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• Numerical simulation of multifluid flows with the particle finite element method

  M. Mier, S. Idelsohn, E. Oñate

  Monograph CIMNE (2010). M115

  
  

  Abstract

  In this monograph we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have extended the Particle Finite Element Method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces. We have developed a numerical scheme able to deal with large jumps in the physical properties (density and viscosity), include surface tension, and accurately represent all types of discontinuities in the flow variables at the interface. The scheme is based on decoupling the nodes position, velocity and pressure variables through the Picard linearization and a pressure segregation method which takes into account the interface conditions. The interface has been defined to be aligned with the moving mesh, so that it remains sharp along time. Furthermore, pressure degrees of freedom have been duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity, and the mesh has been refined in the vicinity of the interface to improve the accuracy of the computations.

  Abstract
  In this monograph we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have [...]

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• Computational model of the human urinary bladder

  V. Monteiro, E. Oñate, S. Oller

  Monograph CIMNE (2014). M148

  
  

  Abstract

  The proposal of an artificial bladder is still a challenge to overcome. Bladder cancer is among the most frequent cases of oncologic diseases in United States and Europe. It is considered a major medical problem once this disease has high rates of reoccurrence, often leading to the extirpation of this organ. The most refined solution to replace this organ is the ileal bladder, which consists of a neobladder made of the patient’s intestinal tissue. Unfortunately this solution presents not only functional mechanical problems, described on the literature as voiding and leaking problems, but also biological ones (i.e. bone loss, given the absorption by the intestine of substances that should be eliminated from the organism). Urged by the urological community of the Hospital Clinic de Barcelona and backgrounded by its experience in the numerical simulation of biomedical structures, the Center of Numerical Methods in Engineering (CIMNE) had the initiative to provide the research of the mechanics of the urinary bladder and the simulation of fluid structure interaction (FSI) to account for the filling and voiding of this organ with urine. The Finite Element Method (FEM) simulation of the real bladder and the comprehensive understanding of the mechanics of this organ and its interaction with urine will give the possibility to propose geometrical improvements and study suitable materials for an artificial solution to address the cases on which the bladder needs to be removed. To reach this goal, first we proceeded to the bibliographic review of mathematical models of the urinary apparatus and to a comprehensive study of the physiology and dynamics of the bladder. A review of the major urological structures, kidney, ureter and urethra, takes place. To consider boundary conditions other surrounding structures to the urinary system are also studied. In the second part of the thesis, we propose the numerical model to study the human urinary bladder. The behavior of the detrusor muscle during filling and voiding of the bladder with urine and its ability to promote the storage of urine under low pressure need to be accurately represented, requiring the implementation of a non-linear constitutive model. The mathematical model needs to be capable to simulate the mechanical variables that govern this organ and the properties of the urine. The nonlinear behavior of living tissues is implemented and validated with examples from the literature. The quasi-incompressibility property of urine and the navierstokes equations for the fluid are taken into account. The geometry of the bladder needs to be taken into account, and the implementation of a 3D computational model obtained from the computerized tomography of a cadaver male adult is considered. The data has been treated to consider boundary conditions. Two models have been conceived: one meshed with four nodes tetrahedral and another meshed with shell elements. FSI must work for the simulation of filling and voiding of the bladder. Due to the close densities of the materials the scheme used to solve fluid-structure needs to be carefully selected. The proposed numerical model and the filling and voiding analysis are finally validated with standardized urodynamic tests. The final part of the thesis, the simulation of a neobladder is presented, being the first step to simulate numerically artificial materials for bladder replacement.

  Abstract
  The proposal of an artificial bladder is still a challenge to overcome. Bladder cancer is among the most frequent cases of oncologic diseases in United States and Europe. [...]

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• Development and applications of the finite point method to compressible aerodynamics problems

  E. Ortega, E. Oñate, S. Idelsohn

  Monograph CIMNE (2014). M143

  
  

  Abstract

  This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating the capabilities of the meshless technique to address practical problems, one of the most outstanding issues in meshless methods. The FPM spatial approximation is studied firstly, with emphasis on aspects of the methodology that can be improved to increase its robustness and accuracy. Suitable ranges for setting the relevant approximation parameters and the performance likely to be attained in practice are determined. An automatic procedure to adjust the approximation parameters is also proposed to simplify the application of the method, reducing problem- and user-dependence without affecting the flexibility of the meshless technique. The discretization of the flow equations is carried out following wellestablished approaches, but drawing on the meshless character of the methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in comparison with a conventional FEM-based technique. Finally, practical applications and extensions of the flow solution scheme are presented. The examples provided are intended not only to show the capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems, as well as a preliminary approach to solve high-Reynolds viscous flows, are a sample of the topics explored. All in all, the results obtained are satisfactorily accurate and competitive in terms of computational cost (if compared with a similar mesh-based implementation). This indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications.

