Papers by Adnan Ibrahimbegovic
Computer Methods in Applied Mechanics and Engineering, 2010
We present the various levels of possible modeling for multiphase flows: coupling of fluid equati... more We present the various levels of possible modeling for multiphase flows: coupling of fluid equations in different domains with a free boundary; coupling (in the same domain) of a fluid equation and a kinetic (Vlasov or Vlasov–Boltzmann) equation; coupling (in the same domain) of two (or more) fluid equations. We briefly present the mathematical results relative to the passage from one of these approaches to another approach, and we give some ideas of how to use those different models on a specific practical example.
Computer Methods in Applied Mechanics and Engineering, 2000
In this work we present the implementation details of a quadratically converging, Newton-method-b... more In this work we present the implementation details of a quadratically converging, Newton-method-based algorithm for direct computation of instability points for 3d structures undergoing finite rotations. The structural model chosen for illustration is the 3d geometrically exact beam. The proposed algorithm makes use of an extended system, where equilibrium equations are supplemented with the loss-of-stability condition which roughly doubles the
Computer Methods in Applied Mechanics and Engineering, 1997
In this work we discuss some aspects of the three-dimensional finite rotations pertinent to the f... more In this work we discuss some aspects of the three-dimensional finite rotations pertinent to the formulation and computational treatment of the geometrically exact structural theories. Among various possibilities to parameterize the finite rotations, special attention is dedicated to a choice featuring an incremental rotation vector. Some computational aspects pertinent to the implementation of the Newton iterative scheme and the Newmark time-stepping algorithm applied to solving these problems are examined. Representative numerical simulations are presented in order to illustrate the performance of the proposed formulation. 0. Dedication Current strong interest in nonlinear analysis of physics phenomena, nourished by ever-growing computational resources, has long been anticipated by J. Tinsley Oden. In the early 1970s he published a book (see [l]), which served as a road-map for many developments which followed. In this and later works, Dr. Oden recognized that the proper setting for these developments is placed at the crossroads between nonlinear mechanics theories and numerical analysis, helping to establish an independent identity of the scientific discipline of Computational Mechanics. In particular, I have always appreciated a distinct style and mathematical rigor of Tinsley's works, which I believe is the only way to make headway in nonlinear problems. I personally benefited from many works of Tinsley Oden, starting from my PhD thesis at UC Berkeley in the late 1980s where the contact model proposed by Oden and Martins [2] proved very useful for structure-foundation interaction problems I was studying at the time. I am also pleased that my contribution selected for this occasion, regarding some computational aspects in structural theories with finite rotations, appears to be related to a very recent work of Tinsley (see [3]) with an ambitious goal of placing these structural theories in a proper harmony with classical continuum theories and delegating some of the traditional engineer's responsibilities to an adaptive modeling procedure.
Computer Methods in Applied Mechanics and Engineering, 2010
In this work we present a new modelling paradigm for computing the complete failure of metal fram... more In this work we present a new modelling paradigm for computing the complete failure of metal frames by combining the stress-resultant beam model and the shell model. The shell model is used to compute the material parameters that are needed by an inelastic stress-resultant beam model; therefore, we consider here the shell model as the meso-scale model and the beam model as the macro-scale model. The shell model takes into account elastoplasticity with strain-hardening and strain-softening, as well as geometrical nonlinearity (including local buckling of a part of a beam). By using results of the shell model, the stress-resultant inelastic beam model is derived that takes into account elastoplasticity with hardening, as well as softening effects (of material and geometric type) in the fractureprocess zone. The beam softening effects are numerically modelled in a localized failure point by using beam finite element with embedded discontinuity. The original feature of the proposed multi-scale (i.e. shellbeam) computational model is its ability to incorporate both material and geometrical instability contributions into the stress-resultant beam model softening response. Several representative numerical simulations are presented to illustrate a very satisfying performance of the proposed approach.
Computer Methods in Applied Mechanics and Engineering, 2002
In this work we present an extension of time-integration energy conserving scheme which introduce... more In this work we present an extension of time-integration energy conserving scheme which introduces desirable properties of controllable energy decay, as well as numerical dissipation of high-frequency contribution to total response. Finite element implementation details are given for the chosen model problem of geometrically exact beam undergoing finite rotations. Several numerical simulations illustrate a very satisfying performance of the proposed timestepping scheme.
