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The main objective of this research is to investigate the newly designed geometry and process parameters in a dual matrix composite filament co-extrusion technology (CFC), a co-extrusion of continuous carbon fiber pre-impregnated with thermoset (1.5K) also known as composite carbon fiber (CCF) filament with a special binder thermoplastic filament. Accordingly, non-isothermal fluid flow and particle tracking analysis were employed in order to examine the melt flow dynamics. In addition, critical parameters like pressure drop, velocity, shear stress, residence time, and swelling/shrinkage ratio were evaluated. In particular, the computational fluid dynamics (CFD) simulations indicates distress in the conventional die design, recirculation and stagnation of melt flow in the dead zones causing longer melt residence leading to the thermal degradation of thermoplastic material. Furthermore, a new print head was designed to expedite the solution for the possible flow instabilities that may lead to a disparity in the material and mechanical properties, a side- fed mandrel die was used as a melt distributor. Consequently, the side- fed mandrel die ensured a homogeneous melt distribution inside the CFC print head, particularly at the die exit.

Laser Beam Melting (LBM) is currently garnering industrial attention and many numerical researches have been carried out in order to understand the physics behind the process. However, due to the gap between the grain scale (micrometres) and the bead scale (millimetres), current state-of-the-art multi-physical models are computationally expensive as each powder grain is individually represented. Hence, simulating more than a single LBM track in a reasonable computational time is a challenging task. To overcome this limitation, a new mesoscopic approach is proposed, which intends to bridge the fine thermo-hydrodynamic representation and the macroscopic thermal models. The powder bed is represented by a homogeneous medium with both equivalent thermal and fluid properties. A bulk heat source is considered when the laser heats the powder bed whereas a surface heat flux is imposed on the melted powder bed surface. Apparent viscosity and surface tension are attributed to the homogenized medium so that modelling powder densification, melting and spheroidization of the melt pool is made possible by solving compressible Navier-Stokes equations. In addition, thermocapillary effects as well as vaporisation-induced recoil pressure are implemented, so that realistic thermo-hydrodynamic phenomena are successfully taken into account.

Additive Manufacturing allows to design and realize 3D parts, integrating additional functionalities offered by the interaction between complex shapes and the material properties. Results can be even more appealing when functional materials, like Shape Memory Alloys, are printed: new opportunities for smart devices can be opened. In the present bulk and lattice structures of Nitinol were additively manufactured with a Seletive Laser Melting. A pulsed laser, which is more suitable for manufacturing thin parts, was selected to process the initial powder. The selection of the process parameters, like laser power and exposure time, was performed for maximizing the relative density. Furthermore, the microstructure and the martensitic transformation temperatures were analyzed through X-rays diffraction and differential scanning calorimetry, respectively. A comparison between the initial powder and SLMed parts was also considered. Finally, the mechanical properties of Niti builts under compression were tested for both bulk and lattice structures.

3D finite element simulation of a FDM printer nozzle region was performed using COMSOL Multiphysics software. The polymer exiting the nozzle of the FDM printer was also included in the simulation in order to capture the dimensional behavior of the polymer. The domain of the simulation consisted of a nozzle, printer table, and the surrounding air. In the simulation, mass and momentum equations were solved to determine the non-Newtonian flow characteristics of the polymer. The interface between the polymer and ambient air was modelled using the level set method. Experiments were conducted to validate the numerical results. One experimental specimen with 30 strips was printed using a 3D printer. In the CAD model of the specimen, each strip had the same width as the nozzle diameter. While printing, it was ensured that the nozzle had only one continuous vertical movement to print each strip. The printed strips were measured with a caliper at five different locations. The difference between the numerical and experimental results of strip width were less than 10%. The developed model provided information about the transient shape of the polymer extrudate and can be used to predict the dimensional accuracy of the FDM-printed parts.

The need to investigate new solutions and novel 3D building strategies not only requires the development of new slicing algorithms and the exploitation of machines with more than 3 Dofs, but also a safe and reliable test-bench to optimize all the phases of the process. The following article describes the assessment by simulation of suitable control architectures for the realization of a Fused Deposition Modeling printer based on a 6 Dofs serial manipulator. The focus is put on the obtained position and speed profiles for unidirectional and multi-directional 3D printing to determine the week points associated with each control strategy.

International audience; Recently, a simplified macroscopic and semi-analytical thermal analysis of Laser Metal Deposition (LMD) has been submitted to publication. The model is fast enough to simulate the entire process. The proposed approach enables to compute: temperature, solidification and solid-state phase transitions kinetics. Process parameters, substrate characteristics and heat sources due to the enthalpy change during phase transitions are taken into account as well as convection due to the carrying and shielding gas. The present work exploits the proposed model to investigate the influence of some process parameters in order to determine whether complex multiphase steels (such as high strength steels) could be controllably obtained by LMD. Indeed, material properties of such steels are not only a matter of chemical composition but also and mostly a matter of phase proportions in a multiphase mixture (austenite, ferrite, pearlite, bainite and martensite). Within this framework, temperature control strategies during the process are numerically tested for a simple cylindrical geometry.

With the help of current approaches in the mechanics of additively manufactured deformable solids, a non-classical mathematical model is developed to predict the stress-strain state of polymer layers gradually formed on a rotating substrate in an arbitrary number of continuous stages of centrifugal material application. On the basis of numerous calculations performed, the qualitative and quantitative features of the residual technological stresses distributions in the finished cylindrical product for different variants of its release from the mechanical loading and the kinematic bonds acting during the manufacturing process are analyzed in detail. Previously unknown mechanical effects are found. The appropriate recommendations of a practical nature are given.

The finite element analysis (FEA) of components’ build-up has recently proved to be a valuable tool for accompanying the product and process development during additive manufacturing (AM). In this numerical method a first key aspect is the heat input modelling of laser scanning for building-up AM products of industrial relevance, as close to reality as possible, by applying equivalent heat source models. Based on these reduction models the stress distribution in a successive thermo-mechanical simulation is calculated approximating the sum of thermal, elastic and plastic stresses during processing and the remaining elastic and plastic stresses after cooling. A further key aspect is, thereupon, to predict the final shape of the additively manufactured component by means of the FEA after its removal from the substrate or the support structures. This work aims to analyze the development of stresses in components during their additive laser processing and cooling to ambient temperature as well as after post-processing cutting operations. Moreover, the associated to stress development simulated final part shape is evaluated with the aid of 3d measurements on an additively manufactured twin cantilever of industrial relevance. Finally, based on the rendered simulation results a compensation of the undesired shape distortions is proposed based on reverse engineering approach.

