts of materials science and engineering. Representative/statistical Volume Elements (RVEs, SVEs) are extensively used to simulate different homogenized properties of an engineered microstructure, facilitating further development or improvement of that materials-system with optimized performance. The reliability of these predicted properties is limited due to various uncertainties which come from various sources like underlying stochastic process, complexity of microstructure etc. These tend to reduce if the size of a volume element (VE) is larger because of incorporation of more information, however, simulations tend to become expensive and cumbersome. Hence, there is a need of finding an acceptable size which balances both higher computational cost and lower uncertainties. A related framework in this regard or an understanding for the estimation of acceptable sizes of a realistic RVE considering a range of properties is necessary. Considering the above background it can be said that the choice of a smaller sized VE could results in pronounced simulation-uncertainties considering a complex material model when used for the same microstructure i.e, a larger size is required for an acceptable RVE if the complexity of the model and the microstructure ncreases and thus, a hierarchy of acceptable sizes can be mapped for the same microstructure using different material models incorporating complex non-linear behaviours. Such an RVE-Map is supposed to be extremely useful in the context of more reliable decision-making based on homogenizationesults and multiscale simulations. In this work, a primary version of an RVE-map has been attempted to be established. Firstly, in order to build statistically equivalent volume-elements (SVE) in terms of necessary microstructural/morphological descriptors, a number of different realizations of increasing size has been generated. Next, a homogenized property is compared by carrying out the similar simulation using all the SVEs and thus, an acceptable size has been selected after convergence study, based on i) the relative error of less than 1% in between two consecutive realizations and ii) a single realization. Thus, the procedure has been repeated by considering a range of properties in order to show the expected hierarchy of selected properties. The sequence modelling capability of deep learning models has been leveraged to get the property-predictions of higher sized SVEs effectively, by saving time and computational cost, and thus facilitating faster decision-making. This is done by learning the sequence formed by the property-curves at lower sizes and having predictions at higher sizes until convergence is achieved. From the established RVE-map, it can be concluded that a cube of side length 60 mm is suffcient for elasticity, while for pure thermal simulation or for thermo-elasticity or for elasto-plasticity under only slip-condition an approximate cube-side of 140 mm is reasonable. On the other hand, if twinning mechanism is added to the plasticity model, then a slightly larger size than that of purely slipcase is expected. When thermal a boundary condition is added to coupled sliptwin based plasticity, then reasonable side-length of the expected RVE reaches to nearly 180 mm.