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• Numerical simulation of flame retardant polymers using a combined Eulerian–Lagrangian finite element formulation

  J. Marti, J. Vega, D. Wang, E. Oñate

  Applied Sciences (2021). Vol. 11(13), 5952

  
  

  Abstract

  Many polymer-made objects show a trend of melting and dripping in fire, a behavior that may be modified by adding flame retardants (FRs). These affect materials properties, e.g., heat absorption and viscosity. In this paper, the effect of a flame retardant on the fire behavior of polymers in the UL 94 scenario is studied. This goal is achieved essentially by applying a new computational strategy that combines the particle finite element method for the polymer with an Eulerian formulation for air. The sample selected is a polypropylene (PP) with magnesium hydroxide at 30 wt.%. For modelling, values of density, conductivity, specific heat, viscosity, and Arrhenius coefficients are obtained from different literature sources, and experimental characterization is performed. However, to alleviate the missing viscosity at a high temperature, three viscosity curves are introduced on the basis of the viscosity curve provided by NIST and the images of the test. In the experiment, we burn the specimen under the UL 94 condition, recording the process and measuring the temperature evolution by means of three thermocouples. The UL 94 test is solved, validating the methodology and quantifying the effect of FR on the dripping behavior. The numerical results prove that well-adjusted viscosity is crucial to achieving good agreement between the experimental and numerical results in terms of the shape of the polymer and the temperature evolution inside the polymer.

  Abstract
  Many polymer-made objects show a trend of melting and dripping in fire, a behavior that may be modified by adding flame retardants (FRs). These affect materials properties, [...]

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• High-fidelity simulation of pathogen propagation, transmission and mitigation in the built environment

  R. Lohner, H. Antil, A. Srinivasan, S. Idelsohn, E. Oñate

  Archives of Computational Methods in Engineering (2021). Special Issue: Modeling and Simulation of Infectious Diseases

  
  

  Abstract

  An overview of high-fidelity modeling of pathogen propagation, transmission and mitigation in the built environment is given. In order to derive the required physical and numerical models, the current understanding of pathogen, and in particular virus transmission and mitigation is summarized. The ordinary and partial differential equations that describe the flow, the particles and possibly the UV radiation loads in rooms or HVAC ducts are presented, as well as proper numerical methods to solve them in an expedient way. Thereafter, the motion of pedestrians, as well as proper ways to couple computational fluid dynamics and computational crowd dynamics to enable high-fidelity pathogen transmission and infection simulations is treated. The present review shows that high-fidelity simulations of pathogen propagation, transmission and mitigation in the built environment have reached a high degree of sophistication, offering a quantum leap in accuracy from simpler probabilistic models. This is particularly the case when considering the propagation of pathogens via aerosols in the presence of moving pedestrians.

  Abstract
  An overview of high-fidelity modeling of pathogen propagation, transmission and mitigation in the built environment is given. In order to derive the required physical and [...]

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• Effects of expandable graphite on char morphology and pyrolysis of epoxy based intumescent fire-retardant coating

  S. Ullah, F. Ahmad, A. Al-Sehemi, M. Raza, M. Assiri, A. Irfan, E. Oñate, G. Yeoh

  Journal of Applied Polymer Science (2021). Vol. 138(41), 51206

  
  

  Abstract

  The current study was designed to investigate the effects of expandable graph-ite (EG) on fire protection properties of intumescent fire-retardant coating forsteel structures. Several formulations of intumescent coating were preparedand tested according to ISO 834 for char expansion. The chars were foundwithout cracks and bonded with the steel substrate. The results showed thatthe coating slowly degraded during the test and char remained in contact withvertically tested coated substrate. The coated substrates were also tested forweather resistance using humid and ultraviolet environment. The char wascharacterized by using FESEM, XRD, FTIR, TGA, and XPS analysis. FESEMexamined char morphology of the coatings after furnace fire test. XRD andFTIR showed the presence of graphite, borophosphate; boron oxide andsassolite in the char. TGA and DTGA results disclosed that EG improved theresidual mass of coating. XPS analysis showed the percentages of carbon andoxygen are 48.50 and 43.45 in char of formulation with 12.8% EG. The resultsof weathering test coatings showed decreased in char expansion because of ahumidity and UV light. The formulation with 9.8% EG showed the maximumchar expansion and high residual mass among the formula tions investigated inthis study. The weathering tested coated samples showed their capability offire protection.

  Abstract
  The current study was designed to investigate the effects of expandable graph-ite (EG) on fire protection properties of intumescent fire-retardant coating forsteel structures. [...]

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• Finite element methods for advection-diffusion-absorption and fluid flow problems

  A. Puigferrat, E. Oñate, I. Pouplana

  Monograph CIMNE (2021). M193, 114 pp.

