Phase Transformation Advancements of the Enriched Analytic Solution Method for Additive Manufacturing Applications

2019 ◽  
Author(s):  
John C. Steuben ◽  
Andrew J. Birnbaum ◽  
Athanasios P. Iliopoulos ◽  
John G. Michopoulos
Keyword(s):  
Finite Element ◽  
Phase Transformation ◽  
Additive Manufacturing ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Element Discretization ◽  
Simulation Tools ◽  
Property Data ◽  
Manufacturing Applications ◽  
Melting And Solidification

Abstract Renewed interest in additive manufacturing (AM) and rapid prototyping technologies has driven great demand for corresponding modeling and simulation tools. While most such models are defined via the finite-element discretization of the relevant multi-physics, the authors have recently developed a method based on the enrichment of classical analytic solutions to the heat equation. The principal advantage of this enriched analytic solution methodology (EASM) is its high computational efficiency that can enable in-the-loop process control in a manner that removes assumptions made for classic analytical solutions and accounts for additional physics. These features enable the efficient and accurate exploration of the high-dimensional AM process parameter space. This work presents a further enrichment of the underlying analytic solutions to include the effects of phase transformation upon melting and solidification, which are shown to be significant in magnitude. It is demonstrated that the available property data for common AM materials are not adequate for accurate thermal modeling (via finite-element, EASM, or other means), and must be improved via future experimental efforts. A discussion of the accuracy and significance of the results achieved, and a summary of further work necessary to bring the EASM to maturity concludes this work.

Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications

2020 ◽  
Vol 5 (4) ◽  
Author(s):  
Aysenur Toptan ◽  
Nathan W. Porter ◽  
Jason D. Hales ◽  
Benjamin W. Spencer ◽  
Martin Pilch ◽  
...  
Keyword(s):  
Finite Element ◽  
Heat Conduction ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Simulation Tool ◽  
Code Verification ◽  
Simulation Tools ◽  
Steady State Heat ◽  
The One ◽  
Selection Of

Abstract When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. Here, we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.

Enriched Analytical Solutions for Additive Manufacturing Modeling and Simulation

2018 ◽  
Author(s):  
John C. Steuben ◽  
Andrew J. Birnbaum ◽  
Athanasios P. Iliopoulos ◽  
John G. Michopoulos
Keyword(s):  
Additive Manufacturing ◽  
Modeling And Simulation ◽  
Analytical Solutions ◽  
Analytic Solutions ◽  
Computational Effort ◽  
Infinite Domain ◽  
Underlying Assumption ◽  
Simulation Tools ◽  
Computational Performance ◽  
Am Processes

Additive Manufacturing (AM) is an increasingly widespread family of technologies for the fabrication of objects based on successive depositions of mass and energy. A strong need for modeling and simulation tools for AM exists, in order to predict thermal histories, residual stresses, microstructure, and various other aspects of the resulting components. In this paper we explore the use of analytic solutions to model the thermal aspects of AM, in an effort to achieve high computational performance and enable “in the loop” use for feedback control of AM processes. It is shown that the utility of existing analytical solutions is limited due to their underlying assumption of a homogeneous semi-infinite domain. These solutions must therefore be enriched from their exact form in order to capture the relevant thermal physics associated with AM processes. Such enrichments include the handling of strong nonlinear variations in material properties, finite non-convex solution domains, behavior of heat sources very near boundaries, and mass accretion coupled to the thermal problem. The enriched analytic solution method (EASM) is shown to produce results equivalent to those of numerical methods which require six orders of magnitude greater computational effort.

scholarly journals A Forward Time Stepping Heat Conduction Model for Spot Melt Additive Manufacturing

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
B. Stump ◽  
A. Plotkowski
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Analytic Solution ◽  
Dimensional Space ◽  
Mathematical Formulation ◽  
Finite Volume Methods ◽  
Analytic Solutions ◽  
Conduction Model ◽  
Time Stepping ◽  
Speed And Accuracy