Computer Methods in Applied Mechanics and Engineering, 2003
In this work we address several issues pertaining to efficiency of the computational approach gea... more In this work we address several issues pertaining to efficiency of the computational approach geared towards modeling of inelastic behavior of a heterogeneous structure, which is represented by a multi-scale model. We elaborate in particular upon the case where the scales remain coupled throughout the computations, implying a constant communication between the finite element models employed at each scale, and only briefly comment upon our treatment of inelastic analysis of a more classical case where the scales can be separated. We also discuss different manners of representing a complex multi-phase microstructure within the framework of the finite element model constructed at that scale, selecting a model problem of two-phase material where each phase has potentially different inelastic behavior. Several numerical examples are given to further illustrate the presented theoretical considerations.
Computer Methods in Applied Mechanics and Engineering, 2006
ABSTRACT
Computer Methods in Applied Mechanics and Engineering, 2000
In this work, we discuss the ®nite element implementation of the internal constraints in a three-... more In this work, we discuss the ®nite element implementation of the internal constraints in a three-dimensional (3D) geometrically exact beam model which can be formulated as holonomic constraint relationships. Model problems chosen for a more detailed consideration include a general joint constraint between beams and the beam connected to a rigid component. Appropriate modi®cations of the standard form of the geometrically exact beam element arrays are carried out in order to impose explicitly these kinds of constraints into time-integration schemes for nonlinear dynamics. Consequently, only the minimum number of unknowns is retained for the global set of nonlinear equations to be solved, thus avoiding the use of the extra variables (the Lagrange multipliers) and the pertinent diculties in integrating the system of dierential±algebraic equations. A number of numerical simulations considering dynamic analysis of multibody systems with rigid±¯exible components and joint constraints are presented in order to illustrate versatility of the proposed procedure.
Computational Mechanics, 2013
ABSTRACT In this work, we present a new finite element for (geometrically linear) Timoshenko beam... more ABSTRACT In this work, we present a new finite element for (geometrically linear) Timoshenko beam model for ultimate load computation of reinforced concrete frames. The proposed model combines the descriptions of the diffuse plastic failure in the beam-column followed by the creation of plastic hinges due to the failure or collapse of the concrete and of the re-bars. A modified multi-scale analysis is performed in order to identify the parameters for stress-resultant-based macro model, which is used to described the behavior of the Timoshenko beam element. For clarity, we focus upon the micro-scale models using the multi-fiber elements with embedded displacement discontinuities in mode I, which would typically be triggered by bending failure mode. More general case of micro-scale model capable of describing shear failure is described by Ibrahimbegovic et al. (Int J Numer Methods Eng 83(4):452–481, 2010).
Computational Mechanics, 2008
In this paper we develop the governing equations of the coupled damage-plasticity model, which is... more In this paper we develop the governing equations of the coupled damage-plasticity model, which is capable of representing the main mechanisms of inelastic behavior including irreversible plastic deformation, change of elastic response and the localized failure. We show in particular how such model should be implemented within the stress-based variational formulation, providing an important advantage for local computation of the internal variables, which thus remains very robust and even non-iterative for the case of linear hardening model. Several simple examples are presented in order to illustrate the kind of response the model can represent. Keywords coupled damage-plasticity ¡ stress interpolation ¡ cyclic loading
Computational Mechanics, 2007
In this work we discuss the finite element model using the embedded discontinuity of the strain a... more In this work we discuss the finite element model using the embedded discontinuity of the strain and displacement field, for dealing with a problem of localized failure in heterogeneous materials by using a structured finite element mesh. On the chosen 1D model problem we develop all the pertinent details of such a finite element approximation. We demonstrate the presented model capabilities for representing not only failure states typical of a slender structure, with crack-induced failure in an elastic structure, but also the failure state of a massive structure, with combined diffuse (process zone) and localized cracking. A robust operator split solution procedure is developed for the present model taking into account the subtle difference between the types of discontinuities, where the strain discontinuity iteration is handled within global loop for computing the nodal displacement, while the displacement discontinuity iteration is carried out within a local, element-wise computation, carried out in parallel with the Gauss-point computations of the plastic strains and hardening variables. The robust performance of the proposed solution procedure is illustrated by a couple of numerical examples. Concluding remarks are stated regarding the class of problems where embedded discontinuity finite element method (ED-FEM) can be used as a favorite choice with respect to extended FEM (X-FEM).