  
  

  Abstract

  The objective of the work is to develop a numerical tool to describe how the concentration of one or more substances distributed in a fluid environment changes under the effect of three transport processes: advection, diffusion and absorption. For that purpose, it is essential to know the interaction of the transported substance with the fluid medium. The work aims to develop stabilized numerical methods for solving the transport and fluid flow equations in a coupled manner for greater accuracy, efficiency and speed when predicting the motion of the transported substances in the fluid. Emphasis is put in the transport of substances in fluids at high P\'eclet numbers. The practical motivation of the work is predicting the transport of a pollutant in air in urban environments. The work document summarizes the research published in three papers published in JCR journals of high impact. The author of the work is also the first author in the three papers. The papers are attached to the document in the corresponding chapters. The description of the work developments has been organized as follows. First, we present the research carried out in the work for the development of a generalized stabilized Finite Increment Calculus-Finite Element Method (FIC--FEM) formulation for solving the multidimensional transient advection-diffusion-absorption equation. The starting point of the developments are the governing equations for the multidimensional steady advection-diffusion-absorption and the unidimensional transient advection-diffusion-absorption problems obtained via the FIC procedure. The good behaviour of the new FIC--FEM formulation is shown in several examples of application. This work was published in the first of the three papers mentioned. In the following chapter we present an innovative numerical method for solving transport problems with high values of advection and / or absorption. A Lagrangian approach based on the updated version of the classical Particle Finite Element Method (PFEM) has been developed to calculate the advection of substances in fluids, while a Eulerian strategy based on the stabilized FIC--FEM formulation is adopted to compute diffusion and absorption effects. The new semi-Lagrangian approach has been validated in its application of a series of academic examples of transport of substances for different values of the P\'eclet and Damk\"ohler numbers. Finally, we derive a procedure for coupling the fluid and transport equations to model the distribution of a pollutant in a street canyon. In our case, we have considered black carbon (BC) as the pollutant. The evolution of the fluid flow is calculated with a standard stabilized finite element method using the Quasi-Static Variational Multiscale (QS-VMS) technique. For the temperature and pollutant transport we use the semi-Lagrangian procedure developed in the work. Several examples of application have been solved to illustrate the accuracy and practicability of the proposed numerical tool for predicting the transport of a pollutant in air in urban environments. One of the examples are presented in the third paper, while another academic one is presented in the appendix of this document.

  Abstract
  The objective of the work is to develop a numerical tool to describe how the concentration of one or more substances distributed in a fluid environment changes under the effect [...]

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• A fully Lagrangian formulation for fluid-structure interaction problems with free-surface flows and fracturing solids (preprint)

  A. Cornejo, A. Franci, F. Zárate, E. Oñate

  Computers & Structures (2021). Vol. 250, 106532

  
  

  Abstract

  This paper presents a novel coupled formulation for fluid-structure interaction (FSI) problems involving free-surface fluid flows, fracture phenomena, solid mutual contact and large displacements. The numerical formulation combines three different Lagrangian computational methods. The Particle Finite Element Method (PFEM) is used to solve the free-surface fluid flow, a Finite Element Method (FEM) with smoothed isotropic damage model is employed for the solution of solid structures and debris, finally, the Discrete Element Method (DEM) is used to manage the contact interaction between different solid boundaries, including the new ones generated by propagating cracks. The proposed method has a high potential for the prediction of the structural damages on civil constructions caused by natural hazards, such as floods, tsunami waves or landslides. Its application field can also be extended to fracture phenomena in structures and soils/rocks arising from explosions or hydraulic fracking processes. Several numerical examples are presented to show the validity and accuracy of the numerical technique proposed.

  Abstract
  This paper presents a novel coupled formulation for fluid-structure interaction (FSI) problems involving free-surface fluid flows, fracture phenomena, solid mutual contact [...]

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• Semi-Lagrangian formulation for the advection–diffusion–absorption equation (preprint)

  A. Puigferrat, M. Masó, I. de-Pouplana, G. Casas, E. Oñate

  Computer Methods in Applied Mechanics and Engineering (2021). Vol. 380, 113807

  
  

  Abstract

  We present a numerical method for solving advective–diffusive–absorptive problems with high values of advection and absorption. A Lagrangian approach based on the updated version of the classical Particle Finite Element Method (PFEM) is used to calculate advection, while a Eulerian strategy based on the Finite Element Method (FEM) is adopted to compute diffusion and absorption. The Eulerian FEM procedure is based on a Finite Increment Calculus (FIC) stabilized formulation recently developed by the authors. The most relevant features of each computational approach are outlined and the coupling scheme is explained. Several problems are solved to validate the method: the evolution of a localized concentration field in two dimensions (2D), the evolution of a spherical field in 3D and three benchmark problems from the literature with high absorption.

  Abstract
  We present a numerical method for solving advective–diffusive–absorptive problems with high values of advection and absorption. A Lagrangian approach based [...]

