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• Multiscale analysis using a coupled discrete/finite element model

  J. Rojek, E. Oñate

  Interaction and Multiscale Mechanics: An International Journal (IMMIJ) (2007). Vol. 1 (1), pp. 1-31

  
  

  Abstract

  The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors’ own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.

  Abstract
  The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical [...]

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• Modelación del ensayo brasileño empleando modelación discreta

  C. Recarey Morfa, E. Oñate, J. Rojek, J. Canet, F. Zárate, G. Cadoce, C. Labra

  Ingeniería Civil (2005). Vol. 139, pp. 112-124

  
  

  Abstract

  Se presenta un modelo de elementos discretos o distintos (MED) en la modelizacion del ensayo de traccion indirecta o ensayo brasileno (Brazilian Test). Se realiza una comparacion entre los resultados obtenidos por el MED, con la de otros autores [26,35] que emplean el MEF. Se obtienen buenos resultados en el proceso de simulacion del ensayo brasileno, y la comparacion con el MEF (método de los elementos finitos) es muy efectiva. Se evidencia la similitud fisica que existe entre los resultados obtenidos por el MED y ensayos experimentales, lo que posibilita demostrar la fiabilidad y veracidad de la formulacion realizada. (A). English abstract: This work deals whit the use of the Distinct Element Method (DEM) to simulate an indirect traction test, also known as "the Brazilian test" A comparison is realized between results obtained with the DEM, and those obtained by other authors [26, 35] using the Finite Element Method (FEM). The Brazilian test's simulation gives good results and the comparison is very effective. There is a similarity between the results obtained using the DEM and those obtained from real experiments, similarity which proves the reliability and the veracity of this formulation. 

  Abstract
  Se presenta un modelo de elementos discretos o distintos (MED) en la modelizacion del ensayo de traccion indirecta o ensayo brasileno (Brazilian Test). Se realiza una comparacion [...]

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• Triangular prismatic solid-shell element with generalised deformation description

  V. Mataix Ferrándiz, F. Flores, R. Rossi, E. Oñate

  European Journal of Computational Mechanics (2018). Vol. 27 (1), pp. 1-32

  
  

  Abstract

  The solid-shells are an attractive kind of element for the simulation of f orming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any kind of additional modification, besides the thermomechanic problem is formulated without additional assumptions. Additionally, this type of element allows the three-dimensional description of the deformable body, thus contact on both sides of the element can be treated easily. The present work consists in the development of a triangular prism element as a solid-shell, for the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation by Flores, a modified right Cauchy-Green deformation tensor () is obtained; in the present work a modified deformation gradient () is obtained, which allows to generalise the methodology and allows to employ a wide range of constitutive laws. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow. Some examples have been evaluated to show the good performance of the element and results.

  Abstract
  The solid-shells are an attractive kind of element for the simulation of f orming processes, due to the fact that any kind of generic 3D constitutive law can be employed without [...]

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• Interpretation of dam deformation and leakage with boosted regression trees

  F. Salazar, M. Toledo, E. Oñate, B. Suarez

  Engineering Structures (2016). (Preprint) Vol. 119, pp. 230-251

  
  

  Abstract

  Predictive models are essential in dam safety assessment. They have been traditionally based on simple statistical tools such as the hydrostatic-season-time (HST) model. These tools are well known to have limitations in terms of accuracy and reliability. In the recent years, the examples of application of machine learning and related techniques are becoming more frequent as an alternative to HST. While they proved to feature higher flexibility and prediction accuracy, they are also more difficult to interpret. As a consequence, the vast majority of the research is limited to prediction accuracy estimation. In this work, one of the most popular machine learning techniques (boosted regression trees), was applied to model 8 radial displacements and 4 leakage flows at La Baells Dam. The possibilities of model interpretation were explored: the relative influence of each predictor was computed, and the partial dependence plots were obtained. Both results were analysed to draw conclusions on dam response to environmental variables, and its evolution over time. The results show that this technique can efficiently identify dam performance changes with higher flexibility and reliability than simple regression models.

  Abstract
  Predictive models are essential in dam safety assessment. They have been traditionally based on simple statistical tools such as the hydrostatic-season-time (HST) model. These [...]

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• Finite element modelling of fracture propagation in saturated media using quasi-zero-thickness interface elements

  I. de-Pouplana, E. Oñate

  Computers and Geotechnics (2018). Vol. 96, pp. 103-117

  
  

  Abstract

  A new computational technique for the simulation of 2D and 3D fracture propagation processes in saturated porous media is presented. A non-local damage model is conveniently used in conjunction with interface elements to predict the degradation pattern of the domain and insert new fractures followed by remeshing. FIC-stabilized elements of equal order interpolation in the displacement and the pore pressure have been successfully used under complex conditions near the undrained-incompressible limit. A bilinear cohesive fracture model describes the mechanical behaviour of the joints. A formulation derived from the cubic law models the fluid flow through the crack. Examples in 2D and 3D, using 3-noded triangles and 4-noded tetrahedra respectively, are presented to illustrate the accuracy and robustness of the proposed methodology.

  Abstract
  A new computational technique for the simulation of 2D and 3D fracture propagation processes in saturated porous media is presented. A non-local damage model [...]

