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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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• A nodal-integration based particle finite element method (N-PFEM) to model cliff recession

  J. Meng, X. Zhang, S. Utili, E. Oñate

  Geomorphology (2021). Vol. 381, pp. 107666

  
  

  Abstract

  Cliff recession poses a significant threat to the built environment, transportation infrastructure and land use. In this paper, a novel computational framework called the Nodal-integration based Particle Finite Element Method (N-PFEM) is developed for modelling the cliff recession resulting from weathering-induced landslides. The N-PFEM combines the nodal-integration technique with the PFEM in second-order cone programming and thus requires no variable mapping operation, which is essential in the classical PFEM for modelling history-dependent materials, for modelling large deformation problems such as landslides in cliff recession processes. To verify the developed N-PFEM, a series of benchmarks have been simulated including the cliff recession under both the weathering-limited and transport-limited conditions. Simulation results from the N-PFEM are validated in detail to these from the limit analysis method, well established geomorphologic models and the discrete element method. Additionally, measures for preventing cliff recession such as the construction of retaining wall structures are also investigated using the N-PFEM.

  Abstract
  Cliff recession poses a significant threat to the built environment, transportation infrastructure and land use. In this paper, a novel computational framework called the [...]

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• A review of graphene reinforced Cu matrix composites for thermal management of smart electronics

  S. Ali, F. Ahmad, P. Yusoff, N. Muhamad, E. Oñate, M. Raza, K. Malik

  Composites Part A: Applied Science and Manufacturing (2021). Vol. 144, pp. 106357

  
  

  Abstract

  Heat dissipation remains a key challenge to be addressed, determining the performance and durability of smart electronic devices. Graphene reinforced metal matrix composites have been extensively studied as a thermal management material due to their high thermal conductivity and low coefficient of thermal expansion. The emphasis of this review is pivoted on the thermal conductivity enhancement of graphene reinforced Cu matrix composites developed in the recent literature. An overview of factors affecting thermal conductivity of composite namely defect processing route, density, graphene derivative, lateral size, concentration, alignment, graphene/matrix interfacial bonding and graphene modification are discussed. An extensive weightage is given to the processing route as it is the most influential factor in determining the enhancement efficiency. Furthermore, graphene based functional products such as heat spreader and heat sink developed for heat dissipation of electronic devices are also reviewed. Finally, the development and outlook for graphene based Cu composites are presented.

  Abstract
  Heat dissipation remains a key challenge to be addressed, determining the performance and durability of smart electronic devices. Graphene reinforced metal matrix composites [...]

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• Methodological-technological framework for construction 4.0

  F. Muñoz, J. Mora-Serrano, I. Valero, E. Oñate

  Archives of Computational Methods in Engineering (2021). Vol. 28, pp. 689–711

  
  

  Abstract

  The construction industry has traditionally been characterised by the high diversity of its agents and processes, high resistance to change and low incorporation of technology compared to manufacturing industries. However, the construction sector is experiencing now a strong renovation process in methodology and tools due to the incorporation of the Building Information Modelling, Lean Construction and Integrated Project Delivery. Meanwhile, in production systems, “Industry 4.0” is a new paradigm that proposes automation, monitoring, sensorisation, robotisation, and digitalisation to improve production and distribution processes. In this context, some authors have proposed the concept of “Construction 4.0” as the counterpart of Industry 4.0 for the construction sector, although the methodological-technological implications are not clear. This research shows a methodological-technological framework adapted to the Architecture, Engineering, Construction, and Operations industry. This papers includes a detailed proposal for a reference frameworks and related technologies that could impact on this sector, responding to its complexities and specific challenges, such as the unique spaces for each work, which are difficult to standardise, arbitrary cost overruns and a productivity far below the average for other industries, increasing competitiveness and globalisation, as opposed to its traditionally local deployment, and an increasing demand to reduce the carbon footprint for all its activities.

  Abstract
  The construction industry has traditionally been characterised by the high diversity of its agents and processes, high resistance to change and low incorporation of technology [...]

