Thermal modeling of Laser Powder Bed Fusion (LPBF) is challenging due to steep, rapidly moving thermal gradients induced by the laser, which are difficult to resolve accurately with conventional Finite Element Methods (FEM). Highly refined, dynamically adaptive spatial discretization is typically required, leading to prohibitive computational costs. Semi-analytical approaches mitigate this by decomposing the temperature field into an analytical point-source solution and a complementary numerical field that enforces boundary conditions. However, state-of-the-art implementations either necessitate extensive mesh refinement near boundaries or rely on restrictive image-source techniques, limiting their efficiency and applicability to complex geometries. This study presents a novel reformulation of the semi-analytical framework using Isogeometric Analysis (IGA). The laser heat input is captured by the analytical point-source solution, while the complementary correction field, which imposes boundary conditions, is solved using a spline-based IGA discretization. The governing heat equation for the correction field is cast in a weak form, discretized with NURBS basis functions, and advanced in time using an implicit θ-scheme. This approach leverages IGA’s key advantages: exact geometry representation, higher-order continuity, and superior accuracy per degree of freedom. These features unlock efficient thermal modeling of realistic parts with complex contours. Our strategy eliminates the need for scan-wise remeshing and robustly handles intricate geometric features like sharp corners and varying cross-sections. Numerical examples demonstrate that the proposed semi-analytical IGA method delivers accurate temperature predictions and achieves substantial computational efficiency gains compared to standard FEM, establishing it as a powerful new tool for high-fidelity thermal simulation in LPBF.

In Metal Additive Manufacturing (MAM), support structures serve not only for mechanical supports but also for heat dissipation, preventing overheating in the melt zone. Although a high support volume aids heat dissipation, it significantly increases printing time, material wastage, and post-processing efforts. Additionally, contact area between the part and the supports often has higher surface roughness, which compromises part quality. This paper presents a novel density-based Topology Optimization (TO) technique for designing support structures optimized for efficient heat evacuation while keeping the part design fixed. First, a simplified MAM model, already established in the literature, is used to identify regions prone to overheating, referred to as ‘hotspots.’ This hotspot information is then used to formulate a TO problem that minimizes support volume while regulating the heat evacuation efficiency of the supports through thermal compliance which is defined as a constraint. For calculation of thermal compliance, a thermal load is defined using the hotspot information while the baseplate acts as a heat sink. To reduce post-processing costs, a concept of vicinity penalization is introduced, promoting the minimization of the part-support interface area. First, a set of 2D results is presented to demonstrate the method’s effectiveness and explain the influence of various parameters. Next, the TO algorithm is applied to a real-size 3D part and the results are discussed. Finally, the performance of the optimized supports is evaluated using a transient layer-by-layer AM simulation.

A framework is proposed for geometric filters in density-based topology optimization. Most geometric filters feature density detection in a specified region of interest. In this method, this operation is decoupled from the finite element mesh by using interpolated densities. This allows for the filter configuration (e.g. tool orientation or printing direction) to be optimized simultaneously with the geometric layout. The framework is presented in a generic manner, and demonstrated on filters for: milling with simultaneous optimization of milling orientation; jetting with simultaneous optimization of jetting positions; and printing with simultaneous optimization of printing orientation. The performance of the framework is tested with numerical examples for compliance in 2D and 3D on a structured mesh, and in 2D on an unstructured mesh. The framework can extend the design freedom of existing filters, and can serve as a basis for the development of new geometric filters.

Advancements in wire-arc directed energy deposition (DED) have created new opportunities for manufacturing efficient large-scale structures. While wire-arc DED is often viewed as more sustainable and economical due to the potential of producing lighter structures, its higher environmental impact and cost per unit of weight necessitate further considerations during the design phase. This paper explores how sustainability and cost can be integrated into conceptual design through topology optimisation. The approach is demonstrated through a case study, including a parametric study on specific environmental impact and the cost of wire-arc DED versus CM, applicable to current data and future estimates. Findings indicate that beams manufactured solely with wire-arc DED are sensitive to fluctuations in specific environmental impact and cost of wire-arc DED, potentially losing their material saving advantage. Conversely, hybrid beams that combine conventional profiles with wire-arc DED offer a better balance between structural performance, sustainability and economic feasibility.