We present a multi-physics model for the approximation of the coupled system formed by the temperature-dependent Navier-Stokes equations with free surfaces. The main application is the industrial process of shallow laser surface melting (SLSM), for laser polishing of metal surfaces. We consider incompressible flow equations with solidification, and we model the laser source through physically-consistent boundary conditions. We incorporate Marangoni effects in the surface tension model to drive internal motion in the liquid metal. The numerical method relies on an operator splitting strategy and a two-grid approach. A proof of concept of the numerical model is achieved through a static laser melting process.

This study analyses canine limb-sparing implants with an integrated lattice structure, manufactured in Ti-6Al-4V ELI alloy using Electron Beam Melting (EBM) technology. The research aim is to determine the technical risk associated with the implant through probabilistic numerical analysis. A series of boundary conditions are employed on the implants in order to investigate the robustness of the design. The output stress and strain values are then employed to further examine fatigue life parameters under cyclic loading of the implants. The probabilistic numerical analysis has successfully identified the location of a key failure mode (yield stress limit) and the modelling correlated to veterinary case-study observations. In regard to the lattice structure, it is shown that the structure does provide mechanical integrity to the implant assembly, but the geometry requires significant simplification while modelling. This is primarily due to: (a) the limitations of CAD tools in generating NURB surfaces from point cloud data, and (b) the node and element count associated with these small structures makes the model computationally expensive.

Additive manufacturing technology provides extraordinary handling of producing mechanical parts regardless of their geometric complexity which traditional way are not sufficient. Furthermore, in the global automotive industry, replacing body components with lightweight designs is an important advantage which distinguishes from competitors. In recent years, topology optimization used as a tool for optimum solutions throughout the product development phase. However, automotive manufacturers must think the global technical regulations. In this study, mechanical properties of different build directional (0°, 45°, and 90°) tensile specimens fabricated from aluminium alloy (AlSi10Mg) using direct metal sintering (DMLS) have been investigated. Specimens are analysed by the mechanical tensile test and the Vickers hardness test. As a case study the development of the vehicle liftgate door hinge will be presented, which has been topological optimized. Complex geometry hinges component designs are manufactured in EOS M290 additive manufacturing system using aluminium alloy (AlSi10Mg) powder. This paper presents, numerical and experimental solutions for behaviour of liftgate door hinge under the regulatory conditions. Referring to the results obtained, an interpretation was made to increase the use of potential of additive manufacturing technology in the automotive industry.

In this work, a numerical model based on the Particle Finite Element Method (PFEM) for the simulation of extrusion-based additive manufacturing of fresh concrete is presented. The balance of momentum and mass are solved with a mixed velocity-pressure formulation in an updated Lagrangian framework. The constitutive law is based on a Bingham model, that is approximated by a Perzyna formulation in order to account for the elastic regime before yielding, which is relevant for the analysis of printed material at rest. The channel flow test, a numerical benchmark for the flow of fresh concrete, is used to validate the model. Finally, 2D examples of extrusion-based additive manufacturing processes of fresh concrete are discussed.

A new design starts from an idea and become a final product, during design process the evaluation stage it’s a necessity, the most useful evaluation tool is prototyping. Conceptual models are very important in product design. Improving product quality is always an important issue of manufacturing, even if a design study is well organized it is possible some errors may still escape from the review of engineers and designers. The touch of the physical objects can reveal unanticipated problems and sometimes spark a better design. With the traditional method, developing of prototypes to validate or optimize a design is often time consuming and costly. Inject Binder is one of the most well-developed rapid prototyping or additive manufacturing technology, actually is a Powder-based inkjet 3D printing method. Mainly is a powder-based RP system in which a binder solution spays onto pre-deposited powder layers. One of the main advantage of this method is the production of fullcolor models suitable for architecture maquets, prototypes of new products like furniture and other objects. In prototyping process, a restriction is production cost that basically depends from the amount of printed material. In current study furniture prototypes are printed in a inject binder printer, the printed models have common design like a chair and a table. The raw materials used in this study were a plaster-based powder (zp151) and an appropriate water based solution with 2-Pyrrolidone as a binder (zb63). Three different model of each model (three chairs and three tables) are printed, the main difference between them is wall thickness, the first model thickness is 5mm, the second 10mm and third is 20mm. The printed parts tested in a compression tester device to check models elasticity and compressive resistance. Then the lab results used to create a FEA (Finite Element Analysis) study in a popular CAE program. In the final stage, the perspective of an optimization study are presented to determine an optimized shell geometry and wall thickness. The paper discusses useful tools for designers and engineers in order to decide the appropriate wall thickness and shell geometry (pattern) of furniture pieces, so to avoid model over dimension. And check functional and aesthetic aspects before massive production.

Directed energy deposition (DED), which is one of additive manufacturing applicable to metals, laminates the material on a baseplate by melting and solidifying with a high-power heat source. In terms of powder-based DED, the material waste tends to be large because powder flow is difficult to converge on the melt pool precisely. This study evaluates the variation in powder distribution when the deposition height is changed in order to obtain the optimal gas-flow rate and powder-nozzle shape. The powder flow is estimated with a computational fluid dynamics simulation based on Euler-Lagrange approach. The simulation results indicate that the proposed nozzles can achieve the high powder convergence stably even if the total amount of gas supply is reduced.

Triply periodic minimal surface (TPMS) based geometries exhibit extraordinary mechanical, thermal, electrical and acoustic properties thanks to their unique topologies. There are various types of structures in the TPMS family. One of the most well-known TPMS structures is the gyroid structure. This paper focuses on the vibrational behavior of a novel sandwiched gyroid structure in terms of their natural frequencies and mode shapes with three different feasible unit sizes at same volume ratio. Powder bed fusion technology is employed to fabricate gyroid porous specimens made of HS188 material. Modal testing is performed to deduce the vibration characteristics of aforementioned cellular structures. Besides the experimental study, the dynamic performance of the considered structures is investigated computationally by performing modal analysis using Finite Element (FE) models. A key challenge facing FE modelling of large scale gyroid structure is computation time and accuracy. For that reason, small size of gyroid lattices are utilized for compression tests in order to extract elastic properties. Then sandwiched gyroid plate is modelled as solid body with calculated elastic properties instead of complex gyroid topology and analyzed. Finally correlation level between experimental and FE results are presented.

