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’s 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.

通过各种建模技术评估孔隙率对铸件性能指标的影响已经取得了重大进展。然而，一个计算效率高的仍然缺乏考虑各种形状和尺寸的孔隙率的框架。这项工作的主要贡献是解决这个限制。具体而言，提出了一种新的孔隙度敏感度方法，它综合了拓扑敏感度和形状敏感度的优点。当无限小的球形孔插入致密（无孔）结构时，拓扑灵敏度近似于感兴趣量的一阶变化，而形状灵敏度估计当小孔的边界连续扰动以类似于从断层扫描表征数据重建的几何。在这种方法中，解决了一个外部问题，以明确地将孔隙应力和应变场表示为形状缩放参数的函数。通过忽略高阶孔间相互作用项，可以通过线性近似估计多个孔的影响。首先在基准示例上研究所提出的方法，以确定不同孔隙参数对估计精度的影响。然后将该方法应用于案例研究，其中孔隙几何来自断层扫描重建或计算机生成的表示。最终使用商业 3D 应用程序证明了该方法的效率和准确性。所提出的方法可以扩展到其他制造（例如，增材制造）引起的孔隙率问题。首先在基准示例上研究所提出的方法，以确定不同孔隙参数对估计精度的影响。然后将该方法应用于案例研究，其中孔隙几何来自断层扫描重建或计算机生成的表示。最终使用商业 3D 应用程序证明了该方法的效率和准确性。所提出的方法可以扩展到其他制造（例如，增材制造）引起的孔隙率问题。首先在基准示例上研究所提出的方法，以确定不同孔隙参数对估计精度的影响。然后将该方法应用于案例研究，其中孔隙几何来自断层扫描重建或计算机生成的表示。最终使用商业 3D 应用程序证明了该方法的效率和准确性。所提出的方法可以扩展到其他制造（例如，增材制造）引起的孔隙率问题。