Designing efficient computer experiments - The step beyond finite element modelling

A common challenge in modern multi-physics simulations like FEM is that the more complex the underlying problems become, the more the simulation depends on a range of not or just poorly understood parameters. At the same time, the increase of FEM computing time with the complexity of the underlying problem makes it impossible to explore the whole parameter space with FE simulations. Gaining as much information as possible from a manageable number of runs clearly requires involving some form of Design of Experiments (DOE), referred to as Design of Computer Experiments (DOCE) for simulation studies. In addition to the decision for which parameter sets simulations should be performed, the results of these simulations are used as data for constructing a statistical “metamodel”. By enabling the calculation of any variable of interest from arbitrary parameter sets without having to run new simulations, these metamodels facilitate an efficient exploration of the entire parameter space with optimal effort. Hence, the DOCE approach is indeed capable of expanding and optimizing the possibilities already achievable by simulation studies alone. For demonstrating the method on a relatively simple example, this work is focused on designing and validating a metamodel for calculating linear, one-directional stresses in rectangular monocrystalline (100) samples. It will be shown that the differences between FEM and the metamodel are always smaller than ≈ 4 MPa for different stress states up to a maximum stress of 215 MPa.