  Abstract
  This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating [...]

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• A general stabilized formulation for incompressible fluid flow using finite calculus and the finite element method

  E. Oñate, J. García, G. Bugeda, S. Idelsohn

  (2003). Fluid Dynamics and Aeronautics New Challenges, Périaux J., Champion M., Gagnepain J.-J., Pironneau O., Stoufflet B. and Thomas Ph.(Eds.), CIMNE, Barcelona, Spain

  
  

  Abstract

  We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the so called finite calculus (FIC) method. The extension of the standard eulerian form of the equations to an arbitrary lagrangian-eulerian (ALE) frame adequate for treating fluid-structure interaction problems is presented. The fully lagrangian form is also discussed. Details of an effective mesh updating procedure are presented together with a method for dealing with free surface effects of importance for ship hydrodynamic analysis and many other fluid flow problems. Examples of application of the eulerian, the ALE and the fully lagrangian flow descriptions are presented.

  Abstract
  We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects [...]

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• Lagrangian formulation for fluid-structure interaction problems using the particle finite element method

  E. Oñate, S. Idelsohn, M. Celigueta

  (2006). Verification and Validation Methods for Challenging Multiphysics Problems, CIMNE, pp. 125-150

  
  

  Abstract

  We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points (called particles) particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. Examples of application of the PFEM to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.

  Abstract
  We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use [...]

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• On the orthogonal subgrid scale pressure stabilization of small and finite deformation J2 Plasticity

  C. Agelet de Saracibar, M. Chiumenti, M. Cervera, Q. Valverde

  Monograph Series on Computational Modeling of Forming Processes, editor C. Agelet (2004). CMFP2, ISBN: 84-95999-62-5

  
  

  Abstract

  The use of stabilization methods is becoming an increasingly well-accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety of applications in computational mechanics. In this monograph a multiscale finite element method technique to deal with pressure stabilization of nearly incompressibility problems in nonlinear solid mechanics at small and finite deformations J2 plasticity is presented. A mixed formulation involving pressure and displacement fields is used as starting point. Within the finite element discretization setting, continuous linear interpolation for both fields is considered. To overcome the Babuˇska-Brezzi stability condition, a multiscale stabilization method based on the Orthogonal Subgrid Scale (OSGS) technique is introduced. Suitable nonlinear expression of the stabilization parameters are proposed. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate and, therefore, very convenient for practical industrial applications. Numerical results obtained using the OSGS stabilization technique are compared with results provided by the P1 standard Galerkin displacements linear triangular/tehrahedral element, P1/P1 standard mixed linear displacements/ linear pressure triangular/tetrahedral element and Q1/P0 mixed bilinear/ trilinear displacements/constant pressure quadrilateral/hexahedral element for 2D/3D nearly incompressible problems in the context of nonlinear small and finite deformation J2 plasticity models.

  Abstract
  The use of stabilization methods is becoming an increasingly well-accepted technique due to their success in dealing with numerous numerical pathologies that arise in [...]

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• On the Computational Modeling and Numerical Simulation of FSW Processes

  C. Agelet de Saracibar, M. Chiumenti, M. Cervera, N. Dialami, D. Santiago, G. Lombera

  Monograph Series on Computational Modeling of Forming Processes, editor C. Agelet (2012). CMFP3, ISBN 84-939640-0-9

  
  

  Abstract

  This paper deals with the computational modeling and numerical simulation of the material flow around the probe tool in a Friction Stir Welding (FSW) process. Within the paradigmatic framework of the multiscale stabilization methods, suitable subgrid scale stabilized coupled thermomechanical formulations have been developed using an Eulerian description. Norton-Hoff and Sheppard-Wright thermo-rigid-viscoplastic constitutive material models have been considered. Constitutive equations for the subgrid scale models have been proposed and an approximation of the subgrid scale variables has been given. In particular Algebraic Subgrid Scale (ASGS) and Orthogonal Subgrid Scale (OSGS) methods for P1/P1/P1 linear elements have been considered. Furthermore, it has been shown that well known classical stabilized formulations, such as the Galerkin Least-Squares (GLS) or Streamline Upwind/Petrov-Galerkin (SUPG) methods, can be recovered as particular cases of the multiscale stabilization framework considered. Within the framework of a product formula algorithm, the resulting algebraic system of equations has been solved using a staggered procedure, in which a mechanical problem, defined by the plastic strain rate incompressibility equation and the quasi-static linear momentum balance equation, is solved at a constant temperature and a thermal problem, defined by the energy balance equation, is solved keeping constant the mechanical variables. The computational model has been implemented in the in-house developed FE software COMET. An assessment of the influence of the thermal deformation in the formulation has been carried out. Results obtained show that the influence of the thermal deformation is very small and can be neglected, getting a fully incompressible formulation. Finally, the computational model implemented in COMET has been validated through a number of examples, including a 3D numerical simulation of a FSW process. Numerical results obtained have been compared with experimental results available in the literature. A good agreement on the temperature distribution has been obtained and predicted peak temperatures compare well, both in value and position, with the experimental results available.