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• The Pseudo-Direct Numerical Simulation method for multi-scale problems in mechanics

  S. Idelsohn, J. Giménez, N. Nigro, E. Oñate

  Computer Methods in Applied Mechanics and Engineering (2021). Vol. 380, 113774

  
  

  Abstract

  We present an overview of the Pseudo-Direct Numerical Simulation (P-DNS in short) method for the solution of multi-scale phenomena. The method can be seen as an adaptation of the variational multi-scale (VMS) method, where the fine solution is solved numerically instead of analytically. Also, from the point of view of homogenization methods it can be seen as an evolution of Finite Element square (FE2) methods, where the most expensive part of the computations is performed offline. The name of P-DNS arises from the premise that in all multi-scale simulations the numerical result obtained with a very fine discretization is correct without the need to introduce any additional model (i.e. turbulence models) or stabilization procedures for transport equation terms (as in residual-based VMS methods). What is intended here is that the P-DNS solution tends to the DNS solution of the problem, accepting as a premise that the DNS solution is a reliable result. In this paper we present first an overview of the P-DNS methodology in the context of an abstract Dirichlet problem involving a second order differential operator that could be non-symmetric and non-necessarily positive definite. Next, the P-DNS approach is applied to the fluid mechanics equations accounting for turbulent phenomena. Examples showing the applicability of the P-DNS method for solving transport problems involving different scales are then presented.

  Abstract
  We present an overview of the Pseudo-Direct Numerical Simulation (P-DNS in short) method for the solution of multi-scale phenomena. The method can be seen as an adaptation [...]

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• Numerical prediction of the distribution of black carbon in a street canyon using a semi-Lagrangian finite element formulation

  A. Puigferrat, I. de-Pouplana, F. Amatto, E. Oñate

  Building and Environment (2021). Vol. 199, 107910

  
  

  Abstract

  We present a procedure for coupling the uid and transport equations to model the distribution of a pollutant in a street canyon, in this case, black carbon (BC). The fluid flow is calculated with a stabilized finite element method using the Quasi-Static Variational Multiscale (QS-VMS) technique. For the temperature and pollutant transport we use a semi-Lagrangian procedure, based on the Particle Finite Element Method (PFEM) combined with an Eulerian method based on a Finite Increment Calculus (FIC) formulation. Both methods are implemented on the open-source KRATOS Multiphysics platform. The coupled numerical formulation is applied to the prediction of the transport of BC in a street canyon, which can be a useful tool to lessen the impact of pollutants on pedestrians. Two test cases have been studied: a 2D simplified case and a more complex 3D one. The main goal of this study is to propose a useful tool to study the effect of pollution on pedestrians in a street-level scale. Good comparison with experimental results is obtained.

  Abstract
  We present a procedure for coupling the uid and transport equations to model the distribution of a pollutant in a street canyon, in this case, black carbon (BC). The fluid [...]

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• Accurate Timoshenko beam elements for linear elastostatics and LPB stability

  C. Felippa, E. Oñate

  Archives of Computational Methods in Engineering (2021). Vol. 28(3), pp. 2021-2081

  
  

  Abstract

  Several methods to derive accurate Timoshenko beam finite elements are presented and compared. Two application problems are examined: linear elastostatics and linearized prebuckling (LPB) stability analysis. Accurate elements can be derived for both problems using a well known technique that long preceeds the Finite Element Method: using homogeneous solutions of the governing equations as shape functions. An interesting question is: can accurate elements be derived with simpler assumptions? In particular, can linear-linear interpolation of displacements and rotations with one-point integration reproduce those elements? The answers are: no if standard variational tools based on classical functionals are used, but yes if modified functionals are introduced. The connection of modified functionals to newer methods, in particular templates, modified differential equations and Finite Increment Calculus (FIC) are examined. The results brings closure to a 50-year conumdrum centered on this particular finite element model. In addition, the discovery of modified functionals provides motivation for extending these methods to full geometrically nonlinear analysis while still using inexpensive numerical integration.

  Abstract
  Several methods to derive accurate Timoshenko beam finite elements are presented and compared. Two application problems are examined: linear elastostatics and linearized prebuckling [...]

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• Mathematical optimization problems for particle finite element analysis applied to 2D landslide modeling

  L. Wang, X. Zhang, F. Zaniboni, E. Oñate, S. Tinti

  Mathematical Geosciences (2021). Vol. 53, pp. 81–103

  
  

  Abstract

  Notwithstanding its complexity in terms of numerical implementation and limitations in coping with problems involving extreme deformation, the finite element method (FEM) offers the advantage of solving complicated mathematical problems with diverse boundary conditions. Recently, a version of the particle finite element method (PFEM) was proposed for analyzing large-deformation problems. In this version of the PFEM, the finite element formulation, which was recast as a standard optimization problem and resolved efficiently using advanced optimization engines, was adopted for incremental analysis whilst the idea of particle approaches was employed to tackle mesh issues resulting from the large deformations. In this paper, the numerical implementation of this version of PFEM is detailed, revealing some key numerical aspects that are distinct from the conventional FEM, such as the solution strategy, imposition of displacement boundary conditions, and treatment of contacts. Additionally, the correctness and robustness of this version of PFEM in conducting failure and post-failure analyses of landslides are demonstrated via a stability analysis of a typical slope and a case study on the 2008 Tangjiashan landslide, China. Comparative studies between the results of the PFEM simulations and available data are performed qualitatively as well as quantitatively.

  Abstract
  Notwithstanding its complexity in terms of numerical implementation and limitations in coping with problems involving extreme deformation, the finite element method (FEM) [...]

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