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• Computational Homogenization of Inelastic Materials using Model Order Reduction

  J. Hernández, J. Oliver, A. Huespe, M. Caicedo, J. Cante

  Monograph CIMNE (2014). M141

  
  

  Abstract

  The present work is concerned with the application of projection-based, model reduction techniques to the ecient solution of the cell equilibrium equation appearing in (otherwise prohibitively costly) two-scale, computational homogenization problems. The main original elements of the proposed Reduced-Order Model (ROM) are fundamentally three. Firstly, the reduced set of empirical, globally-supported shape functions are constructed from pre-computed Finite Element (FE) snapshots by applying, rather than the standard Proper Orthogonal Decomposition (POD), a partitioned version of the POD that accounts for the elastic/inelastic character of the solution. Secondly, we show that, for purposes of fast evaluation of the nonane term (in this case, the stresses), the widely adopted approach of replacing such a term by a low-dimensional interpolant constructed from POD modes, obtained, in turn, from FE snapshots, leads invariably to ill-posed formulations. To safely avoid this ill-posedness, we propose a method that consists in expanding the approximation space for the interpolant so that it embraces also the gradient of the global shape functions. A direct consequence of such an expansion is that the spectral properties of the Jacobian matrix of the governing equation becomes a ected by the number and particular placement of sampling points used in the interpolation. The third innovative ingredient of the present work is a points selection algorithm that does acknowledge this peculiarity and chooses the sampling points guided, not only by accuracy requirements, but also by stability considerations. The eciency of the proposed approach is critically assessed in the solution of the cell problem corresponding to a highly complex porous metal material under plane strain conditions. Results obtained convincingly show that the computational complexity of the proposed ROM is virtually independent of the size and geometrical complexity of the considered representative volume, and this a ords gains in performance with respect to nite element analyses of above three orders of magnitude without signi cantly sacri cing accuracy |hence the appellation High-Performance ROM.

  Abstract
  The present work is concerned with the application of projection-based, model reduction techniques to the ecient solution of the cell equilibrium equation appearing in (otherwise [...]

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• Validation of the particle finite element method (PFEM) for simulation of rock slides in lakes and reservoirs

  J. Irazábal, F. Salazar, E. Oñate

  (2012). Research Report, Nº PI390

  
  

  Abstract

  The analysis of landslides in reservoirs is particularly interesting because the oscillation of the water surface elevation (especially rapid drawdowns) can foster their occurrence. The existence of the reservoir for a long enough time makes the material of the slopes turn saturated, thus its pore pressure raises and, as a consequence, its effective stress is reduced. This unstabilizing effect is partially compensated by the raise of total stress due to hydrostatic pressure generated by the water in the reservoir. A rapid drawdown eliminates the stabilization in a lapse which is frequently not enough for the pore pressure to be dissipated (this depends on the permeability of the material as well as on the velocity of the water level drop, but is quite frequent). In this situation, the probability of occurrence of a landslide is greater. In this report some validation cases are described, where the impact of sliding blocks against a mass of water is simulated, as well as the generation and propagation of the subsequent impulse wave. They are based on the experiments performed by Sælevik et al. [21].

  Abstract
  The analysis of landslides in reservoirs is particularly interesting because the oscillation of the water surface elevation (especially rapid drawdowns) can foster their occurrence. [...]

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• Multi-scale topological design of structural materials: an integrated approach

  A. Ferrer, J. Oliver, J. Cante

  Monograph CIMNE (2017). M172

  
  

  Abstract

  The present dissertation aims at addressing multiscale topology optimization problems. For this purpose, the concept of topology derivative in conjunction with the computational homogenization method is considered. In this study, the topological derivative algorithm, which is non standard in topology optimization, and the optimality conditions are first introduced in order to a provide a better insight. Then, a precise treatment of the interface elements is proposed to reduce the numerical instabilities and the time-consuming computations that appear when using the topological derivative algorithm. The resulting strategy is examined and compared with current methodologies collected in the literature by means of some numerical tests of different nature. Then, a closed formula of the anisotropic topological derivative is obtained by solving analytically the exterior elastic problem. To this aim, complex variable theory and symbolic computation are considered. The resulting expression is validated through some numerical tests. In addition, different anisotropic topology optimization problems are solved to show the macroscopic topological implications of considering anisotropic materials. Finally, the two-scale topology optimization problem is tackled. As a first approach, an structural stiffness increase is achieved by considering the microscopic topologies as design variables of the problem. An alternate direction algorithm is proposed to address the high non-linearity of the problem. In addition, to mitigate the unaffordable time-consuming computations, a reduction technique is presented by means of pre-computing the optimal microscopic topologies in a computational material catalogue. As an extension of the first approach, besides designing the microscopic topologies, the macroscopic topology is also considered as design variables, leading to even more optimal solutions. In addition, the proposed algorithms are modified in order to obtain manufacturable optimal designs. Two-scale topology optimization examples display the potential of the proposed methodology.