Computational Mechanics, 2003
In this work, we present a finite element model capable of describing both the plastic deformatio... more In this work, we present a finite element model capable of describing both the plastic deformation which accumulates during the hardening phase as the precursor to failure and the failure process leading to softening phenomena induced by shear slip lines. This is achieved by activating subsequently hardening and softening mechanisms with the localization condition which separates them. The chosen model problem of von Mises plasticity is addressed in detail, along with particular combination of mixed and enhanced finite element approximations which are selected to control the locking phenomena and guarantee mesh-invariant computation of plastic dissipation. Several numerical simulations are presented in order to illustrate the ability of the presented model to predict the final orientation of the shear slip lines for the case of nonproportional loading.
Computational Mechanics, 2000
In this work we develop a geometrically nonlinear version of the method of incompatible modes, su... more In this work we develop a geometrically nonlinear version of the method of incompatible modes, suitable for quasi-incompressible finite deformation hyperelasticity. The proposed method is featuring the principal axis representation of the theory, facilitating the choice of the strain energy function (in terms of the principal stretches) and simplifying the stress computation. The choice of the spatial Cauchy-Green strain measure, leading to a very sparse structure of the strain-displacement operators, and the operator split solution of equilibrium equations, leading to reduced secondary storage requirements, further increase the computational efficiency. A set of numerical examples is used to illustrate a robust performance of the constructed plane strain element with a single incompatible mode in quasi-incompressible deformation patterns.
Computational Mechanics, 2011
In this work we consider the fluid-structure interaction in fully nonlinear setting, where differ... more In this work we consider the fluid-structure interaction in fully nonlinear setting, where different space discretization can be used. The model problem considers finite elements for structure and finite volume for fluid. The computations for such interaction problem are performed by implicit schemes, and the partitioned algorithm separating fluid from structural iterations. The formal proof is given to find the condition for convergence of this iterative procedure in the fully nonlinear setting. Several validation examples are shown to confirm the proposed convergence criteria of partitioned algorithm. The proposed strategy provides a very suitable basics for code-coupling implementation as discussed in Part II. Keywords fluid-structure interaction • partitioned iterations • nonlinear stability proof.
Computational Mechanics, 2008
Comptes Rendus Mécanique, 2007
In this Note we present a stochastic approach to model size effects in quasi-brittle materials st... more In this Note we present a stochastic approach to model size effects in quasi-brittle materials structures. Contrary to Weibull's theory, the key ingredient is the use of correlated random fields in order to describe the material properties. Thus, a stochastic problem has to be solved that we handle using Monte Carlo method. The numerical results show the capability to retrieve size effects in a range between the two classical bounds which are Continuum Damage Mechanics and Linear fracture Mechanics.
Comptes Rendus Mécanique, 2003
In this survey paper we reexamine the theoretical formulation of structural mechanics, introducin... more In this survey paper we reexamine the theoretical formulation of structural mechanics, introducing no restrictions with respect to the size of displacements, rotations or deformations, which is commonly referred to as geometrically exact. A special attention is given to clarifying the computational aspects of finite rotations as the key ingredient of any such formulation. We briefly discuss several novel applications of the geometrically exact formulation to dynamics, control and optimization. To cite this article: A.
… System Dynamics, 2000
In this work we discuss an application of the finite element method to modeling of flexible multi... more In this work we discuss an application of the finite element method to modeling of flexible multibody systems employing geometrically exact structural elements. Two different approaches to handle constraints, one based on the Lagrange multiplier procedure and another based on the use of release degrees of freedom, are examined in detail. The energy conserving time stepping scheme, which is proved to be well suited for integrating stiff differential equations, gouverning the motion of a single flexible link is appropriately modified and extended to nonlinear dynamics of multibody systems.
Applied Mechanics Reviews, 1997
This article reviews the significant progress on shell problem theoretical foundation and numeric... more This article reviews the significant progress on shell problem theoretical foundation and numerical implementation attained over a period of the last several years. First, a careful consideration of the three-dimensional finite rotations is given including the choice of optimal parameters, their admissible variations and the much revealing relationship between different parameters. A non-conventional derivation of the stress resultant shell theory is presented, which makes use of the virtual work principle and local Cartesian frames. The presented derivation introduces no simplifying hypotheses regarding the shell balance equations, hence the resulting shell theory is referred to as being geometrically exact. The strain measures energy-conjugate to the chosen stress resultants are identified and the nature of the stress resultants with respect to the three-dimensional stress tensor is explained along with the resulting constitutive restrictions. Comments are made regarding a rather ...
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Papers by Adnan Ibrahimbegovic