  Abstract
  This paper deals with the computational modeling and numerical simulation of the material flow around the probe tool in a Friction Stir Welding (FSW) process. Within the paradigmatic [...]

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• Residual stress and distortion of rectangular and S-shaped Ti-6Al-4V parts by Directed Energy Deposition: Modelling and experimental calibration

  X. Lu, X. Lin, M. Chiumenti, M. Cervera, Y. Hu, X. Ji, L. Ma, H. Yang, W. Huang

  Additive Manufacturing (2019). (preprint) Vol. 26, pp. 166-179

  
  

  Abstract

  Residual stresses and distortion in Additive Manufactured (AM) parts are two key obstacles which seriously hinder the wide application of this technology. Nowadays, understanding the thermomechanical behavior induced by the AM process is still a complex task which must take into account the effects of both the process and the material parameters, the microstructure evolution as well as the pre-heating strategy. One of the challenges of this work is to increase the complexity of the geometries used to study the thermomechanical behavior induced by the AM process. The reference geometries are a rectangular and a S-shaped structures made of 44-layers each. The samples have been fabricated by Directed Energy Deposition (DED). In-situ thermal and distortion histories of the substrate are measured in order to calibrate the 3D coupled thermo-mechanical model. Once the numerical results showed a good agreement with the temperature measurements, the validated model has been used to predict the residual stresses and distortions. Different process parameters have been analyzed to study their sensitivity to the process assessment. Different preheating strategies have been also analyzed to check their effectiveness on the mitigation of both distortions and residual stresses. Finally, some simplifications of the actual scanning sequence are proposed to reduce the computational cost without loss of the accuracy of the simulation framework.

  Abstract
  Residual stresses and distortion in Additive Manufactured (AM) parts are two key obstacles which seriously hinder the wide application of this technology. Nowadays, understanding [...]

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• In situ measurements and thermo-mechanical simulation of Ti–6Al–4V laser solid forming processes

  X. Lu, X. Lin, M. Chiumenti, M. Cervera, Y. Hu, X. Ji, L. Ma, W. Huang

  Int. J. Mechanical Sciences (2019). (preprint) Vol. 153-154, pp. 119-130

  
  

  Abstract

  Residual stresses and distortions are two technical obstacles for popularizing the additive manufacturing (AM) technology. The evolution of the stresses in AM components during the thermal cycles of the metal depositing process is not yet clear, and more accurate in situ measurements are necessary to calibrate and validate the numerical tools developed for its simulation. In this work a fully coupled thermo-mechanical analysis to simulate the laser solid forming (LSF) process is carried out. At the same time, an exhaustive experimental campaign is launched to measure the temperature evolution at different locations, as well as the distortions and both the stress and strain fields. The thermal and mechanical responses of single-wall coupons under different process parameters are recorded and compared with the numerical models. Good agreement between the numerical results and the experimental measurements is obtained. Sensitivity analysis demonstrates that the AM process is significantly affected by the laser power and the feeding rate, while poorly influenced by the scanning speed.

  Abstract
  Residual stresses and distortions are two technical obstacles for popularizing the additive manufacturing (AM) technology. The evolution of the stresses in AM components during [...]

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• Out-of-plane seismic response and failure mechanism of masonry structures using finite elements with enhanced strain accuracy

  G. Vlachakis, M. Cervera, G. Barbat, S. Salaustros

  Engineering Failure Analysis (2019). (preprint) Vol. 97, pp. 534-555

  
  

  Abstract

  The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are the material properties, the quality of the walls, the geometry of the structure, the connections between structural elements and the stiffness of the diaphragms. During the last years, a wide variety of numerical methods has been employed to assess the out-ofplane behaviour of unreinforced masonry structures. Finite element macro-modelling approaches are among the most famous as they allow modelling large structures at a reasonable computational cost. However, macro-modelling approaches may result in a non-realistic representation of localized cracks and a dependency of the numerical solution on the finite element mesh. Mixed strain/displacement finite elements have been recently proposed as a remedy to the above numerical pathologies. Due to the independent interpolation of strains and displacements these finite element formulations are characterized by an enhanced accuracy in strain localization and crack propagation problems, being at the same time practically mesh independent. For these reasons, mixed finite elements are employed in this work for the out-of-plane assessment of unreinforced masonry structures, being at the same time their first real-scale application. A full-scale experimental campaign of two masonry structures, a stone and a brick one, subjected to shaking-table tests is chosen as reference benchmark. Their structural response under seismic actions is numerically assessed through nonlinear static analysis. The proposed approach is validated through the comparison of the numerical results with the experimental ones, as well as with the results obtained using standard irreducible finite elements.

  Abstract
  The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are [...]

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