Stochastic Modeling and identification of material parameters on structures produced by additive manufacturing

A methodology enabling the representation, sampling, and identification of spatially-dependent stochastic material parameters on complex structures produced by additive manufacturing is presented. The modeling component builds upon earlier works by the authors and relies on the combination of two ingredients. First, a fractional stochastic partial differential equation is introduced and parameterized in order to automatically capture the complex features of additively manufactured parts. Information-theoretic transport maps are subsequently introduced with the aim of ensuring well-posedness in the forward propagation problem. The identification of stochastic elasticity tensors on titanium scaffolds produced by laser powder bed fusion is then discussed. To this end, we consider an isotropic approximation at a mesoscale where fluctuations are aggregated over several layers, and address both the calibration and validation of the probabilistic model by using different sets of physical structural experiments. Despite the high sensitivity of the forward map to applied boundary conditions, geometrical parameters, and structural porosity, it is shown that the calibrated stochastic model can generate non-vanishing probability levels for all experimental observations.