Part-scale thermal process simulations play an important role in improving the part quality of the Laser Powder Bed Fusion (LPBF) process. The semi-analytical simulation method relies on the superposition of analytical fields to represent laser-induced heat sources in a semi-infinite space and a complementary temperature field to enforce boundary conditions. So far, boundary conditions have been imposed by analytical image fields for straight boundaries and numerically for non-straight boundaries. The latter requires considerable refinement on the spatial discretization, at least near the boundaries, and compromises the computational efficiency of the simulations. In this paper, we derive a closed-form solution for the image fields that can accurately enforce the boundary conditions for non-straight boundaries. A geometrically complex part boundary is represented by B-splines, and with the aid of an offset method and reparameterization, the positions of the image sources are determined. The image field's closed-form expression is then found using the boundary's local curvature calculated from the local tangent lines. Numerical examples on different levels of complexity revealed that the net heat lost along an adiabatic boundary vanishes when the novel image source solutions are used, and the thermal evolution of complex parts can be accurately predicted with high computational efficiency. Simulations involving multiple lasers can also be performed with no extra computational cost.

A novel feature mapping topology optimization method is presented, allowing for the creation of features with highly flexible shapes. The method easily integrates with conventional density-based formulations. Feature shapes are implicitly described by NURBS control points. The feature shape dictates the locations of two sets of projection points to represent the solid void boundaries. At these projection points, density values are projected onto a finite element mesh. The method optimizes feature shapes in a gradient-based manner, while allowing more specific control of the feature shapes than classical level set methods. Several feature fields can be combined to create a final output design. It is found that the eminent flexibility of the NURBS-based feature definition is a benefit but also requires additional regularization to guarantee stability of the optimization.

Topology optimization methods are used to design high performance structural components that often have complex geometric layouts. In several industries, components are required to be cleanable, and for this research cleaning by jetting is considered. Thus, being able to ensure jet access on the entire surface of a structure is of interest in topology optimization. In this paper, a jetting filter is proposed, that turns a blueprint design into a jet accessible design. Two methods are considered to find an access field for each jet. These individual jet access fields are then combined into a total access field, to obtain a cleanable design. Consistent sensitivity analysis is used and the additional computational cost of the jetting filter is modest compared to the finite element analysis. The performance of the two methods is demonstrated with 2D and 3D numerical examples for mechanical and thermal topology optimization problems.

Wire arc additive manufacturing (WAAM) enables the manufacturing of efficient and lightweight structural elements in which material can be utilised wherever needed in an optimised shape, in contrast to standard prismatic profiles used in construction. However, the specific energy consumption (SEC) of WAAM is higher than that of conventional manufacturing (CM) techniques (i.e., hot-rolling) for standard profiles. Therefore, it is an open question whether the material savings through computational design realised via WAAM is environmentally beneficial or not. This systematic study aims to provide a better understanding of the environmental impact of hybrid manufacturing, which is defined as the combination of WAAM and CM rather than using any of them alone. Topology optimisation (TO) is used to design a series of beams with an identical performance (i.e., stiffness) but with a reduced material consumption depending on the hybrid ratio. The environmental impact of the designs has been used to determine when and how hybridisation can become advantageous. The results show that although the optimal proportions of WAAM and CM are dependent on their relative SEC, the hybrid solutions have always been environmentally superior compared to that of WAAM or CM alone for the realistic SEC values, exhibiting up to a 60% reduction in environmental impact compared to that of CM.