  Abstract
  The present dissertation aims at addressing multiscale topology optimization problems. For this purpose, the concept of topology derivative in conjunction with the computational [...]

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• On the arc length method: combining ideas and implementations aspects

  N. Lafontaine, X. Wang, K. Huang, M. Yuan, E. Oñate

  (2013). Research Report, Nº PI399

  
  

  Abstract

  In this work we introduced and implemented the AL method in NOLM program. Basically the actual implementation in NOLM is based in the work proposed by Lam and Morley (1992) and was coded with take into account the sign for no tracking back the solution. An ecient method was included for avoid complex roots and if the problem persist, two method is available to get the convergence. In case of no convergence is reached, we introduce a user factor, for reducing the arc-length, that should be taken betweens (0:5 - 0:75) per cent of the actual arc length. A linear truss-element, together to the isotropic smeared crack model was introduced for testing and benchmarking the AL method . During the work, we found several diculties to converge in the standard constitutive law implemented in NOLM when a softening parameter was introduced. It is caused by the no mechanical dissipation in the model. However, for a perfect plastic an hardening they get the corresponding results. All meshing process and post-processing was made with Gid[4], proving that it is possible to connect the developed owner software and this Pre-and post processing program.

  Abstract
  In this work we introduced and implemented the AL method in NOLM program. Basically the actual implementation in NOLM is based in the work proposed by Lam and Morley (1992) [...]

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• Advances in the simulation of multi-fluid flows with the Particle Finite Element Method. Application to bubble dynamics

  M. Mier-Torrecilla, S. Idelsohn, E. Oñate

  Int. J. Numer. Meth. Fluids (2010). Vol. 67 (11), pp. 1516-1539

  
  

  Abstract

  In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces. We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method which takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the computations. We apply the resulting scheme to the benchmark problem of a two-dimensional bubble rising in a liquid column presented in [[#cite-1|[1]]], and propose two breakup and coalescence problems to assess the ability of a multi-fluid code to model topology changes.

  Abstract
  In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well [...]

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• Simulación del comportamiento al fuego de paneles de lana de roca

  D. Capua

  (2011). Technical Report, IT608

  
  

  Abstract

  En este trabajo se presenta el informe correspondiente al estudio del comportamiento bajo la acción del fuego de un panel de lana de roca fabricado por la empresa de prefabricados Pretersa-Prenavisa. La referencia de la pieza a estudiar es PANEL DE 20 CON LANA DE ROCA           con una longitud de 10m. El objetivo final es analizar la estabilidad global del panel sometido a la acción del fuego. Dicha estabilidad global puede verse comprometida si las deformaciones térmicas son suficientemente grandes como para que el panel salga fuera del pilar de borde que le confiere estabilidad lateral.

  Abstract
  En este trabajo se presenta el informe correspondiente al estudio del comportamiento bajo la acción del fuego de un panel de lana de roca fabricado por la empresa de [...]

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• Estudio de la seguridad de presas e identificación de escenarios de riesgo mediante sistemas inteligentes (SEPRISIS)

  J. Miquel, J. González

  (2011). Technical Report, IT610

  
  

  Abstract

  El proyecto SEPRISIS tiene como objetivo el desarrollo de sistemas inteligentes basados en redes neuronales, para analizar el comportamiento de una presa, y con ello prever e identificar escenarios de riesgo. Dichos sistemas inteligentes servirán por tanto, como herramienta de soporte a la toma de decisiones.

  Abstract
  El proyecto SEPRISIS tiene como objetivo el desarrollo de sistemas inteligentes basados en redes neuronales, para analizar el comportamiento de una presa, y con ello prever [...]