This paper presents a Compliant Rotational Reducer Mechanism (CRRM), under development in the context of a space project. The CRRM is optimized using structural and flexural topology optimization for respectively, the structural and flexure problems. With respect to the structural optimization, a mass reduction of 20 % and a shift of the lowest undesirable eigenfrequency from 400 to 1000 Hz was obtained. For the flexural optimization, a Rotational Center Constraint (RCC) and a Floating Structure Modal Objective Function (FSMOF) are introduced. The FSMOF allows to impose a desired eigenmode of a mechanism. The RCC and FSMOF are applied to generate a flexure pivot with eigenmodes of a typical flexure pivot. Finally, these results are integrated into a novel version of the CRRM.

A finite element model for prediction of the temperatura field in the poder bed fusión process is presented and compared to measurements. Accurate temperatura predictions at the base plate are essential to accurately predict the formation of cristals in a metallic glass forming material. The temperatura measurements were performed by equipping the base plate with thermocouples during manufacturing of a cylinder with the glass forming alloy AMZ4. Boundary conditions for heat losses through the base plate/machine contact interfaces was calibrated to fitthe measurements. Additional heat losses was used to account for radiation at the top Surface and conduction through the poder bed. An interface boundary condition based on conservation of heat flux was examined to match the heat flow to the machine structure and the temperatura predictions was satisfying. Still,temperatura predictions with a constant heat transfer coefficient matched the measurements within 1.5oC during the entire building process of about 9 hours.

In this paper, we present a generative design optimization (GDO) approach for additive manufacturing (AM) by using topology optimization, support vector machines, cellular lattice structures (CLS), design of experiments, morphing and metamodel-based design optimization. By starting from appropriate design domains, a trade-off curve of design concepts is generated by SIMP-based topology optimization (TO). Then, a smooth implicit representation of the TO-solution is established by classifying the discrete density values using soft non-linear support vector machines (SVM). Instead of using the standard soft non-linear SVM of Cortez and Vapnik, we classify the TO solutions by using the 1-norm SVM of Mangasarian. In such manner, the classification is obtained by linear programming instead ofquadratic programming. The implicit SVM-model is further modified by incorporating cellular lattice structures, such as e.g. Gyroid lattice structures, by applying boolean operators. Design of experiments using finite element analysis are then set up by morphing the CLS-modified SVM models for different volume fractions. Finally, metamodel-based design optimization is performed by using optimal ensembles of polynomial regression models, Kriging, radial basis function networks, polynomial chaos expansion and support vector regression. The steps presented above constitute our proposed generative design optimization approach for additive manufacturing and are presented in more detail in the paper.

The present work is related to the fabrication of a scaffold with a customized shape through a variant of an additive manufacturing process often called liquid frozen deposition manufacturing, which consists in depositing layer by layer a polymer solution in a low temperature platform or chamber with an x-y-z motion platform. In this specific application, the x-y stage is actuated by high precision linear motors, located into a thermal chamber and must work at the temperature of -15° C, facing control problems related to variations of the electromagnetic interactions. Hence a multi-physics simulation has been developed in Open Modelica environment to understand the motor behavior and to allow the development of an amended control system.

We live in a time where resources are scarce and tools are developed to control their use. One of the most powerful material-saving tools is shape optimization. This latter is a computational method in which the shape of a designed part is adapted by adding or removing material according to the environment in which this part will be used. This method produces complex shapes, difficult to manufacture using classical techniques. In such situations, additive manufacturing appears to be as an appealing approach. In this paper, a non intrusive average stress based shape optimization technique is presented. This technique is composed of a processing phase followed by a post processing smoothing phase. In the processing phase, the stresses in a certain part are calculated using finite elements analysis. Then the Von mises effective stresses are calculated and compared to the average stress in the part. The low stress elements are removed, and hence in each iteration the average stress is changing as well as the standards deviation. After several iterations, the algorithm converges and the part is ready for the post processing phase. In the next phase, the part has non smooth surface because of the element removal. Each node on the non smooth surface is detected and the concavity of the surface to which it belongs is found with respect to the topology of its environment, using a weighted Laplacian algorithm linking the selected node to its neighbors. The obtained concavity is then applied to each node. The process is repeated for several iterations until the surface is smooth as desired and the final shape is found and ready for printing. This technique has been tested on several load configurations and the obtained results were in agreement with other techniques from the open literature [1]. This method is attractive since it doesn’t need to re-mesh the domain at every iteration. In addition, it does not require a high processing power since the results were obtained during half an hour using a medium fine mesh on an i5 processor with a home made code. Furthermore, at the end of this algorithm the stress distribution in the part is quasi-homogeneous and it gives flexibility for the user to choose the desired stress criterion which suitable for the studied application.

We present the results of a 3D modeling of the laser powder bed fusion process on the mesoscale level with an advanced multiphysical numerical tool. High-performance simula- tion allowed to conduct a vast parametric study. Thus, the model has been extensively verified against experimental results in a large parameter range, and, further, it has been used to con- struct detailed process maps in the range not covered by the available experimental data. The analysis of the results that were obtained in the model along with the data in the pub- lished research allowed to propose the quantitative criteria for determining the behavior of the track formation. The key phenomena that affect this behavior have been studied. We conclude that the productivity limit that arises with the proportional increase in scanning speed and laser beam power is caused by the spatter ejection. The sensitivity analysis shows that the transition to the spattering regime is caused by the overheating of the meltpool surface layer, and, conse- quently, the development of the surface instability. The instability development is assumed to be due to the fact that the recoil pressure becomes much higher in comparison with the surface tension.

