The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Ted Belytschko - One of the best experts on this subject based on the ideXlab platform.
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gradient and dilatational stabilizations for Stress Point integration in the element free galerkin method
International Journal for Numerical Methods in Engineering, 2009Co-Authors: Qinglin Duan, Ted BelytschkoAbstract:Stabilized Stress-Point integration schemes based on gradient stabilization and dilatational stabilization methods are presented for linear elastostaticity problems in the framework of element-free Galerkin (EFG) method. The instability in Stress fields associated with the Stress-Point integration is treated by the addition to the Galerkin weak form of stabilization terms which contain product of the gradient of the residual or the trace of the gradient of the residual; the latter is called dilatational stabilization. Numerical results show that the oscillations in the Stress fields are successfully removed by the presented stabilization methods, and that the convergence and stability properties of direct Stress-Point integration are greatly improved. These stabilization methods are particularly suitable for the solution of non-linear continua with explicit time integration methods. Copyright © 2008 John Wiley & Sons, Ltd.
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Gradient and dilatational stabilizations for Stress‐Point integration in the element‐free Galerkin method
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Qinglin Duan, Ted BelytschkoAbstract:Stabilized Stress-Point integration schemes based on gradient stabilization and dilatational stabilization methods are presented for linear elastostaticity problems in the framework of element-free Galerkin (EFG) method. The instability in Stress fields associated with the Stress-Point integration is treated by the addition to the Galerkin weak form of stabilization terms which contain product of the gradient of the residual or the trace of the gradient of the residual; the latter is called dilatational stabilization. Numerical results show that the oscillations in the Stress fields are successfully removed by the presented stabilization methods, and that the convergence and stability properties of direct Stress-Point integration are greatly improved. These stabilization methods are particularly suitable for the solution of non-linear continua with explicit time integration methods. Copyright © 2008 John Wiley & Sons, Ltd.
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Convergence and stabilization of Stress‐Point integration in mesh‐free and particle methods
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Thomaspeter Fries, Ted BelytschkoAbstract:Stress-Point integration provides significant reductions in the computational effort of mesh-free Galerkin methods by using fewer integration Points, and thus facilitates the use of mesh-free methods in applications where full integration would be prohibitively expensive. The influence of Stress-Point integration on the convergence and stability properties of mesh-free methods is studied. It is shown by numerical examples that for regular nodal arrangements, good rates of convergence can be achieved. For non-uniform nodal arrangements, Stress-Point integration is associated with a mild instability which is manifested by small oscillations. Addition of stabilization improves the rates of convergence significantly. The stability properties are investigated by an eigenvalue study of the Laplace operator. It is found that the eigenvalues of the Stress-Point quadrature models are between those of full integration and nodal integration. Stabilized Stress-Point integration is proposed in order to improve convergence and stability properties. Copyright © 2007 John Wiley & Sons, Ltd.
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convergence and stabilization of Stress Point integration in mesh free and particle methods
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Thomaspeter Fries, Ted BelytschkoAbstract:Stress-Point integration provides significant reductions in the computational effort of mesh-free Galerkin methods by using fewer integration Points, and thus facilitates the use of mesh-free methods in applications where full integration would be prohibitively expensive. The influence of Stress-Point integration on the convergence and stability properties of mesh-free methods is studied. It is shown by numerical examples that for regular nodal arrangements, good rates of convergence can be achieved. For non-uniform nodal arrangements, Stress-Point integration is associated with a mild instability which is manifested by small oscillations. Addition of stabilization improves the rates of convergence significantly. The stability properties are investigated by an eigenvalue study of the Laplace operator. It is found that the eigenvalues of the Stress-Point quadrature models are between those of full integration and nodal integration. Stabilized Stress-Point integration is proposed in order to improve convergence and stability properties. Copyright © 2007 John Wiley & Sons, Ltd.
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On the Stabilization of Stress-Point Integration in the Element Free Galerkin Method
Lecture Notes in Computational Science and Engineering, 1Co-Authors: Qinglin Duan, Ted BelytschkoAbstract:Stabilized Stress-Point integration schemes based on Least-Squares Stabilization (LSS), Taylor series Expansion Based Stabilization (TEBS) and Finite Increment Gradient (FIG) are compared for linear elastostaticity problems and some relations between them are described. Particular emphasis is placed on Stress-Point integration procedures with stabilization. The convergence and stability properties of stabilized methods in the framework of the element free Galerkin (EFG) method with Stress-Point integration are studied by numerical examples. It is shown that stabilized Stress-Point integration consumes much less computational time than full integration and exhibits higher accuracy and much better convergence and stability than unstabilized Stress-Point integration and stabilized nodal integration.
