Documents published in Scipedia

• Numerical model for the laser metal deposition additive manufacturing process: Multiphysics modeling and experimental validation

  G. Dali

  SIM-AM2023.

  
  

  Abstract

  Metallic Additive Manufacturing (AdM) technologies (3D printing) is rapidly spreading to a variety of industrial applications. In recent years, advances in AdM have gradually transformed the way in which manufactured products are designed and produced. It enables easy manufacturing of complex shaped parts with high performance, less material waste and short development cycle. Laser Metal Deposition (LMD) is one of the processes in this growing field. This process can produce high performance parts by the injection of powders into a melt-pool created by a laser heat source. However, the LMD is complex and several defects may appear during the printing process. In this context, numerical simulation could be a helpful tool to describe the involved physical phenomena and then to predict the impact of process parameters on the material state. Such numerical tool can predict the heat exchanges and the fluid flow within the molten pool enabling defect prediction and process optimization. In this work, a multi-physics numerical model of the LMD process, at a mesoscopic scale, (i.e. at the layer thickness scale) is developed to predict thermal cycles during fabrication, as well as the complex relationships between part construction and operating parameters. For this purpose, the finite element code COMSOL Multiphysics is used. The developed model takes into account fluid flow and heat transfer in the different phases (gas, substrate and melt pool). As a key feature, the developed model simulates the growth of the track using the generation of droplets when the powder flow is intercepted by the laser beam. Material addition, interface tracking, and strong topological changes are handled using the level set technique. The numerical results are compared to the experimental results for validation purposes. This validation includes the comparison between the predicted molten pool cross-section and measurements from macrographs and high-speed videos.

  Abstract
  Metallic Additive Manufacturing (AdM) technologies (3D printing) is rapidly spreading to a variety of industrial applications. In recent years, advances in AdM have gradually [...]

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• Multiphysical modeling of soft-tissue stent interaction (Plenary Lecture)

  S. Reese, K. Manjunatha, J. Shi, M. Sesa, M. Behr, F. Vogt

  coupled2023.

  
  

  Abstract

  The efficacy of cardiological interventions, including the implantation of prostheses, is highly dependent on patient-specific immunohistology and can be enhanced with computational predictive tools. Therefore, an in silico replication of neointimal hyperplasia shall provide the necessary insights about the biochemical and cellular interactions within the vessel wall, and eventually address the risks of in-stent restenosis in a patient-specific manner. In this context, we set up a multiphysics framework considering key mediators of restenosis and couple them to a continuum mechanical vessel wall model. The governing set of coupled partial PDEs for the underlying mechanobiological system is solved via the finite element method and the results are compared to those obtained using a deep learning framework employing physics-informed neural networks (PINNs). Another interesting cardiological intervention-related problem is the maturation of tissue-engineered cardiovascular implants wherein the evolution of the collagen density affects the tissue’s mechanical behavior. The model we present allows us to predict the evolution of collagen density within textile-reinforced heart valves.

  Abstract
  The efficacy of cardiological interventions, including the implantation of prostheses, is highly dependent on patient-specific immunohistology and can be enhanced with computational [...]

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• A coupled model for the formation of Atherosclerosis due to inflammation processes

  P. Wriggers, M. Gierig, A. Haverich

  coupled2023.

  
  

  Abstract

  Atherosclerosis is a disease in blood vessels that often results in plaque formation and lumen narrowing. It is an inflammatory response of the tissue caused by disruptions in the vessel wall nourishment. Blood vessels are nourished by nutrients originating from the blood of the lumen. In medium-sized and larger vessels, nutrients are additionally provided from outside through a network of capillaries called vasa vasorum. It has recently been hypothesized [1] that the root of atherosclerotic diseases is the malfunction of the vasa vasorum. This, so called outside-in-theory, is supported by a recently developed numerical model [2] accounting for the inflammation initiation in the adventitial layer of the blood vessel. Building on the previous findings, this presentation proposes an extended material model for atherosclerosis formation that is based on the outside-in-theory. Beside the description of growth kinematics and nutrient diffusion, the roles of monocytes, macrophages, foam cells, smooth muscle cells and collagen are accounted for in a nonlinear continuum mechanics setting. Cells are activated due to a lack of vessel wall nourishment and proliferate, migrate, differentiate and synthesize collagen, leading to the formation of a plaque. Numerical studies show that the onset of atherosclerosis can qualitatively be reproduced. Thus, the in silico model backs the new theory.