Wire and Arc Additive Manufacturing (WAAM) emerged as a manufacturing process for large scale structures with extensive form and design freedom. WAAM can be fully exploited once the relation between the transient thermal history and its relation to microstructure development and resultant mechanical properties is established. This relation can be further used for computational design tools such as Topology Optimization. This paper presents a model to predict the relation between the thermal history and solid-state phase transformations in a widely applicable High Strength Low Alloy steel ER110S-G. The transient thermal history of parts manufactured by WAAM is modelled using finite element analysis. The modelled thermal history is validated with thermocouple measurements. Our results show that a critical cooling cycle is responsible for the solid-state phase transformation in an AM part. The cooling rate of this particular cooling cycle is superimposed onto an experimentally constructed Continuous Cooling Transformation (CCT) diagram to determine the local solid-state phase fractions. The predicted phase fractions in three wall samples with different design and processing conditions of AM parts are used to predict the hardness. The predicted hardness is 10% higher than the measured hardness of AM samples. The effect of tempering is also considered in the model through JMAK equation. The results show that the tempering is caused in regions with high martensite content and it lowers the hardness by 8 − 10%. The micrographs of the AM parts show that the microstructural features are same for the AM parts with similar critical cooling rates.

Sub-size specimen testing offers a potentially elegant solution to accompany fatigue life assessments in determining vital fatigue parameters such as effective fatigue crack growth propagation thresholds (ΔK_th,eff). Additively manufactured parts stand to benefit from this in potential build-by-build fatigue validation without foregoing process-inherent material saving and low lead times. In this study, sub-size Laser Powder Bed Fusion (LPBF) produced Ti-6Al-4 V SENB specimens built in two orientations with stress relieved and annealed material states are considered. Scanning electron microscopy with electron backscatter diffraction is used to consider both meso- and microstructural features, complimented by digital image correlation (DIC) for determining local stress intensity and triaxiality around the crack tip. Results show inconsistent near-threshold fatigue behaviour linked to the microstructure of annealed material, where the fatigue threshold in sub-size specimens is reduced. Furthermore, reducing specimen size influences both in- and out-of-plane crack tip constraint, with higher constraint experienced by the sub-size specimens. Overall, this study presents and discusses the domain and suitability in using sub-size specimen FCGR threshold testing for LPBF produced Ti-6Al-4 V builds considering their unique meso- and microstructural features.

Overheating is a major issue especially in metal Additive Manufacturing (AM) processes, leading to poor surface quality, lack of dimensional precision, inferior performance and/or build failures. A 3D density-based topology optimization (TO) method is presented which addresses the issue of local overheating during metal AM. This is achieved by integrating a simplified AM thermal model and a thermal constraint within the optimization loop. The simplified model, recently presented in literature, offers significant computational gains while preserving the ability of overheating detection. The novel thermal constraint ensures that the overheating risk of optimized designs is reduced. This is fundamentally different from commonly used geometry-based TO methods which impose a geometric constraint on overhangs. Instead, the proposed approach takes the process physics into account. The proposed method is validated via an experimental comparative study. Optical tomography (OT) is used for in-situ monitoring of process conditions during fabrication and obtained data is used for evaluation of overheating tendencies. The novel TO method is compared with two other methods: standard TO and TO with geometric overhang control. The experimental data reveals that the novel physics-based TO design experienced less overheating during the build as compared to the two classical designs. A study further investigated the correlation between overheating observed by high OT values and the defect of porosity. It shows that overheated regions indeed show higher defect of porosity. This suggests that geometry-based guidelines, although enhance printability, may not be sufficient for eliminating overheating issues and related defects. Instead, the proposed physics-based method is able to deliver efficient designs with reduced risk of overheating.