The recent appearance of hybrid CNC machines – which can both add and remove material to an object – has facilitated a new type of approach to the problem of repairing damaged com- ponents. Up to now, repair operations have been carried out manually and for this reason they are errors prone, costly and time consuming. The use of precise and repeatable CNC machines in this field is therefore very attractive for the sake of reliability and repeatability. One of the biggest obstacles on the automation of the repairing process is that the CAM software requires a solid CAD model to create the toolpaths needed to perform additive operations. The present work proposes the use of octrees to detect the damaged spot starting from the 3D scan of the damaged object. A software named DUOADD has been developed to convert these informa- tions into a CAD model suitable to be used by the CAM software. The new workflow designed to perform a complete repair operation is here described. DUOADD allows to approach the repairing problem from a new point of view opening the doors to save both time and money. The successful application of the entire process to repair a damaged die injection mold is also here reported. §DUOADD=DUOADD Uses Octree sAs Damage Detector

Selective laser melting (SLM), with the advantages in producing complex geometry, is becoming one of the most promising additive manufacturing (AM) technologies [1]. In order to understand the multiple physical phenomena which is crucial for successful manufacturing during SLM process, different computational models that are less expensive but challenging compared with experiments and real-time monitor technologies have been developed in the past years.In order to investigate particle scale thermal-physical phenomenain SLM process,a three-dimensional model considering Fresnelreflectionis developed to and the volume of fluid approach isused to track melting and solidification phenomena.Numerical results show that the melt track is broken into several regions to minimize surface energy because of surface tension.The molten liquid tends to flow outwards from the laserspot caused by Marangoni effects.Thesolidified surfaceof multiple particle diameterpowders is much roughercompared with powder bed with layer thickness of one particle diameter.The developed model provides acomprehensive understanding about physical phenomena during SLM process.

Projectwork accompanying an undergraduatecourse on software engineering has been re-designed to provide early student expose to data analysis for process monitoring in additive manufacturing.For originaldata from alocal research group active in selective laser melting (SLM) process development,i.e. forsensormeasurements and control flags,aset of established mathematical and statistical routines were made conveniently availableby developing scientific software tools.Standardized procedures for software engineering were taught and applied.Students experienced challengesand professional approachesinvolved in collaborative software development, implementedproject management ideas and delivered a working software tool together with proper documentation.Gain indomain knowledge on process monitoring for additive manufacturing supported the activityas a motivating factor.

This document provides a method to derive guidelines for a post processing oriented design of additive manufactured parts based on experimental investigations.

In this research, an optimization design of the lattice structure is investigated, which is based on the ground structure method. In recent years, as a result of rapid development of additional manufacturing technology, it has become possible to manufacture complicated shapes including periodic lattice structure. However,in real metal lattice samples, geometric imperfections may exist in every unit because of the stochastic influence of feasible processing path. In this study, a new ground structure method which does not leave elements with small cross sectional area was proposed. In particular, the effect of geometric constraints caused by additive manufacturing techniques on optimized results are discussed based on the robust topology optimization combining perturbation methods for quantifying uncertainty. In the end, a robust topology optimization was also discussed as a problem to minimize expected value and standard deviation of compliance.

The selective laser melting process causes high thermal-induced residual stresses that may result in unwanted part distortion and may affect fatigue strength of the part. This study initially presents the fatigue behavior obtained by testing directional specimens of SLM AlSi10Mg in the as-built condition (i.e. no heat treatment after fabrication). Then, the SLM process of specimen fabrication is simulated using the inherent strain approach to determine residual stresses at the location and in the direction of fatigue crack initiation. A direct correlation of the computed residual stresses and the actual fatigue behavior provides qualitative insight into the simulation accuracy.

A numerical model based on the Smoothed Particle Hydrodynamics (SPH) method is developed for 2D and 3D simulations of the laser sintering process of polyamide 12 (PA12) powder on the grain scale. Melt track simulations yield detailed insights in the visco-thermal dynamics of the process including the porosity evolution. The simulations are validated by measurements of the transient surface temperature. A dimensional analysis of the process allows for quantification of the importance of all involved physical mechanisms and predicts the magnitudes of the observable physical quantities with good accuracy.

Additive Manufacturing (AM) allows unprecedented design freedom, which can be explored by the Topology Optimization (TO) algorithm. Their interplay allows a new engineer- ing cycle with the potential to design and manufacture disruptive concepts. Thus, a systematic methodology for designing AM parts is presented, being the main goal of this study. The methodology is subdivided into several phases, each phase contains several tasks. Moreover, the data flow between phases is considered and solutions are provided. Finally, the methodol- ogy is applied to a space case study and preliminary results of the AM engineering cycle (TO, part design and structural analysis) are depicted.

Heart valve diseases are among the leading causes of cardiac failure around the globe. Current advances in imaging technology, in numerical simulation and in additive manufacturing are opening new frontiers in the field of development of new personalised prosthetic devices. The 3D printing technique could allow the realisation of personalised models for each patient undergoing valve replacement surgery. A CAD model of an aortic valve prosthesis was designed on the basis of elliptic-hyperboloid formulation. The resulting CAD model was used both to perform numerical in-silico simulation and to design a modular mould for AV fabrication. Simulations were performed through a novel hybrid approach based on RBF mesh morphing technique and CFD simulations. The polymeric aortic valve was manufactured by 3D printed process and spray deposition technique. To assess the in-vitro valve properties, the prototype was inserted in a custom mock circulatory loop to reproduce the aortic flow conditions. The manufacturing process of both the mould and the valve was successful and the in-vitro testing showed an effective orifice area (2.5 mm2) and regurgitation fraction (5%) in accordance with the ISO-5840-2. The novel simulation strategies have revealed to be a promising approach to test both structural and functional device performances.

