  Significant progress has been made for assessing the influence of porosity on
the performance metrics for cast components through various modeling
techniques. However, a computationally efficient framework to account for
porosity with various shapes and sizes is still lacking. The main contribution
of this work is to address this limitation. Specifically, a novel porosity
sensitivity method is proposed, which integrates the merits of topological
sensitivity and shape sensitivity. While topological sensitivity approximates
the first order change on the quantity of interest when an infinitesimally
small spherical pore is inserted into a dense (no pore) structure, shape
sensitivity estimates the subsequent change in the quantity when the small pore
boundary is continuously perturbed to resemble the geometry reconstructed from
tomography characterization data. In this method, an exterior problem is solved
to explicitly formulate pore stress and strain fields as functions of shape
scaling parameters. By neglecting higher order pore-to-pore interaction terms,
the influence of multiple pores can be estimated through a linear
approximation. The proposed method is first studied on a benchmark example to
establish the impact of different pore parameters on the estimation accuracy.
The method is then applied onto case studies where the pore geometry is either
from tomography reconstruction or computer-generated representations.
Efficiency and accuracy of the method are finally demonstrated using a
commercial 3D application. The proposed method can be extended to other
manufacturing (e.g., additive manufacturing) induced porosity problems.