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• Numerical modelling of the growth and remodelling phenomena in biological tissues

  E. Comellas, S. Oller, F. Bellomo

  Monograph CIMNE (2016). M165

  
  

  Abstract

  Living biological tissues are complex structures that have the capacity of evolving in response to external loads and environmental stimuli. The adequate modelling of soft biological tissue behaviour is a key issue in successfully reproducing biomechanical problems through computational analysis. This study presents a general constitutive formulation capable of representing the behaviour of these tissues through finite element simulation. It is based on phenomenological models that, used in combination with the generalized mixing theory, can numerically reproduce a wide range of material behaviours. First, the passive behaviour of tissues is characterized by means of hyperelastic and finite-strain damage models. A generalized damage model is proposed, providing a flexible and versatile formulation that can reproduce a wide range of tissue behaviour. It can be particularized to any hyperelastic model and requires identifying only two material parameters. Then, the use of these constitutive models with generalized mixing theory in a nite strain framework is described and tools to account for the anisotropic behaviour of tissues are put forth. The active behaviour of tissues is characterized through constitutive models capable of reproducing the growth and remodelling phenomena. These are built on the hyperelastic and damage formulations described above and, thus, represent the active extension of the passive tissue behaviour. A growth model considering biological availability is used and extended to include directional growth. In addition, a novel constitutive model for homeostatic-driven turnover remodelling is presented and discussed. This model captures the stiffness recovery that occurs in healing tissues, understood as a recovery or reversal of damage in the tissue, which is driven by both mechanical and biochemical stimuli. Finally, the issue of correctly identifying the material parameters for computational modelling is addressed. An inverse method using optimization techniques is developed to facilitate the identification of these parameters.

  Abstract
  Living biological tissues are complex structures that have the capacity of evolving in response to external loads and environmental stimuli. The adequate modelling of soft [...]

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• Updated Lagrangian mixed finite element formulation for quasi and fully incompressible fluids

  E. Oñate, J. Carbonell

  (2013). Research Report, Nº PI393

  
  

  Abstract

  We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing equations for the conservation of momentum and mass are given in both differential and variational form. The finite element interpolation uses an equal order approximation for the velocity and pressure unknowns. The procedure for obtaining stabilized FEM solutions is outlined. The solution in time of the discretized governing conservation equations using an incremental iterative segregated scheme is described. The linearization of these equations and the derivation of the corresponding tangent stiffness matrices is detailed. Other iterative schemes for the direct computation of the nodal velocities and pressures at the updated configuration are presented. The advantages and disadvantages of choosing the current or the updated configuration as the reference configuration in the Lagrangian formulation are discussed.

  Abstract
  We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing [...]

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• Computational multiscale modeling of fracture problems and its model order reduction

  M. Caicedo, J. Oliver, A. Huespe

  Monograph CIMNE (2017). M176

  
  

  Abstract

  This work focuses on the numerical modeling of fracture and its propagation in heterogeneous materials by means of hierarchical multiscale models based on the FE2 method, addressing at the same time, the problem of the excessive computational cost through the development, implementation and validation of a set of computational tools based on reduced order modeling techniques. For fracture problems, a novel multiscale model for propagating fracture has been developed, implemented and validated. This multiscale model is characterized by the following features: - At the macroscale level, were adapted the last advances of the Continuum Strong Discontinuity Approach (CSDA), developed for monoscale models, devising a new finite element exhibiting  good ability to capture and model strain localization in bands which can be intersect the finite element in random directions; for failure propagation purposes, the adapted Crack-path  field technique, was used. - At the microscale level, for the sake of simplicity, and thinking on the development of the reduced order model, the use of cohesive-band elements, endowed with a regularized isotropic   continuum damage model aiming at representing the material decohesion, is proposed. These cohesive-band elements are distributed within the microscale components, and their boundaries. The objectivity of the solution with respect to the failure cell size at the microscale, and the finite element size at the macroscale, was checked. In the same way, its consistency with respect to Direct Numerical Simulations (DNS), was also tested and verified.  

  Abstract
  This work focuses on the numerical modeling of fracture and its propagation in heterogeneous materials by means of hierarchical multiscale models based on the FE2 method, [...]

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