Computational simulations represent a powerful tool for the pre-procedural clinical assessment of minimally invasive cardiovascular interventions [1]. Patient-specific simulations rely on the accurate numerical implementation of both geometrical and mechanical features. While current imaging techniques are able to depict accurately patient-specific anatomies, at date, a similar image-based tool capable to retrieve subject-specific material properties is missing. The scope of this study is to present a framework, involving in silico tools and 3D printing, for the refinement of an image-based technique [2] capable to retrieve in vivo patient-specific mechanical information from functional and morphological magnetic resonance imaging (MRI) data. The workflow consists in three main steps: (i) selection and mechanical testing of 3D commercially available deformable 3D printed materials; (ii) fluid-structure interaction (FSI) simulation of a vessel model under pulsatile regime; (iii) 3D printing of the model and experimental replica in MRI environment. Finally, the imagebased technique is applied to both numerical (ii) and MRI data (iii) to retrieve material information to compare to reference (i). The described workflow strategy was successfully implemented by our group. The deformable material TangBlackPlus FLX980 was selected and mechanically tested, resulting in an elastic module (E) of 0.50 0:02 MPa. A vessel model was designed for FSI simulations (E=0.50 MPa) as well as 3D printed with an Objet500 Connex machine (Stratasys, Minnesota, USA) to acquire MRI data. The image-based technique was used to retrieve the E value from numerical and experimental data. In silico, the indirect material evaluation resulted in E=0.49 MPa, while in vitro we found E=0.51 0:04 MPa. Moreover, other values of E (up to 32 MPa) were tested in silico, leading to matching results as well. Other deformable materials will be investigated, i.e. Agilus30 (Stratasys, Minnesota, USA) and Elastic and Flexible resins (Formlabs, Massachusetts, USA), by using the described framework. With further refinements, this strategy would lead to an indirect and image-based tool for the in vivo assessment of patient-specific material properties, thus enhancing the confidence of patient-specific computational models.

We present a functionally graded material design (FGMD) approach relying on at opology optimization procedure based on asymptotic homogenization and phase-field method. We also introduce a complete framework from which numerical results lead to 3D printed structures. We firstly present numerical experiments to verify the proposed methodology and, subsequently, we discuss experimental measurements comparing optimized FGMD with a constant density structure having the same weight. Experimental evidence shows the effectiveness of the proposed methodology in improving the overall stiffness of optimized structures.

New methodologies of Design for Additive Manufacturing (DFAM) and relative CAx tools are the key enabling technologies allowing to get the major benefits from AM. It is evident that an increased integration of all CAx phases would lead to a more efficient design and engineering workflow. One of the major bottlenecks of such a holistic approach, which affects AM product time-to-market and restricts its commercial exploitation, is the need of a high amount of time and human resources for simulation, modelling and postprocessing of all the engineering activities. That is not always manageable, especially during a preliminary stage of concept design or feasibility analysis. Modern mathematical approaches are facing, with the ambition to contribute to some of the most challenging engineering tasks to fulfil strict requirements of structural resistance, lightness, noise, static and dynamic stiffness. The effectiveness of analytical and geometrical tools and methods for the study and the optimization of shapes were already demonstrated. As an example, it is well known that small fillet radius are stress concentrators and must be avoided for a robust design of structural parts. In the same way, we can demonstrate that poorly uniform temperature distribution of the material during additive layer manufacturing can be correlated with geometrical section areas and variations along the growing axis, as well as with supports shape configurations. In this paper, a novel approach is presented which identifies optimal orientation and support configurations, uniquely based on geometrical criteria. The benefits are avoiding long structures to minimise the amount of waste material, accounting for the distribution of the piece weight, effectively draining the thermal field from all the areas of the piece to the build platform. With FE based macroscale process simulations, it is possible to evidence improved thermal strain distributions of the optimised configuration. As part of the R&D activity within the “STAMP” project financed by Regione Piemonte, an innovative function was developed and successfully applied to minimize distortions and residual stresses of SLM parts. Within the same project, a software interface was developed for setting user parameters and individual jobs. The interface provides detailed information of the laser path and physical variables, which can be used for off-line or in-line monitoring and control and provides a model for process simulation. It is also possible to view the entire laser path and the detail of each individual trait, and to generate a file containing structured data as a FEM model, for setting boundary conditions and process parameters. The algorithms are included in the integrated platform for AM developed by ITACAe, named AMTOP®. Starting from geometrical, functional and structural product specifications, the platform includes a topological optimization phase, new geometry construction, FEM discretization, FEA validation, optimal orientation and supports creation, so representing a fully integrated product & process engineering workflow.

This contribution focuses on the experimental investigation and material modelling of the crosslinking of UV curing polymers used in additive manufacturing processes such as dig- ital light processing and stereolithography. First photocalorimetric measurements with varying temperature and light intensity are shown. From the exothermic specific heat flows measured during the crosslinking reaction, the degree of cure can be determined for each experimental scenario. It is shown that the test temperature and light intensity have a significant influence on the crosslinking reaction. A first modelling approach for the mathematical description of the crosslinking reaction is pre- sented. Moreover, parameter identification of the proposed model is conducted using the com- mercial optimisation program LS-OPTQR

The urgency of mathematical model development for wire-based electron-beam additive manufacturing process analysis is shown. The procedure of solving heat equation for metal in the solid phase and the Navier-Stokes equations in the liquid phase, based on the use of the finite-difference method and the predictor-corrector procedure is described. An algorithm for numerical approximation of free melt surface motion, using the concept of the volume of fluid (VOF), is described as well. A numerical algorithm for surface tension force calculating is proposed. The model described above was realized as a program in the Microsoft Visual Studio environment. Series of computational experiments were carried out to calculate metal flow during deposition with the use of 316L steel wire. The results of experiments are compared with experimental data.

Due to its high design freedom and flexibility, Additive Manufacturing is often used as an alternative to the conventional manufacturing. In order to be competitive, as many advantages of additive manufacturing as possible should be used. Lightweight construction is one of the biggest advantages of Additive Manufacturing. However, implementing lightweight design for AM requires different product design approaches compared to conventional development. To achieve the lowest possible part volume combined with a high strength, it is possible to optimize the topology. At first, stresses in the part are localized by means of a numerical simulation. Subsequently, by comparing them with a reference, high and low-loaded regions can be separated. Thus, a targeted volume reduction can be implemented. In order to be able to respond to the restrictions of the manufacturing processes, these must be considered before the optimization. This paper presents a procedure for a production-oriented simulation and topology optimization for the SLM process (Selective Laser Melting). An approach to optimizing the topology is presented with regard to technical as well as economic aspects. In doing so, methods for the quantitative assessment of success factors are used. Since various procedural restrictions exist for the SLM process, such as anisotropy or thermal distortion, these must be considered before the topology optimization. This is done by adjusting the simulation and optimization parameters. Through this adaptation, it is also possible to take into account the previous assembly concept and to improve it by an integrated design. In order to comply with required tolerances, both a thermal and mechanical postprocessing is necessary. This in turn must already be considered in the optimization task. This approach is illustrated by the optimization of the topology of the pelvis of "Sweaty", the humanoid robot. This robot was developed by students and is able to play football. It is a participant in the annual RoboCup, where he is currently Vice World Champion. In a previous study, three different materials were already evaluated. Among these is a novel high-tech material called Scalmalloy, which is used in this case study. It has been developed for the aircraft industry and has excellent properties in terms of density and strength. Two design variants were developed using topology optimization and iteratively optimized by adjusting the parameters. These each have different mounting concepts. Finally, the design variants were compared in terms of weight, stiffness and cost to find the best technical and economical solution. For this purpose, an economic analysis was carried out to evaluate the costs and benefits. This design solution was subsequently validated and manufactured using the SLM process.

