A novel numerical framework for simulation of multiscale spatio-temporally non-linear systems in additive manufacturing processes.

New computationally efficient numerical techniques have been formulated for multi-scale analysis in order to bridge mesoscopic and macroscopic scales of thermal and mechanical responses of a material. These numerical techniques will reduce computational efforts required to simulate metal based Additive Manufacturing (AM) processes. Considering the availability of physics based constitutive models for response at mesoscopic scales, these techniques will help in the evaluation of the thermal response and mechanical properties during layer-by-layer processing in AM. Two classes of numerical techniques have been explored. The first class of numerical techniques has been developed for evaluating the periodic spatiotemporal thermal response involving multiple time and spatial scales at the continuum level. The second class of numerical techniques is targeted at modeling multi-scale multi-energy dissipative phenomena during the solid state Ultrasonic Consolidation process. This includes bridging the mesoscopic response of a crystal plasticity finite element framework at inter- and intragranular scales and a point at the macroscopic scale. This response has been used to develop an energy dissipative constitutive model for a multi-surface interface at the macroscopic scale. An adaptive dynamic meshing strategy as a part of first class of numerical techniques has been developed which reduces computational cost by efficient node element renumbering and assembly of stiffness matrices. This strategy has been able to reduce the computational cost for solving thermal simulation of Selective Laser Melting process by ~100 times. This method is not limited to SLM processes and can be extended to any other fusion based additive manufacturing process and more generally to any moving energy source finite element problem. Novel FEM based beam theories have been formulated which are more general in nature compared to traditional beam theories for solid deformation. These theories have been the first to simulate thermal problems similar to a solid beam analysis approach. These are more general in nature and are capable of simulating general cross-section beams with an ability to match results for complete three dimensional analysis. In addition to this, a traditional Cholesky decomposition algorithm has been modified to reduce the computational cost of solving simultaneous equations involved in FEM simulations. Solid state processes have been simulated with crystal plasticity based nonlinear finite element algorithms. This algorithm has been further sped up by introduction of an interfacial contact constitutive model formulation. This framework has been supported by a novel methodology to solve contact problems without additional computational overhead to incorporate constraint equations averting the usage of penalty springs

Study and Design of Reconfigurable Intelligent Surfaces

In this thesis, we introduce the fundamental equations behind the estimation of the link budget in a communications channel, highlighting the key limitations of conventional systems. Furthermore, we investigate the use of reconfigurable intelligent surfaces as a modern method of overcoming obstruction losses, while making use of numerical methods and computational electromagnetics to understand its physical mechanism and probe its theory of operation. Additionally, a preprint on computational geometry is presented, applicable to the field of computational electromagnetics, enabling the simulation of systems such as reconfigurable intelligent surfaces using open-source tools. Lastly, we provide a tool for the physical optimization of radio-frequency networks, based on mathematical programming. Such a tool may be used for the optimization of reconfigurable intelligent surfaces, ultimately improving the communication channel between a transmitter and receiver.Comment: 76 pages, 26 figures. arXiv admin note: text overlap with arXiv:2209.1026

A Posteriori Error Control for the Binary Mumford-Shah Model

The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented region. To this end, a suitable strictly convex and non-constrained relaxation of the originally non-convex functional is investigated and Repin's functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the $L^2$-norm. In combination with a suitable cut out argument, a fully practical estimate for the area mismatch is derived. This estimate is incorporated in an adaptive meshing strategy. Two different adaptive primal-dual finite element schemes, and the most frequently used finite difference discretization are investigated and compared. Numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications.Comment: 18 pages, 7 figures, 1 tabl

Optimization of support structures for selective laser melting.

Additive Manufacturing (AM) users rely on experiments and experience to predict the performance of AM processes. This trial and error approach for qualifying AM parts takes significant time and money. Simulation tools are an urgent need for today’s AM industry. One area of need is the automatic generation of optimized support structures based upon the scan patterns used to produce those structures. This research seeks to develop support structure generation tools based on real scan pattern and thermo-mechanical simulation tools for Selective Laser Melting (SLM) developed at the University of Louisville and being commercialized by 3DSIM, LLC. In order to benchmark the 3DSIM thermo-mechanical simulation tool, a thermal finite element model has been developed in ANSYS which uses the similar multi-scale meshing strategies as 3DSIM. The use of the sub-modeling approach for dynamic meshing was verified by comparing it against a uniform fine mesh model. The results of the two models match within an acceptable tolerance. Also, a mesh sensitivity analysis was carried out in order to show solution convergence as a function of increasing mesh density. The results of this analysis were also validated using experiments to show a match between experimental and simulated melt pools. Finally, the ANSYS solution was compared with 3DSIM results. The result of 3DSIM for a simple represented model is validated compared against the ANSYS model. What is more, it was significantly faster than their ANSYS counterparts for solving problems using a dynamic mesh. A scan pattern generation tool has been implemented to enable the input of real scan patterns as it is used in fabrication. The scan pattern is arbitrarily varied using user-defined parameters including hatching space, orientation angle, scanning start point, etc. Several types of scan patterns such as traditional S and chessboard are included in the tool. A simplified representation of the thermomechanical properties of support structures in order to accelerate the simulation of supports has been formulated. The effective thermal properties of support structures are represented using thermal homogenization. The effective thermal properties of the support structures have been found to be a function of their geometry, anisotropy and constituent independent thermal properties. The results from this study have been compared against standard models and a good match has been found. A novel framework for a support structure generation and optimization tool has been developed to overcome the difficulty of dealing with support structures in SLM. Supports are optimized and designed based on the thermal stress accumulated in parts as they are made as well as geometrical rules. The support structure is designed to be withstand the thermal stress at locations where it could cause damage to the part and support structure, while minimizing the overall need for support structure materials. The support structure is designed with non-uniform parameters so as to make it flexible to alter based upon thermal stress. Experiments were conducted to explore the threshold for block support structure parameters and results were applied to adjust and verify the tool

Methodology for automatic recovering of 3D partitions from unstitched faces of non-manifold CAD models

Data exchanges between different software are currently used in industry to speed up the preparation of digital prototypes for Finite Element Analysis (FEA). Unfortunately, due to data loss, the yield of the transfer of manifold models rarely reaches 1. In the case of non-manifold models, the transfer results are even less satisfactory. This is particularly true for partitioned 3D models: during the data transfer based on the well-known exchange formats, all 3D partitions are generally lost. Partitions are mainly used for preparing mesh models required for advanced FEA: mapped meshing, material separation, definition of specific boundary conditions, etc. This paper sets up a methodology to automatically recover 3D partitions from exported non-manifold CAD models in order to increase the yield of the data exchange. Our fully automatic approach is based on three steps. First, starting from a set of potentially disconnected faces, the CAD model is stitched. Then, the shells used to create the 3D partitions are recovered using an iterative propagation strategy which starts from the so-called manifold vertices. Finally, using the identified closed shells, the 3D partitions can be reconstructed. The proposed methodology has been validated on academic as well as industrial examples.This work has been carried out under a research contract between the Research and Development Direction of the EDF Group and the Arts et Métiers ParisTech Aix-en-Provence