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• A fully Lagrangian formulation for fluid-structure interaction between free-surface flows and multi-fracturing solids and structures

  A. Cornejo Velázquez, E. Oñate, F. Zarate

  Monograph CIMNE (2021). M192

  
  

  Abstract

  It is well known that in civil engineering structures are designed so that they remain, whenever possible, in an elastic regime and with their mechanical properties intact. The truth is that in reality there are uncertainties either in the execution of the work (geometric errors or material quality) or during its subsequent use (loads not contemplated or its value has been estimated incorrectly) that can lead to the collapse of the structure. This is why the study of the failure of structures is inherently interesting and, once is known, its design can be improved to be the less catastrophic as possible or to dissipate the maximum energy before collapsing. Another area of application of fracture mechanics is that of processes of which interest lies in the breakage or cracking of a medium. Within the mining engineering we can enumerate several processes of this nature, namely: hydraulic fracture processes or fracking, blasting for tunnels, explosion of slopes in open pit mines, among others. Equally relevant is the analysis of structural failures due to natural disasters, such as large avenues or even tsunamis impacting protection structures such as walls or dikes. In this work numerous implementations and studies have been made in relation to the mentioned processes. That said, the objective of this work is to develop an advanced numerical method capable of simulating multi-fracture processes in materials and structures. The general approach of the proposed method can be seen in various publications made by the author and directors of this work. This methodology is meant to cover the maximum spectrum of engineering applications possible. For this purpose, a coupled formulation of the Finite Element Method (FEM) and the Discrete Element Method (DEM) is used, which employs an isotropic damage constitutive model to simulate the initial degradation of the material and, once the strength of the material has been completely exhausted, those Finite Element (FE) are removed from the FEM mesh and a set of Discrete Element (DE) are generated at its nodes. In addition to ensure the conservation of the mass of the system, these DE prevent the indentation between the fissure planes thanks to the frictional repulsive forces calculated by the DEM, if any. Additionally, in this work it has been studied how the proposed coupled method named FEM-DEM together with the smoothing of stresses based on the super-convergent patch is able to obtain reasonably meshindependent results but, as one can imagine, the crack width is directly related to the size of the elements that have been removed. This favours the inclusion of an adaptive remeshing technique that will refine the mesh where it is required (according to the Hessian of a nodal indicator of interest) thus improving the discretization quality of the crack obtained and thereby optimizing the simulation cost. In this sense, the procedures for mapping nodal and internal variables as well as the calculation of the nodal variable of interest will be discussed. As far as the studies of natural disasters are concerned, especially those related to free-surface water flows such as tsunamis, one more level of coupling between the aforementioned method FEM-DEM and one Computational Fluid Dynamics (CFD) formulation commonly referred to as Particle Finite Element Method (PFEM) has been implemented. With this strong coupled formulation, many cases of wave impacts and fluid flows have been simulated against solid structures such as walls and dikes, among others.

  Abstract
  It is well known that in civil engineering structures are designed so that they remain, whenever possible, in an elastic regime and with their mechanical properties intact. [...]

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• Development of New Lagrangian Computational Methods for Ice-Ship Interaction Problems: NICESHIP Project

  J. García-Espinosa, E. Oñate, B. Servan Camas, M. Celigueta, S. Latorre, J. Colom-Cobb

  (2020). Computation and Big Data for Transport. Computational Methods in Applied Sciences. In Diez P., Neittaanmäki P., Periaux J., Tuovinen T., Pons-Prats J. (eds), Vol 54, pp.121-153, Springer, Cham

  
  

  Abstract

  This document presents the activities carried out to date (04/2019) in the project ‘Development of new Lagrangian computational methods for ice-ship interaction problems’ (NICE-SHIP). The NICE-SHIP project aims at developing a new generation of computational methods, based on the integration of innovative Lagrangian particle-based and finite element procedures for the analysis of the operation of a vessel in an iced sea, taking into account the different possible conditions of the ice. It is expected that the computational analysis techniques to be developed in NICE-SHIP will allow ice-class vessel designers to accurately evaluate the loads acting on the structure of a ship navigating in iced-seas and, in particular, to determine the ice resistance of the ship in different ice conditions.

  Abstract
  This document presents the activities carried out to date (04/2019) in the project ‘Development of new Lagrangian computational methods for ice-ship interaction problems’ [...]

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