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• Numerical modelling of granular materials with spherical discrete particles and the bounded rolling friction model. Application to railway ballast

  J. Irazábal González, F. Salazar, E. Oñate

  Computers and Geotechnics (2017). Vol. 85, pp. 220-229

  
  

  Abstract

  The Discrete Element Method (DEM) was found to be an effective numerical method for the calculation of engineering problems involving granular materials. However, the representation of irregular particles using the DEM is a very challenging issue, leading to different geometrical approaches. This document presents a new insight in the application of one of those simplifications known as rolling friction, which avoids excessive rotation when irregular shaped materials are simulated as spheric particles. This new approach, called the Bounded Rolling Friction model, was applied to reproduce a ballast resistance test.

  Abstract
  The Discrete Element Method (DEM) was found to be an effective numerical method for the calculation of engineering problems involving granular materials. [...]

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• Computationally optimized formulation for the simulation of composite materials and delamination failures

  X. Martinez, F. Rastellini, S. Oller, F. Flores, E. Oñate

  Composites Part B: Enginnering (2011). Vol. 42 (2), pp. 134-144

  
  

  Abstract

  The numerical simulation of complex failure modes of composite materials, such as delamination, can be computationally very demanding, as it requires special elements and/or numerical strategies to characterize damage onset and propagation. This work presents several formulations developed to optimize the computational performance of an explicit finite element code designed specifically for the simulation of large scale composite structures. The composite mechanical performance is obtained with the matrix-reinforced mixing theory, a simplified version of the serial/parallel mixing theory that does not require an iterative procedure or the calculation of the tangent stiffness matrix. The number of elements required to perform the simulation is reduced by stacking several layers inside a single finite element. This work also proposes a modification of the isotropic damage law, capable of taking into account the residual strength provided by friction in type II fracture modes. The ability of these formulations to successfully predict the mechanical performance of composite materials is assessed with the ply drop-off test. In this test a laminate with a change of thickness in its mid-span is loaded until it breaks due to a delamination process. The formulation proposed obtains a very accurate prediction of the experimental response of the test, as it provides a very good characterization of the initial laminate stiffness, the delamination onset, and its propagation along the specimen. 

  Abstract
  The numerical simulation of complex failure modes of composite materials, such as delamination, can be computationally very demanding, as it [...]

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• A hierarchical finite element for composite laminated beams using a refined zigzag theory

  L. Nallim, S. Oller, E. Oñate, F. Flores

  Composite Structures (2017). Vol. 163, pp. 168-184

  
  

  Abstract

  In this work a kinematics for laminated beams enriched with a refined formulation ZigZag (RZT), originally presented by Tessler et al. in 2007, introduced in a hierarchical one dimensional type “p” finite element is presented. The finite element employs Lagrange polynomials for the approximation of the degrees of freedom of the ends (nodes) and orthogonal Gram-Schmidt polynomials to the internal degrees of freedoms. This finite element allows a very low discretization, is free of shear locking and behaves very well when the analysis of laminated composites with accurate determination of local stresses and strains at laminar level is necessary. This element has been validated in the analysis of laminated beams with various sequences of symmetric and asymmetric stacking, studying in each case its accuracy and stability.

  Abstract
  In this work a kinematics for laminated beams enriched with a refined formulation ZigZag (RZT), originally presented by Tessler et al. in 2007, introduced in a hierarchical [...]

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• Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory

  D. Di Capua, E. Oñate

  Composite Structures (2015). Vol. 132, pp 1192-1205

  
  

  Abstract

  We present a new 2-noded beam element based on the refined zigzag theory and the classical Euler–Bernoulli beam theory for the static analysis of composite laminate and sandwich beams. The proposed element is able to take into account distortion effects due to shear elastic strains and can predict delamination. The element has four degrees of freedom per node. A C1 cubic Hermite interpolation is used for the vertical deflection while a C0 linear interpolation is employed for the other kinematics variables. The stiffness matrix and the load vector are calculated in explicit form using exact integration. The element is free from shear locking as confirmed with numerical tests on a wide range of the slenderness ratios. Numerical results show the ability of the EEBZ2 element to reproduce accurately the vertical deflection along the beam length and complex zigzag distributions of the axial displacement and the stresses across the thickness. Delamination effects are modeled by incorporating of an additional zigzag function corresponding to the kinematics of a zero thickness layer where delamination occurs. An example showing the capability of the new EEBZ2 element for accurately reproducing delamination effects is presented.

  Abstract
  We present a new 2-noded beam element based on the refined zigzag theory and the classical Euler–Bernoulli beam theory for the static analysis of composite laminate [...]

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• Delamination in laminated plates using the 4-noded quadrilateral QLRZ plate element based on the refined zigzag theory

  A. Eijo, E. Oñate, S. Oller

  Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2022). 247

  
  

  Abstract

  A numerical method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated plate/shell structures is presented. The originality of this method is the use of 4-noded quadrilateral plate finite elements whit only seven variables per node to discretize the plate/shell geometry. The ability to capture the relative displacement between consecutive layers in fracture mode II and III is the more important advantage of this element, denoted QLRZ. A continuum isotropic damage model is used to model the mechanical behavior of the plies. The material non-lineal problem is solved with the modified Newton–Raphson method. The RZT plate theory, the QLRZ finite element and the isotropic damage model are described in this work. Also, the implicit integration algorithm is presented. The performance of the numerical model is analyzed by studying the delamination in a rectangular plate for two different laminates, using the 3D analysis as the reference solution

  Abstract
  A numerical method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated plate/shell structures is presented. The originality of this method [...]

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