  Abstract
  Atherosclerosis is a disease in blood vessels that often results in plaque formation and lumen narrowing. It is an inflammatory response of the tissue caused by disruptions [...]

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• Reduced-Order Models in Bayesian solvers for inverse problems

  P. Diez, S. Zlotnik, A. Muixí, A. García-González

  coupled2023.

  
  

  Abstract

  Challenging inverse problems aim at identifying large sets of parameters using data from different sources and diverse accuracy. This is the case of data assimilation for geophysical crust dynamics, were the number of parameters to identify amounts to thousands. In this context, Bayesian inverse solvers combined with Markov-Chain Monte Carlo (MCMC) strategies are an affordable strategy, accounting for the uncertainty of the input data and quantifying also uncertainty of the output. Despite the efficiency of the MCMC approach, the direct problem has to be evaluated an extremely large number of times, many (after the burn-in phase) with the input parameters lying in a narrow range. This is the ideal situation for Reduced-Order Models (ROM): many repeated queries to the model corresponding to parameters lying in a limited manifold. Thus, we aim at applying ROM to large-dimensional parametric forward problems. In this case, it is important optimising the dimensionality reduction technique inherent to the ROM strategy. For instance, Proper Orthogonal Decomposition (POD) is associated with a linear Principal Component Analysis (PCA). PCA is linear in the sense that assumes the reduceddimension manifold to be Euclidean. We explore using kernel PCA (kPCA) to further reduce the dimension, thus devising a kPOD approach. Different options to select physically inspired kernels, based on the knowledge of the problem under consideration, are discussed. Moreover, the computational strategy to explore the feature space (the reduced-dimensional space) is also discussed. 

  Abstract
  Challenging inverse problems aim at identifying large sets of parameters using data from different sources and diverse accuracy. This is the case of data assimilation for [...]

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• Model Order Reduction in the Parametrized Multi-Scale and Coupled Setting

  K. Veroy-Grepl

  coupled2023.

  
  

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• A New Paradigm for Multiphysics Simulation: Its Initial Application to Fluid-Structure Interaction

  K. Park, J. González

  coupled2023.

  
  

  Abstract

  A new paradigm for simulating mulitipysics systems is presented with initial focus on FluidStructure Interaction (FSI). For each single-field governing equations adopting Lagrangian frame, a projection operator couples the coupled field without invoking interface Lagrange multipliers. For FSI problems where fluids are modeled by employing ALE kinematics, a physics-based interface equations are formulated as an independent set of third-field equations. This approach facilitates the connection of non-matching meshes and provides consistent dynamic equations of motion for the interface that can be integrated in parallel. The proposed simulation paradigm adopts stand-alone software modules for the fluid and the structure, which is coupled through a third interface system treating their interaction, which preserves the modularity of the singlediscipline software modules. The new FSI simulation paradigm is demonstrated as applied to several FSI benchmark examples, demonstrating its efficiency and accuracy. Extension of the proposed new multiphysics simulation paradigm to treat other multiplhysics problems are suggested.

  Abstract
  A new paradigm for simulating mulitipysics systems is presented with initial focus on FluidStructure Interaction (FSI). For each single-field governing equations adopting [...]

