Reconciled Top-Down and Bottom-Up Hierarchical Multiscale Calibration of BCC Fe Crystal Plasticity

Hierarchical top-down bottom-up calibration with consideration for uncertainty and inter-scale discrepancy of Peierls stress of bcc Fe

“…The impact of the discrepancy layer is evaluated in this section. To provide a point of comparison, the uncertainty estimates made in previous work without a model discrepancy treatment are included (Tallman et al, 2017). As mentioned above, DDD simulations of a Frank-Read source in bcc Fe are also included to highlight the assumptions which underlie the mechanistic description of the scale discrepancy used to motivate this work.…”

“…In this section, the likelihood functions are described and the inter-scale discrepancy is formulated. The data from TD and BU are combined using the method of reconciliation previously detailed (Tallman et al, 2017), which multiplicatively combines surrogate model-based TD likelihood functions and BU penalty functions of Gaussian form to inform a TDBU posterior for parameters. In the TDBU calibration approach, a standard likelihood formulation for the top-down model (or its surrogate) is multiplied by a function which penalizes large differences between BU and TD parameters.…”

“…In the approach without discrepancy, the TD basis is arrived at using a one-to-one correspondence. Here, a summary of the connection test is given, which is described in more detail elsewhere (Tallman et al, 2017). The BU penalty functions and TD likelihood functions are included in a constrained likelihood function (CLF).…”

“…The practice of evaluating a connection in a HMM between top-down (TD) and bottomup (BU) information pathways is a recent development (Tallman et al, 2017). In the approach, discrepancies in the TD and BU estimates of model parameters which reflect given physical quantities are reconciled through the use of a statistical likelihood framework.…”

“…Hierarchical multiscale models (HMM) of materials depend on assumed connections between independently validated models at different length and time scales (McDowell, 2010;Narayanan et al, 2014;Tallman et al, 2017). In a HMM, a mapping between parameters is used to establish this connection.…”