metal additive manufacturing engineers

Abstract: Bone scaffolds must reconcile a macroscale mechanical response with microscale geometric feasibility, yet conventional approaches to their design restrict attainable constitutive properties. This work presents a concurrent two-scale topology optimization framework; a conditional rectified flow generates periodic lattice microstructures, which are then refined in latent space by exact finite-element homogenization sensitivities. The resulting unit-cell geometries and their spatial assignments are jointly optimized under mechanical and feature-size constraints. In a distal rabbit femur benchmark, all eight flow-started refinements produce printable cells with maximum relative errors under 1\% across six prescribed engineering moduli. Constructing the implant from a single tiled cell reproduces intact whole-femur compliance within 0.1\% and regional strain energy within 0.35\% under four loading conditions. In human femoral reconstruction, multiscale concurrent optimization produces a cortical mid-shaft scaffold with porosity 63\% while satisfying the compliance constraint within 2\% under walking and stair-climbing loads. It achieves an 84\% porosity on a proximal cancellous scaffold with strain-energy deviations below 0.25\% under the same loads. Analysis of the learned representations reveals distinct architectural families in latent space. Further, the attention heads of the rectified-flow transformer specialize for spatial shifts -- learning the analogue of a finite-difference stencil -- and coordinate symmetries, with ablations showing their influence on generated topologies. These results establish a route to printable, mechanically constrained scaffold designs. The framework is general enough for extending to many other multiscale structural design applications including topology-microstructure co-design in metal additive manufacturing.

Abstract: Accurate thermal modeling is essential in metal additive manufacturing (AM) for understanding the process-structure-property chain. Physics-informed neural networks (PINNs) offer effective surrogate thermal modeling by minimizing physics-based residual losses at collocation points. However, prior works typically rely on manually-crafted, static collocation sampling strategies, which are neither principled nor scalable across process conditions, hindering their generalization capability. In this work, we provide theoretical analysis through empirical risk minimization, showing that process condition-aware adaptive sampling is strictly more favorable than conventional static sampling for generalization. Building on this insight, we propose an adaptive sampling strategy within a two-stage framework: (1) a conditional Flow Matching model that learns approximate high-residual distributions across different process conditions, and (2) a mixed sampling strategy combining this distribution with a domain-informed base distribution to generate adaptive collocation points for refining the PINN predictor. Experiments on metal AM numerical benchmarks demonstrate that our method consistently outperforms state-of-the-art PINN baselines, achieving an average 62.1\% reduction in relative $L_2$ error under an identical collocation budget, by capturing process-dependent heat dissipation regions often overlooked in the literature. To the authors' knowledge, this is the first adaptive sampling strategy for PINNs in metal AM, contributing to the enhanced generalization and broader applicability.

Abstract: This paper proposes a topology optimization method for reducing the residual stress arising in the building process of metal additive manufacturing. First, a layer-by-layer process analysis model based on an elastoplastic inherent strain method is introduced. In this model, the incremental displacement is solved anew at each layer step, and the stress history is explicitly incorporated into the constitutive equation as the stress accumulated up to the previous step, which guarantees the stress continuity across layer interfaces without introducing activation strains. Next, the design sensitivity of this analysis model is derived based on the adjoint method. Taking the pair of the stress and the equivalent plastic strain as the state variables reduces the dependency between layer steps to a one-step recurrence, and the adjoint fields are constructed as a layer-by-layer reverse sweep that reuses the coefficient tensors obtained in the forward analysis. Consequently, the cost of the sensitivity analysis scales linearly with the number of layers and remains of the same order as that of the forward analysis. An optimization problem is then formulated based on the density method to minimize the P-norm of the residual stress at the completion of the building process under the volume and final-use compliance constraints, and the derived sensitivities are verified by comparison with central finite differences. Finally, the proposed method is demonstrated through two- and three-dimensional examples of residual stress minimization under a compliance constraint. The results clarify that, under the elastoplastic analysis, the maximum residual stress is bounded by the yield surface, and the optimization therefore reduces the extent of the yielded and plastic strain accumulating regions rather than the peak stress value.