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• CECM: A continuous empirical cubature method with application to the dimensional hyperreduction of parameterized finite element models

  J. Hernández, J. Bravo, S. Parga

  Computer Methods in Applied Mechanics and Engineering (2023). Vol. 418 (Part B), 116552

  
  

  Abstract

  We propose a method for finding optimal quadrature/cubature rules with positive weights for parameterized functions in 1D, 2D or 3D spatial domains. The method takes as starting point the values of the functions at the Gauss points of a finite element (FE) mesh of the spatial domain for a representative sample of input parameters, and then construct an elementwise continuous orthogonal basis for such functions using the truncated Singular Value Decomposition (SVD) along with element polynomial fitting. To avoid possible memory bottlenecks in computing the SVD, we propose a Sequential Randomized SVD (SRSVD) in which the matrix is provided in a column-partitioned format, and which uses randomization to accelerate the processing of each individual block. After computing the basis functions, the method determines an exact integration rule for such functions, featuring as many points as functions, and in which the points are selected among the Gauss points of the FE mesh. Finally, the desired optimal rule is obtained by an sparsification process in which the algorithm zeroes one weight at a time while readjusting the positions and weights of the remaining points so that the constraints of the problem are satisfied. We apply this methodology to multivariate polynomials in cartesian domains to demonstrate that the method is indeed able to produce optimal rules – i.e., Gauss product rules –, and to a 2-parameters, 3D sinusoidal–exponential function to illustrate the use of the SRSVD in scenarios in which the standard SVD cannot handle the operation because of memory limitations. Lastly, the fact that the method does not require the analytical expression of the integrand functions – just their values at the FE Gauss points – makes it suitable for dealing with the so-called hyperreduction of parameterized finite element models. We exemplify this by showing its performance in the derivation of low-dimensional surrogate models in the context of the multiscale FE method. The Matlab source codes of both the CECM and the SRSVD, along with the scripts for launching the numerical tests, are openly accessible in the public repositoryhttps://github.com/Rbravo555/CECM-continuous-empirical-cubature-method.

  Abstract
  We propose a method for finding optimal quadrature/cubature rules with positive weights for parameterized functions in 1D, 2D or 3D spatial domains. The method takes as starting [...]

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• Empirical Interscale Finite Element Method (EIFEM) for modeling heterogeneous structures via localized hyperreduction

  J. Hernández, A. Giuliano, E. Soudah

  Computer Methods in Applied Mechanics and Engineering (2023). Vol. 418 (Part A), 116492

  
  

  Abstract

  This work proposes a special type of Finite Element (FE) technology – the Empirical Interscale FE method – for modeling heterogeneous structures in the small strain regime, for both dynamic and static analyses. The method combines a domain decomposition framework, where interface conditions are established through “fictitious” frames, with dimensional hyperreduction at subdomain level. Similar to other multiscale FE methods, the structure is assumed to be partitioned into coarse-scale elements, each of these elements is equipped with a fine-scale subgrid, and the displacements of the boundaries of the coarse-scale elements are described by standard polynomial FE shape functions. The distinguishing feature of the proposed method is the employed “interscale” variational formulation, which directly relates coarse-scale nodal internal forces with fine-scale stresses, thereby avoiding the typical nested local/global problems that appear, in the nonlinear regime, in other multiscale methods. This distinctive feature, along with hyperreduction schemes for nodal internal and external body forces , greatly facilitate the implementation of the proposed formulation in existing FE codes for solid elements. Indeed, one only has to change the location and weights of the integration points, and to replace a few polynomial-based FE matrices with “empirical” operators, i.e., derived from the information obtained in appropriately chosen computational experiments. We demonstrate that the elements resulting from this formulation are not afflicted by volumetric locking when dealing with nearly-incompressible materials, and that they can handle non-matching fine-scale grids as well as curved structures. Last but not least, we show that, for periodic structures, this method converges upon mesh refinement to the solution delivered by classical first-order computational homogenization. Thus, although the method does not presuppose scale separation, it can represent solutions in this limiting case by taking sufficiently small coarse-scale elements.

  Abstract
  This work proposes a special type of Finite Element (FE) technology – the Empirical Interscale FE method – for modeling heterogeneous structures in the small strain [...]

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• Experiment and SHM on the membrane structure of Shanghai Kunshan Football Stadium

  Q. Zhang, Y. Huang, G. Zhang

  membranes2023.

  
  

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• Form-finding of lightweight tension-compression structures with equilibrium-based graphical methods

  P. D'Acunto

  membranes2023.

  
  

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