Computational process modelling of metal additive manufacturing has gained significant research attention in recent past. The cornerstone of many process models is the transient thermal response during the AM process. Since deposition-scale modelling of the thermal conditions in AM is computationally expensive, spatial and temporal simplifications, such as simulating deposition of an entire layer or multiple layers, and extending the laser exposure times, are commonly employed in the literature. Although beneficial in reducing computational costs, the influence of these simplifications on the accuracy of temperature history is reported on a case-by-case basis. In this paper, the simplifications from the existing literature are first classified in a normalised simplification space based on assumptions made in spatial and temporal domains. Subsequently, all types of simplifications are investigated with numerical examples and compared with a high-fidelity reference model. The required numerical discretisation for each simplification is established, leading to a fair comparison of computational times. The holistic approach to the suitability of different modelling simplifications for capturing thermal history provides guidelines for the suitability of simplifications while setting up a thermal AM model.

Additive manufacturing (AM) processes have proven to be a perfect match for topology optimization (TO), as they are able to realize sophisticated geometries in a unique layer-by-layer manner. From a manufacturing viewpoint, however, there is a significant likelihood of process-related defects within complex geometrical features designed by TO. This is because TO seldomly accounts for process constraints and conditions and is typically perceived as a purely geometrical design tool. On the other hand, advanced AM process simulations have shown their potential as reliable tools capable of predicting various process-related conditions and defects. Thus far, geometry design by topology optimization and multiphysics manufacturing simulations have been viewed as two mostly separate paradigms, whereas one should really conceive them as one holistic computational design tool. More specifically, AM process models provide input to physics-based TO, where consequently, not only the designed component will function optimally, but also will have near-to-minimum manufacturing defects. In this regard, we aim at giving a thorough overview of holistic computational design tool concepts applied within AM. First, literature on TO for performance optimization is reviewed and then the most recent developments within physics-based TO techniques related to AM are covered. Process simulations play a pivotal role in the latter type of TO and serve as additional constraints on top of the primary end-user optimization objectives. As a natural consequence of this, a comprehensive and detailed review of non-metallic and metallic additive manufacturing simulations is performed, where the latter is divided into micro-scale and deposition-scale simulations. Material multi-scaling techniques, which are central to the process-structure-property relationships, are reviewed next, followed by a subsection on process multi-scaling techniques, which are reduced-order versions of advanced process models and are incorporable into physics-based TO due to their lower computational requirements. Finally the paper is concluded and suggestions for further research paths discussed.

In metal Additive Manufacturing (AM), the deposited material is subjected to a series of heating and cooling cycles. The locally occurring temperature extremes and cooling rates determine solid-state phase fractions, material microstructure, texture, and ultimately the local material properties. As the shape of a part determines the local thermal history during AM, this offers an opportunity to influence these material properties through design. In this paper, we present a way to obtain desired properties by controlling the local thermal history. This is achieved through topology optimization of the printed part while considering its entire transient thermal history. As an example of this approach, this work focuses on high strength low alloy steels, where resulting phase fractions significantly influence mechanical properties such as yield strength and ductility. These solid-state phase fractions depend on cooling rates in a particular critical temperature range. The phase composition and hence the local yield strength in target regions can be controlled by constraining the cooling time in this range. Numerical examples illustrate the capability of the proposed approach in adapting part designs to achieve various desired material properties.

A novel constraint to prevent local overheating is presented for use in topology optimization (TO). The very basis for the constraint is the Additive Manufacturing (AM) process physics. AM enables fabrication of highly complex topologically optimized designs. However, local overheating is a major concern especially in metal AM processes leading to part failure, poor surface finish, lack of dimensional precision, and inferior mechanical properties. It should therefore be taken into account at the design optimization stage. However, including a detailed process simulation in the optimization would make the optimization intractable. Hence, a computationally inexpensive thermal process model, recently presented in the literature, is used to detect zones prone to local overheating in a given part geometry. The process model is integrated into density-based TO in combination with a robust formulation, and applied in various numerical test examples. It is found that existing AM-oriented TO methods which rely purely on overhang control do not ensure overheating avoidance. Instead, the proposed physics-based constraint is able to suppress geometric features causing local overheating and delivers optimized results in a computationally efficient manner.