Ronaldo I Borja - One of the best experts on this subject based on the ideXlab platform.
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Discrete micromechanics of elastoplastic crystals in the finite deformation range
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Ronaldo I Borja, Helia RahmaniAbstract:Abstract We present a rate-independent crystal plasticity theory in the finite deformation range. The formulation revolves around theory of distribution and strong discontinuity concepts applied to the slip systems. Uniform and conforming deformation fields are introduced, from which deformation gradients for the crystal lattice and the crystal itself are derived. For a crystal deforming in single slip, we show that the crystal rotates the active slip system the same way as the lattice does, leading to an elegant and exact Stress-Point integration algorithm for the overall crystal Stresses. For a crystal deforming in multiple slips the crystal no longer rotates the slip systems exactly as the lattice does. For this case, we present a Stress-Point integration algorithm accounting for the exact push-forward operation induced by the lattice on the active systems. We also consider a simplified Stress-Point integration algorithm for multislip systems that remains highly accurate for a wide range of Stress paths considered. The framework for system activation and the selection of linearly independent slip systems follows a well-established ‘ultimate algorithm’ for rate-independent crystal plasticity developed for infinitesimal deformation.
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Cam-Clay plasticity, Part IV : Implicit integration of anisotropic bounding surface model with nonlinear hyperelasticity and ellipsoidal loading function
Computer Methods in Applied Mechanics and Engineering, 2001Co-Authors: Ronaldo I Borja, Francisco J. MontánsAbstract:Abstract This paper describes a fully implicit Stress-Point integration algorithm for a class of anisotropic bounding surface plasticity models with ellipsoidal loading function. The plasticity model is coupled with a nonlinear hyperelastic model to ensure that the elastic component of the combined model is energy-conserving. A key feature of the integration algorithm for the combined model is a return mapping in strain space, which allows fully implicit integration and consistent linearization of the constitutive equations. For this class of bounding surface models the consistency condition on the bounding surface is shown to be mathematically equivalent to the consistency condition on the loading surface, thus allowing practically all attributes of the standard return mapping algorithm of classical plasticity theory to be carried over to the bounding surface theory with little modification. As a specific example, the infinitesimal version of modified Cam-Clay theory is used to represent the bounding surface model, and an exponential function is used to interpolate the plastic modulus on the loading surface. Isoerror maps are generated describing the accuracy of the integration algorithm on the Stress-Point level. Finally, a boundary-value problem involving a strip footing on lightly overconsolidated clay is analyzed to demonstrate the robustness of the algorithm in a finite element setting.
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A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation
Computer Methods in Applied Mechanics and Engineering, 2000Co-Authors: Ronaldo I BorjaAbstract:Abstract This paper presents a finite element model for strain localization analysis of elastoplastic solids subjected to discontinuous displacement fields based on standard Galerkin approximation. Strain enhancements via jumps in the displacement field are captured and condensed on the material level, leading to a formulation that does not require static condensation to be performed on the element level. The mathematical formulation revolves around the dual response of a macroscopic Point cut by a shear band, which requires the satisfaction of the yield condition on the band as the same Stress Point unloads elastically just outside the band. Precise conditions for the appearance of slip lines, including their initiation and evolution, are outlined for a rate-independent, strain-softening Drucker–Prager model, and explicit analytical expressions are used to describe the orientation of the slip line in a plane strain setting. At post-localization the Stress-Point integration algorithm along the band is exact and amenable to consistent linearization. Numerical examples involving simple shearing of elastoplastic solids with deviatoric plastic flow, as well as plane strain compression of dilatant cohesive/frictional materials, are presented to demonstrate absolute objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions.
Antonio Gens - One of the best experts on this subject based on the ideXlab platform.
