Data-Driven Computing in Dynamics
We formulate extensions to Data Driven Computing for both distance minimizing and entropy maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here formulations assign data points a variable relevance depending on distance to the solution and on maximum-entropy weighting, with distance minimizing schemes discussed as a special case. The resulting schemes consist of the minimization of a suitably-defined free energy over phase space subject to compatibility and a time-discretized momentum conservation constraint. We present selected numerical tests that establish the convergence properties of both types of Data Driven solvers and solutions.
© 2017 John Wiley & Sons, Inc. Accepted manuscript online: 31 October 2017; Manuscript Revised: 11 October 2017; Manuscript Accepted: 11 October 2017; Manuscript Received: 12 June 2017. The support of Caltech's Center of Excellence on High-Rate Deformation Physics of Heterogeneous Materials, AFOSR Award FA9550-12-1-0091, is gratefully acknowledged.
Submitted - 1706.04061.pdf