Hydrogen plays a vital role in the utilisation of renewable energy, but ingress and diffusion of hydrogen in a gas turbine can induce hydrogen embrittlement on its metallic components. This paper aims to investigate the hydrogen transport in a non-hydride forming alloy such as Alloy 690 used in gas turbines inspired by service conditions of turbine blades, i.e. under the combined effects of stress and temperature. An appropriate hydrogen transport equation is formulated, accounting for both stress and temperature distributions of the domain in the non-hydride forming alloy. Finite element (FE) analyses are performed to predict steady-state hydrogen distribution in lattice sites and dislocation traps of a double notched specimen under constant tensile load and various temperature fields. Results demonstrate that the lattice hydrogen concentration is very sensitive to the temperature gradients, whilst the stress concentration only slightly increases local lattice hydrogen concentration. The combined effects of stress and temperature result in the highest concentration of the dislocation trapped hydrogen in low-temperature regions, although the plastic strain is only at a moderate level. Our results suggest that temperature gradients and stress concentrations in turbine blades due to cooling channels and holes make the relatively low-temperature regions susceptible to hydrogen embrittlement.

Discrete dislocation plasticity is a modeling technique that treats plasticity as the collective motion of dislocations. The dislocations are described through their elastic Volterra fields, outside of a cylindrical core region, with a few Burgers vectors of diameter. The contribution of the core fields to the dislocation dynamics is neglected, because it is assumed that their range is too short to be of influence. The aim of this work is to assess the validity of this assumption. In recent ab-initio studies it has been demonstrated that the dislocation core fields are significant up to a distance of ten Burgers vector from the dislocation line. This is a longer range influence than expected and can give rise to changes in the evolving dislocation structure and in the overall response of a plastically deforming body. It is indeed experimentally observed that dislocations pile up against strong interfaces, and that the spacing between dislocations at the front of these pile-ups can be less than ten Burgers vectors. In this work, 2-D discrete dislocation plasticity simulations are performed to investigate the effect of core fields on edge dislocation interactions. The results of the simulations, which include core fields for the first time, show indeed that dislocations that are very closely spaced experience additional glide or climb due to core fields. The effect is however negligible when compared to glide and climb due to Volterra fields or due to the external load.

Topology optimization typically generates designs that exhibit significant geometrical complexity, which can pose difficulties for manufacturing and assembly. The number of occurrences of an important design feature, in particular intersections, increases with geometrical complexity. Intersections are essential for load transfer in many engineering structures. For certain upcoming manufacturing processes, such as direct metal deposition, the size of an intersection plays a role. During metal deposition, slim intersections are more prone to manufacturing defects than bulkier ones. In this study, a computationally tractable methodology is proposed to both control occurrence and size of intersections in topology optimization. To identify intersections, a stress-based quantity is proposed, denoted as Intersection Indicator. This quantity is based on the local degree of multi-axiality of the stress state, and identifies material points at intersections. The proposed intersection indicator can identify intersections in both single as well as multi-load case problems. To detect the relative size of intersections, the average density in the vicinity of an intersection is used to penalize or promote intersection sizes of interest. The corresponding sensitivity analysis involves solving a set of adjoint equations for each load case. Numerical 2D experiments demonstrate a controllable reduction of penalized slim intersections compared to the designs obtained from conventional compliance minimization. The overall geometrical complexity of the design is reduced due to the promotion of bulkier intersections which leads to an increase in compliance. The designs obtained are more suitable for manufacturing processes such as direct metal deposition.

A remarkable elastic anisotropy in plates of austenitic stainless steel produced by the Wire and Arc Additive Manufacturing process is recently reported. The Young's modulus depends on the angle of orientation with respect to the material deposition direction. Here, for the first time, this anisotropy is exploited to maximize structural stiffness by simultaneously optimizing the structural design layout and the local deposition path direction for WAAM. The results obtained indicate deposition that is commonly preferred along the load-path directions for WAAM is sub-optimal and stiffness can be increased at least 53% upon optimizing the deposition directions.