One important advantage of Additive Manufacturing (AM) in relation to optimization for light weight construction is that there is a reduction in manufacturing constraints compared to classical manufacturing methods [5]. To make full use of these advantages and to exploit the resulting potential, the components previously have to be designed using optimization (see[5]). Against this backdrop, a Mixed Integer Program (MIP) is developed in order to be able to use the methods of Technical Operations Research (TOR) in the context of Topology Optimization (TO) on the basis of a fitted Ground Structure Method (GSM) for lattice and truss structures. In addition, an optimization-oriented construction workflow (see figure 3) is developed in order to fully exploit the advantages in design freedom of AM. As shown in figure 3, this work addresses three interdisciplinary subareas; Operations Research (OR), AM as the manufacturing method and a link between this sub-areas in the form of a Computer Aided Design (CAD) solution, resulting in a TOR application.

In the industrial application of additive manufacturing processes, a significant amount of time and resources is dedicated to the orientation and pre- print setup of the geometry. Steps such as the generation of support structures and the process simulation are among the most time-consuming. For the thorough assessment of an orientation of a given geometry, even more criteria, like print time or surface quality, need to be considered. POEAM proposes a method for an efficient assessment of a set of orientations, by means of well formulated criteria and an early elimination of insufficient orientations. The goal is to narrow the search field, so costly preparation steps will only be performed on orientations that promise a superior end result. Furthermore, POEAM is an automated process, which means it can be performed with minimal human interaction, resulting in an optimum regarding cost- efficiency and evaluation time. The method was applied to a representative geometry and has shown results that confirm the above mentioned advantages.

The conception (or risk assessment) of complex mechanical systems has to take into account a series of constraints. Such constraints can be due to certification criteria, performance objectives, cost limitations, and so on. In this context, the role of simulation has kept increasing for the last decades, as it should be able to predict if a given configuration of the system is likely to fulfill these constraints without having to build it and to test it experimentally. In many cases, the computation of these constraints is associated with a series of computer software, whose physics can vary a lot. For instance, in the car industry, the conception of a new vehicle can be subjected to constraints on its size and weight, which are rather easy to compute, but also on its emergency stopping distance, its crash or aerodynamic resistance, which can be much more difficult to evaluate. Thus, several software (structure dynamics, multibody modeling, fluid dynamics software for instance) are generally needed to verify all the constraints. Numerical methods to identify the limits of such “conception domains”, that is to say domains in which all the constraints are verified, are needed [1]. As the computational costs associated with the constraints can be very different, the question then arises of how to optimize the number of evaluations of each code to minimize the uncertainties about these limits, for a given computational budget. In this prospect, this paper presents an innovative approach to predict the limits of the considered conception domain, but also to quantify the uncertainty associated with this prediction. Based on an adaptive Gaussian process regression, this method allows us to find iteratively the new code evaluations that will maximize the knowledge about the searched limits at the minimal computational cost. First, the scientific basis of such an approach will be presented. The efficiency of such a method will then be illustrated on an analytical example.

International audience; In this work, we are interested in the propagation of electromagnetic waves in complex media. More precisely, we would like to study time dependent wave propagation problems with strong multiscale features (possibly in space and time). In this context we would like to contribute in the design of innovative numerical methods particularly well suited to the simulation of such problems. Indeed when a PDE model is approximated via classical finite element type method, it may suffer from a loss of accuracy when the solution presents multiscale features on coarse meshes. To address this issue, we rely on the concept of multiscale basis functions that is one solution to allow for accuracy even on coarse meshes. These basis functions are defined via algebraic relations. Contrary to classical polynomial approximation, they render by themselves a part of the high-contrast features of the problem at hand. Recently, a new family of finite element methods has been introduced in [1]-[2], referred as " Multiscale Hybrid-Mixed methods " (MHM), which is well adapted to the simulation of high-contrast or heterogeneous problems. The underlying approach relies on a two level discretization. Shortly, basis functions computed on a fine (second level) mesh allow for the reconstruction of the solution on a coarse (first level) mesh. Such MHM have been initially designed in the context of stationary problems, such as Darcy flows. In this work, we propose to extend the concept of MHM to time dependent electromagnetic wave propagation problems. The model problem relies on the time dependent Maxwell's equations. The continuity of the electric field is relaxed via the introduction of a Lagrange multiplier. The solutions are expressed on a basis computed at the second level that incorporates the heterogeneity of the problem via the resolution of a PDE. Several schemes are proposed from implicit to explicit time schemes and continuous finite elements to discontinuous ones for the spatial discretization of the local problems at the second level.

Mechanics, like other domains, continues to supply numerous engineering problems that, despite the impressive progress of computational simulation techniques, remain intractable today. RB, POD and PGD model reduction methods are leading to a new generation of high-performance computational tools which provide solutions to engineering problems which are inaccessible to standard codes based on classical and well-established numerical techniques. This is a true breakthrough with a potential gain of several orders of magnitude. The approach we are considering here is the Proper Generalized Decomposition (PGD) which can be seen as an extension of POD. The main idea consists in calculating the shape functions and the solution itself simultaneously offline using an iterative procedure. A priori, these shape functions are arbitrary and must satisfy only a variable separation hypothesis, this hypothesis being also at the center of POD and RB reduction methods. First, the aim of the lecture is to examine the validity of the variable separation hypothesis, which is central in the PGD. For that, we use a benchmark proposed by S. Idelshon which is a unidimensional transient thermal problem with a moving load, the parameter being the velocity of the load. Non-separated shape functions are also studied. The second part of the lecture deals with the different techniques for the computation of PGD approximation. They include a new one based on the “PGD-error indicator” introduced in [2,3]. The reference to quantify the effectivity is the H1-SVD of the “exact” solution. Some error estimators are also computed.

