Computationally Efficient, Fully Coupled Multiscale Modeling of Materials Phenomena Using Calibrated Localization Linkages

Abstract

Most modern physics-based multiscale materials modeling and simulation tools aim to take into account the important details of the material internal structure at multiple length scales. However, they are extremely computationally expensive. In recent years, a novel data science enabled framework has been formulated for effective scale-bridging that is central to practical multiscaling. A salient feature of this new approach is its ability to capture heterogeneity of fields of interest at different length scales. In this approach, the computations at the mesoscale are handled using a novel data science approach called materials knowledge systems (MKS). The MKS approach has enjoyed tremendous success in building highly accurate and computationally efficient metamodels for localization (i.e., mesoscale spatial distribution of a macroscale imposed field such as stress or strain rate) in simulating a number of different multiscale materials phenomena. MKS derives its accuracy from the fact that it is calibrated to results from previously established numerical models for the phenomena of interest, while its computational efficiency comes from the use of fast Fourier transforms. The current capabilities and the future outlook for the MKS framework are expounded in this paper.

Structure–property linkages using a data science approach: Application to a non-metallic inclusion/steel composite system

“…This is accomplished by performing a large number of regressions to calibration dataset produced using a numerical simulation tool (e.g., finite element models). Data science approaches similar to these have also been successfully employed by our research group in different, but related, applications [60][61][62][63][64][65].…”

Data-Driven Microstructure Property Relations

“…The n-point spatial correlation functions represent a widely used mathematical framework for microstructural characterization [23,24]. Roughly described, the n-point correlation is obtained by placing a polyline consisting of (n − 1) nodes defined relative to the first point by vectors r 1 , r 2 , .…”

“…For instance, a PCA of the n-point correlation functions of the microstructure is performed and the principal scores are used to in a polynomial regression model in order to predict material properties. The MKS is actively researched for different material structures [19][20][21]. For instance, [19,20] successfully predict the elastic strain and yield stress for the underlying microstructure using the MKS approach, however they confine their focus on either the topological features of the microstructure or a confined range of allowed volume fractions (0-20%), often held constant in individual studies.…”

A Computational Framework for Material Design

“…MKS is a statistical tool using a response variable of the local material state to estimate the local phase or stress status of the microstructure in an applied thermal or strain field [28,29,46]. MKS provides efficient calculations to simulate the elastic deformation of the microstructure.…”