Abstract Solidification dynamics are crucial for determining microstructure development in additively manufactured parts. Multiphysics models based on finite element or finite volume methods may help gain insight for complicated phenomena such as fluid flow, keyholing, and porosity but are too computationally expensive to use for simulating actual builds. Recent analytic and semi-analytic solutions for moving heat sources in a semi-infinite three-dimensional space provide a way to accurately estimate the solidification conditions for entire builds. The downside to these methods is that, unlike finite element or finite volume methods, they cannot use the temperature distribution of the previous timesteps to march the solution forward in time. This paper provides the mathematical formulation and implementation of a forward time stepping (FTS) approach to an existing semi-analytic solution. The speed and accuracy of the two methods are then compared for various scan patterns. The result is that, for spot melts, the forward time-stepping model provides improvements in both speed and accuracy. This is especially true for longer simulations, where the simulation can be orders of magnitude faster. The longest simulation analyzed in this paper was roughly 30× faster when using the forward time-stepping model versus the straightforward implementation of the semi-analytic solution.

scholarly journals Generalities on finite element discretization for fractional pressure diffusion equation in the fractal continuum

2019 ◽  
Vol 65 (3) ◽  
pp. 251
Author(s):  
H. D. Sánchez Chávez ◽  
C. A. López-Ortiz ◽  
And L. Flores-Cano
Keyword(s):  
Finite Element ◽  
Diffusion Equation ◽  
Differential Operators ◽  
Analytic Solution ◽  
Three Dimensional ◽  
The Novel ◽  
The Finite Element Method ◽  
Element Discretization ◽  
Pressure Diffusion ◽  
Interpolation Functions

In this study we explore the application of the novel fractional calculus in fractal continuum (FCFC), together with the finite element method (FEM), in order to analize explicitly how these differential operators act in the process of discretizing the generalized fractional pressure diffusion equation for a three-dimensional anisotropic continuous fractal flow. The master finite element equation (MFEE) for arbitrary interpolation functions is obtained. As an example, MFEE for the case of a generic linear tetrahedron in $\mathbb{R}^3$ is shown. Analytic solution for the spatial variables is determined over a canonical tetrahedral finite element in global coordinates.

Lignin-Containing Photoactive Resins for 3D Printing by Stereolithography

2018 ◽  
Author(s):  
Jordan T. Sutton ◽  
Kalavathy Rajan ◽  
David P. Harper ◽  
Stephen Chmely
Keyword(s):  
Additive Manufacturing ◽  
New Products ◽  
High Surface ◽  
Fold Increase ◽  
Print Quality ◽  
Renewable Materials ◽  
Lignin Concentration ◽  
Environmentally Sustainable ◽  
Manufacturing Applications ◽  
Modified Lignin

Generating compatible and competitive materials that are environmentally sustainable and economically viable is paramount for the success of additive manufacturing using renewable materials. We report the successful application of renewable, modified lignin-containing photopolymer resins in a commercial stereolithography system. Resins were fabricated within operable ranges for viscosity and cure properties, using up to 15% modified lignin by weight with the potential for higher amounts. A four-fold increase in ductility in cured parts with higher lignin concentration is noted as compared to commercial SLA resins. Excellent print quality was seen in modified lignin resins, with good layer fusion, high surface definition, and visual clarity. These materials can be used to generate new products for additive manufacturing applications and help fill vacant material property spaces, where ductility, sustainability, and application costs are critical.

Lignin-Containing Photoactive Resins for 3D Printing by Stereolithography

2018 ◽  
Author(s):  
Jordan T. Sutton ◽  
Kalavathy Rajan ◽  
David P. Harper ◽  
Stephen Chmely
Keyword(s):  
Additive Manufacturing ◽  
New Products ◽  
High Surface ◽  
Fold Increase ◽  
Print Quality ◽  
Renewable Materials ◽  
Lignin Concentration ◽  
Environmentally Sustainable ◽  
Manufacturing Applications ◽  
Modified Lignin

Generating compatible and competitive materials that are environmentally sustainable and economically viable is paramount for the success of additive manufacturing using renewable materials. We report the successful application of renewable, modified lignin-containing photopolymer resins in a commercial stereolithography system. Resins were fabricated within operable ranges for viscosity and cure properties, using up to 15% modified lignin by weight with the potential for higher amounts. A four-fold increase in ductility in cured parts with higher lignin concentration is noted as compared to commercial SLA resins. Excellent print quality was seen in modified lignin resins, with good layer fusion, high surface definition, and visual clarity. These materials can be used to generate new products for additive manufacturing applications and help fill vacant material property spaces, where ductility, sustainability, and application costs are critical.