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A Stress Point algorithm for an elastoplastic model in unsaturated soils
International Journal of Plasticity, 2000Co-Authors: Jean Vaunat, J. C. Cante, A. Ledesma, Antonio GensAbstract:Abstract Two Stress fields, combination of total Stresses, liquid pressure and gas pressure have to be considered to explain the deformational behaviour of unsaturated media. Elastoplastic models developed for these materials consider generally two yield surfaces, each one associated to a Stress field, and whose intersection produces a corner in the space of generalised Stress components. In this paper, a Stress Point algorithm is proposed to cope with the integration of such constitutive laws, which can be seen as non smooth multisurface plastic models in the space of the two Stress fields. The basic model developed by Alonso et al. (Alonso, E.E., Gens, A., 1990. A constitutive model for partially saturated soils. Geotechnique 40 (3), 405–430), which will be used to test the algorithm, is first described. Generalised Stress and strain variables are then defined. Implementation of the return mapping algorithm, based on an implicit integration scheme, is presented with special attention devoted to the problem of mixed control imposed by the F.E. formulation generally used to analyse the hydromechanical behaviour of unsaturated media. Validation results on distinct generalised Stress paths are given at the end.
Qinglin Duan - One of the best experts on this subject based on the ideXlab platform.
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gradient and dilatational stabilizations for Stress Point integration in the element free galerkin method
International Journal for Numerical Methods in Engineering, 2009Co-Authors: Qinglin Duan, Ted BelytschkoAbstract:Stabilized Stress-Point integration schemes based on gradient stabilization and dilatational stabilization methods are presented for linear elastostaticity problems in the framework of element-free Galerkin (EFG) method. The instability in Stress fields associated with the Stress-Point integration is treated by the addition to the Galerkin weak form of stabilization terms which contain product of the gradient of the residual or the trace of the gradient of the residual; the latter is called dilatational stabilization. Numerical results show that the oscillations in the Stress fields are successfully removed by the presented stabilization methods, and that the convergence and stability properties of direct Stress-Point integration are greatly improved. These stabilization methods are particularly suitable for the solution of non-linear continua with explicit time integration methods. Copyright © 2008 John Wiley & Sons, Ltd.
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Gradient and dilatational stabilizations for Stress‐Point integration in the element‐free Galerkin method
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Qinglin Duan, Ted BelytschkoAbstract:Stabilized Stress-Point integration schemes based on gradient stabilization and dilatational stabilization methods are presented for linear elastostaticity problems in the framework of element-free Galerkin (EFG) method. The instability in Stress fields associated with the Stress-Point integration is treated by the addition to the Galerkin weak form of stabilization terms which contain product of the gradient of the residual or the trace of the gradient of the residual; the latter is called dilatational stabilization. Numerical results show that the oscillations in the Stress fields are successfully removed by the presented stabilization methods, and that the convergence and stability properties of direct Stress-Point integration are greatly improved. These stabilization methods are particularly suitable for the solution of non-linear continua with explicit time integration methods. Copyright © 2008 John Wiley & Sons, Ltd.
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On the Stabilization of Stress-Point Integration in the Element Free Galerkin Method
Lecture Notes in Computational Science and Engineering, 1Co-Authors: Qinglin Duan, Ted BelytschkoAbstract:Stabilized Stress-Point integration schemes based on Least-Squares Stabilization (LSS), Taylor series Expansion Based Stabilization (TEBS) and Finite Increment Gradient (FIG) are compared for linear elastostaticity problems and some relations between them are described. Particular emphasis is placed on Stress-Point integration procedures with stabilization. The convergence and stability properties of stabilized methods in the framework of the element free Galerkin (EFG) method with Stress-Point integration are studied by numerical examples. It is shown that stabilized Stress-Point integration consumes much less computational time than full integration and exhibits higher accuracy and much better convergence and stability than unstabilized Stress-Point integration and stabilized nodal integration.
Narayanaswamy Balakrishnan - One of the best experts on this subject based on the ideXlab platform.
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Optimal step-Stress test under progressive type-I censoring
IEEE Transactions on Reliability, 2004Co-Authors: E. Gouno, Ananda Sen, Narayanaswamy BalakrishnanAbstract:We consider in this work a k-step-Stress accelerated test with equal duration steps /spl tau/. Censoring is allowed at each change Stress Point i/spl tau/, i=1,...k. The problem of choosing the optimal /spl tau/ is addressed using variance optimality as well as determinant-optimality criteria. We investigate in detail the case of progressively Type-I right censored data with a single Stress variable.