The proposed communication will address the following question: Find an approximate solution such that the approximation error norm in L2 is less than a prescribed ε. And indeed we are interested by a small complexity in terms of floats. Answering to this assumes that the algorithm involves a mechanism increasing mesh size. No innovation from this side, the outer loop will be a nested iteration with new 2D meshes four times richer (in terms of vertices) than the previous ones. Decision to continue relies on a corrector. For efficiency the nested iteration is combined with a multigrid (MG) resolution, which will be the most inner loop. The MG cycling also stops on an evaluation of the L2 error estimate. In between, the intermediate loop is a mesh adaptation loop. A novel formulation allows looking for the metric parametrization which minimizes the L2 norm of approximation error. This approach relies on the association of an adjoint state, a corrector field, and a local error, the sensitivity of which with respect to the metric is computed. The calculation of a boundary layer with an error of 0.1% is obtained in 10 seconds of adapted FMG, 1000 of FMG. The extension to Euler flows is illustrated with the scramjet flow of second figure (second-order convergence is obtained). Extension to Navier-Stokes is on-going.

TIn the computational physics community, a consensus is forming on the superior efficiency of high-order numerical schemes for problems with high resolution requirements. However, manycontributions show that a linear discretization of the geometrical model can limit the accuracy ofhigh-order methods. Thus, it becomes necessary to develop robust and efficient methods forcurvilinear mesh generation and adaptation.In a previous work [1], a method for generating valid high-order meshes has been presented. Themeshing procedure starts with a mesh that is straight-sided everywhere in the domain, except on theboundary, where high-order nodes are placed on the real geometry. An optimization procedure is usedto untangle the invalid elements that often appear in the vicinity of curved boundaries, whilepreserving the original mesh as much as possible.In this talk, we focus on the problem of estimating and controlling the geometrical accuracy of high-order meshes as well as their impact on the stability and accuracy of the simulation.The geometrical accuracy of curvilinear meshes can be estimated by measuring a distance between amesh boundary and the corresponding geometrical model entity. Distance measures defined in theliterature, namely the Hausdorff and the Fréchet distances, rely on a solid mathematical basis.However, they are complex to implement, and their computational cost is prohibitive in the presentcontext, even in an approximate form. We present an alternative estimate for the geometrical error,that is simple and computationally efficient enough to be used in 2D and 3D applications.The curvilinear character of high-order meshes also impacts the performance of the numericalscheme. In most Finite Element methods, the functional space of approximation locally defined on areference element is affected by curved elements in physical space, which may lead to a degradedaccuracy [2]. The conditioning of the spatial discretization is also influenced, with possibly negativeconsequences on the maximum time step that can be used with explicit time integration schemes [1].We put these effects in evidence and identify Jacobian-based measures that quantify them.Finally, we describe how the existing mesh optimization procedure can be adapted to take intoaccount the geometrical error or the numerical effects of the mesh. We illustrate the benefits of thismethod with several examples.

National audience; Despite the important progress in computer sciences, the cost associated with the resolution of multi- parametric problems can be extremely prohibitive. This is especially important when dealing with problems depending on numerous parameters, as encountered in optimization studies, which are becoming more and more mandatory for the design of new products. Reduced Order Modelling (ROM) is a convenient answer to circumvent this issue, usually called curse of dimensionality. However, a main drawback of ROM is the lack of robust a posteriori error estimators to measure the quality of the approximated solution, even if first advances have been performed [1,2].This paper extends the a posteriori verification procedure proposed in [3] that enables to control and certify PGD-based model reduction techniques, which are currently the subject of many research activities [4]. This procedure uses the concept of constitutive relation error allowing to get guaranteed global/goal-oriented error estimator taking both discretization and PGD truncation error into account. By splitting the errors sources, it also leads to a natural greedy adaptive strategy, which can be driven in order to optimize the accuracy of PGD approximation [5,6]. We extend it to the cases of geometrical parameters models and PGD separation of space variables [7].The focus of the talk is on two technical points: (i) construction of equilibrated fields required to compute guaranteed error bounds for those specific cases; (ii) error splitting and adaptive process when performing PGD-based model reduction.

In this paper, the approach proposed by Ladevèze and Pelle in 1989 [1] for deriving computable, sharp and guaranteed lower bounds for eigenvalues is revisited. The key lies in a static quotient where a load space and a corresponding statically admissible stress space are introduced. The difficulty is on the computation of strict lower bound of the first nonzero eigenvalues. There are two additional eigenvalue problems to be solved. The first one is global and one computes only the first eigenvalue; the second one is defined over the element and then local. The goal of this work is twofold. First, we would like to make easier the implementation of these additional problems which are not classical [2-6]. The second aim is to get sharper the computed lower bound. Our answer introduced here is a multiscale approach, the smaller scale being used for the computation of the additional problems. It is developed in this paper for P1-triangle elements.

Cohesive zones models are commonly used in numerical simulations to take into account the onset and the propagation of microcracks leading to the fracture of materials. Their numerical implementation in finite element schemes is based on embedding surface traction-separation law between two adjacent bulk elements. The traction between two neighboring elements is linked to the corresponding opening by a cohesive relationship. The objective of the work reported here is to extend the approach developed in [1, 2] to identify the shape and parameters of the cohesive zone models in metal matrix composites with brittle inclusions and adapt this method to the study of initially heterogeneous material (e.g. graded metals or ceramics). To treat these applications where mechanical fields are heterogeneous, local stress fields are to be estimated in addition to conventional kinematic fields to build the energy balance associated with the transformation. Here we propose to estimate these fields by an identification method using kinematic and thermal data from imaging. The proposed method is based on the minimization of a functional associated with the error in constitutive relation (Constitutive equation gap method) [3]. In its classical (mechanical) formulation, this functional depends on two sets of parameters: the stress field and the mechanical material properties (elasticity, plasticity, damage). We show here that the identification procedure is capable to estimate the stress fields and material properties for elastic and elastoplastic behavior. The method was applied on noisy measured displacement fields to assess its robustness in the case of elastic behavior. The method is now being extended to damageable plasticity. The introduction of a second (calorimetric) term in the functional, related to the heat sources is also examined.