scholarly journals Size Effects in Finite Element Modelling of 3D Printed Bone Scaffolds Using Hydroxyapatite PEOT/PBT Composites

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1746
Author(s):  
Iñigo Calderon-Uriszar-Aldaca ◽  
Sergio Perez ◽  
Ravi Sinha ◽  
Maria Camara-Torres ◽  
Sara Villanueva ◽  
...  
Keyword(s):  
Finite Element ◽  
Additive Manufacturing ◽  
Tissue Regeneration ◽  
Finite Element Modelling ◽  
Bulk Material ◽  
Bone Tissue Regeneration ◽  
Patient Specific ◽  
Design Factor ◽  
Element Modelling ◽  
Uncertainty Sources

Additive manufacturing (AM) of scaffolds enables the fabrication of customized patient-specific implants for tissue regeneration. Scaffold customization does not involve only the macroscale shape of the final implant, but also their microscopic pore geometry and material properties, which are dependent on optimizable topology. A good match between the experimental data of AM scaffolds and the models is obtained when there is just a few millimetres at least in one direction. Here, we describe a methodology to perform finite element modelling on AM scaffolds for bone tissue regeneration with clinically relevant dimensions (i.e., volume > 1 cm3). The simulation used an equivalent cubic eight node finite elements mesh, and the materials properties were derived both empirically and numerically, from bulk material direct testing and simulated tests on scaffolds. The experimental validation was performed using poly(ethylene oxide terephthalate)-poly(butylene terephthalate) (PEOT/PBT) copolymers and 45 wt% nano hydroxyapatite fillers composites. By applying this methodology on three separate scaffold architectures with volumes larger than 1 cm3, the simulations overestimated the scaffold performance, resulting in 150–290% stiffer than average values obtained in the validation tests. The results mismatch highlighted the relevance of the lack of printing accuracy that is characteristic of the additive manufacturing process. Accordingly, a sensitivity analysis was performed on nine detected uncertainty sources, studying their influence. After the definition of acceptable execution tolerances and reliability levels, a design factor was defined to calibrate the methodology under expectable and conservative scenarios.

The influence of infill density gradient on the mechanical properties of PLA optimized structures by additive manufacturing

2021 ◽  
pp. 146442072110071
Author(s):  
AIL Pais ◽  
C Silva ◽  
MC Marques ◽  
JL Alves ◽  
J Belinha
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Additive Manufacturing ◽  
Structural Optimization ◽  
Meshless Method ◽  
Load Case ◽  
Fused Filament Fabrication ◽  
Ductile Metals ◽  
Four Point Bending ◽  
Bending Load

The aim of this work is the development of a novel framework for structural optimization using bio-inspired remodelling algorithm adapted to additive manufacturing. The fact that polylactic acid (PLA, E = 3145 MPa (Young’s modulus) according to the supplier for parts obtained by injection) shows a similar parameterized behavior with ductile metals, in the sense that both materials are characterized by a bi-linear elastic-plastic law, allows to simulate and prototype parts to be further constructed in ductile metals at a lower cost and then be produced with more expensive fabrication processes. Moreover, cellular materials allow for a significant weight reduction and therefore reduction of production costs. Structural optimization algorithms based on biological phenomena were used to determine the density distribution of the infill density of the specimens. Several simple structures were submitted to distinct complex load cases and analyzed using the mentioned optimization algorithms combined with the finite element method and a meshless method. The surface was divided according to similar density and then converted to stereolitography files and infilled with the gyroid structure at the desired density determined before, using open-source slicing software. Smoothing functions were used to smooth the density field obtained with the remodeling algorithms. The samples were printed with fused filament fabrication technology and submitted to mechanical flexural tests similar to the ones analyzed analytically, namely three- and four-point bending tests. Thus, the factors of analysis were the smoothing parameter and the remodeling method, and the responses evaluated were stiffness, specific stiffness, maximum force, and mass. The experimental results correlated (obtaining accuracy of 35% for the three-point bending load case and 5% for the four-point bending load case) to the numerical results in terms of flexural stiffness and it was found that the complexity of the load case is relevant for the efficiency of the functional gradient. The fused filament fabrication process is still not accurate enough to be able to experimentally compare the results based of finite element method and meshless method analyses.

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