A Multiscale Design Approach With Random Field Representation of Material Uncertainty

A multiscale design approach is proposed in this paper considering the impacts of product manufacturing process and material on product performance. A framework is established to integrate designs of manufacturing process, material and product based on the information flow across these three domains. Random field is employed to realistically model the uncertainty existing in material microstructure which spatially varies in a product inherited from the manufacturing process. An efficient procedure for uncertainty propagation from the material random field to the end product performance is established. To reduce the dimensionality of random field representation, a reduced order Karhunen-Loeve expansion is used with a discretization scheme applied to finite element meshes. The univariate dimension reduction method and the Gaussian quadrature formula are used to efficiently quantify the uncertainties in product performance in terms of its statistical moments, which are critical information for design under uncertainty. A control arm example is used to demonstrate the proposed approach. The impact of the initial microscale porosity random field produced during a casting process on the product damage is studied and a reliability-based design of the control arm is performed.