In this paper we presenta methodology to performelasticity analyses of trabecular bone fromhuman wrist micro CT scans, with the final purpose of providing datawhich can be used, together with other measures, to develop new diagnostic tools to improve the characterisation of bone quality and its structural behaviour.This analysis is carried out by using a version of the Cartesian grid Finite Element Method (cgFEM) for medical images. As inimage based methods, which assign one element to each voxel, cgFEM takes advantage of the fact that both the mesh and the image have compatible Cartesian structures in order to create the FE modelfrom the image, in an automatic way, without any intermediate step. In contrast to the image based methods, cgFEM can keep the number of degrees of freedom relatively low, by using an efficient h-adaptive process to adapt the mesh to the heterogeneity of the image.H-adaptivity allows cgFEM to capture the borders of the bodies represented in the medical images without the necessity of creatingthem explicitly as in the usual geometry based methods. As a consequence,it does not require the cumbersome, often manual, process of creatingintermediate geometrical modelsfrom the bitmap which areusually one of the most expensive stages in patient specific simulations.Here, in particular, we show results of trabecular bone overall stiffness tensor evaluation obtained by using cgFEM in a homogenisation procedure.

Energy dissipation by dislocation plasticity in metals provides the resistance against crack growth that makes metals tough engineering materials. However, homogenized plasticity constitutive laws must fail at a singular crack tip, one consequence of which is that the conditions for crack growth are typically calibrated using experimental data rather than computed from fundamental mechanics. This issue, along with the size-dependence of plasticity and the need to address chemical aspects of fracture, dictates that plasticity and fracture be studied at smaller scales – from the dislocation level down to the atomistic and quantum levels. The severe challenges in simultaneously capturing the macroscopic plasticity and the nanoscale behavior at the crack tip, and doing so on time scales appropriate to real materials, are first discussed. Emerging multiscale methods for addressing some of these challenges are presented, including the Coupled Atomistic/Discrete-Dislocation (CADD) model, its extension to Quantum Mechanics, its extension from plane strain to full 3d problems, and the Coupled Discrete-Dislocation/Crystal-Plasticity model, which taken together bridge from quantum to continuum scales of plasticity. Examples of successes are shown and limitations identified. Relevant to MATHICSE interests, these advanced multiscale methods, i.e. those that go beyond the basic coupling of atomistics to a hyperelastic continuum (e.g. the Quasicontinuum model), are highly algorithmic, or recipe-based. The coupling is accomplished through ideas akin to domain decomposition but, because the different domains have different constitutive descriptions, the “boundary conditions” at the domain interfaces are non-standard and often non-local. Thus, while these methods preserve important fundamental physics and mechanics with demonstrated high and often controllable accuracy, putting such methods on a firm mathematical foundation appears to be very difficult. However, finding alternative new methods that are derived from a more-formal structure is also a huge challenge because the loss of degrees of freedom (electrons, atoms, dislocations) with increasing scale of description precludes the development of, for instance, a single energy functional from which the mechanics would emerge naturally.

We propose a numerical method for approximate the solution of a class of infinite dimensional parabolic problems. In particular, for the Fokker-Planck-Kolmogorov (FPK) equations in an infi- nite dimensional Hilbert space. The FPK equations are partial differential equation that describe the time evolution of the probability density function of the velocity of a particle under the influ- ence of drag forces and random forces, it is a kind of continuity equation for densities. This type of equations have been deeply studied in the last years, see for instance [1], [2], [3], [4] and the references therein. In a separable infinite-dimensional Hilbert space H with inner product (·, ·)H we define a Gaussian measure µ with mean zero and nuclear covariance operator Λ with Tr(Λ) < +∞. We focus on the stochastic differential equation in H dXt = AXtdt + B(Xt)dt + ✓QdWt, (1) where the operator A : (A) is the infinitesimal generator of a strongly continuous semigroup etA in , Q is a bounded operator from another Hilbert space to and B : (B) is a nonlinear mapping. The equation (1) can be associated to a Kolmogorov equation in the next way, we define x t where u0 : R and Xx is the solution to (1) with initial conditions X0 = x where x . Then u satisfies the Kolmogorov equation: ∂u 1 = Tr(QD2u)+ (Ax, Du) + (B(x), Du) . (3) ∂t 2 H H ion (3) in the following way. u(t, x) = un(t)Hn(x), x ∈ H, t ∈ [0,T ], (4) n∈J where un : [0,T ] R and Hn(x) are the Hermite functionals which take values on . After some calculations the Kolmogorov equation becomes u˙n(t)Hn(x) = − un(t)λnHn(x)+ un(t) B(x), DxHn(x)lH (5) By truncation the infinite system (5) we obtain a matrix differential equation and by solving it we fix the functions un(t) and then we set up the numerical solution by using (4). We test the method for the simple case of a 1-d diffusion and we will present the description of the method and the results for this test case. The future of the research is apply this method to the solution of the stochastic Navier-Stokes equations and study the stability of the method, rate of convergence of the approximations to the theoretical solution.

Some industrial processes, such as polymer curing, require control algorithms in order to guarantee a certain level of quality for the components that are being processed. These control algorithms work in a real time constraint because they need to modify, on-line, the operating parameters. Additionally, the material parameters, such as the diffusion coefficient, are not necessarily constant along time or, in some situations, they are simply unknown. This makes difficult that existing techniques provide, in real time, enriched information about the process to the control algorithm. In this work we propose a novel approach that makes use of a reduced basis obtained form the multi-parametric solution provided by the Proper Generalized Decomposition [1]. This reduced basis accounts with the explicit dependence of the solution of the parameters. Thus, by only solving a system of equations of the size of the reduced bases, we are able to both, obtain the reconstructed solution and identify the parameters that define it. Additionally, we also augment the method with a technique to place the sensors where best suits to the reduced bases, based on the Discrete Empirical Interpolation Method (DEIM) [2]. Finally we provide an a priori error indicator, with upper-bounding properties, useful to evaluate the size of the reduced bases for a certain level of accuracy, and also an a posteriori error indicator to control the accuracy of the results.