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Ted Belytschko - One of the best experts on this subject based on the ideXlab platform.

  • A method for dynamic crack and shear band propagation with phantom nodes
    International Journal for Numerical Methods in Engineering, 2006
    Co-Authors: Jeong-hoon Song, Pedro M. A. Areias, Ted Belytschko
    Abstract:

    A new method for modelling of arbitrary dynamic crack and shear band propagation is presented. We show that by a rearrangement of the extended finite element basis and the nodal degrees of freedom, the discontinuity can be described by superposed elements and phantom nodes. Cracks are treated by adding phantom nodes and superposing elements on the original mesh. Shear bands are treated by adding phantom degrees of freedom. The proposed method simplifies the treatment of element-by-element crack and shear band propagation in explicit methods. A quadrature method for 4-node quadrilaterals is proposed based on a single quadrature point and Hourglass Control. The proposed method provides consistent history variables because it does not use a subdomain integration scheme for the discontinuous integrand. Numerical examples for dynamic crack and shear band propagation are provided to demonstrate the effectiveness and robustness of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.

  • Suppression of spurious intermediate frequency modes in under‐integrated elements by combined stiffness/viscous stabilization
    International Journal for Numerical Methods in Engineering, 2005
    Co-Authors: William J.t. Daniel, Ted Belytschko
    Abstract:

    Solutions employing perturbation stiffness or viscous Hourglass Control with one-point quadrature finite elements often exhibit spurious modes in the intermediate frequency range. These spurious frequencies are demonstrated in several examples and their origin is explained. Then it is shown that by critically damping the Hourglass modes, these spurious mid-range frequency modes can be suppressed. Estimates of the Hourglass frequency and damping coefficients are provided for the plane 4-node quadrilateral and a 4-node shell element. Results are presented that show almost complete annihilation of spurious intermediate frequency modes for both linear and non-linear problems. Copyright (c) 2005 John Wiley & Sons, Ltd.

  • Implementation and accuracy of mixed-time implicit-explicit methods for structural dynamics
    Computers & Structures, 2003
    Co-Authors: Kam Liu, Ted Belytschko, Yi Fei Zhang
    Abstract:

    Abstract This paper deals with some practical computational aspects and numerical evaluation of the previously developed mixed-time implicit-explicit methods for structural dynamics. Three different topics: computer implementation of the mixed-time procedures; Hourglass Control for bilinear quadrilaterals using one-point quadrature and its effect on numerical stability in the explicit partition; and spurious oscillations in solutions are discussed. Two numerical examples are presented to examine the accuracy and effectiveness of mixed-time formulations.

  • Finite Element Technology for Penetration Problems.
    1994
    Co-Authors: Ted Belytschko, Kam Liu
    Abstract:

    Abstract : Finite element methods for penetration mechanics are developed. A pinball contact-impact algorithm which is easily vectorizable has been implemented on partitioned memory SIMD computers. The pinball algorithm is further extended to problems with friction and erosion; Lagrange and augmented Lagrange multiplier methods, and its convergence have also been studied. Multiple-quadrature elements with Hourglass Control and physical stabilization and multi-time step integration have also been studied. Numerical results of the multiple quadrature elements with stabilization showed what simple stabilization forces can be obtained which are convergent and based on physical parameters. The implementation of this algorithm on massively parallel machines has also been investigated. (AN)

  • Multiple quadrature underintegrated finite elements
    International Journal for Numerical Methods in Engineering, 1994
    Co-Authors: Kam Liu, Ted Belytschko
    Abstract:

    New multiple-quadrature-point underintegrated finite elements with Hourglass Control are developed. The elements are selectively underintegrated to avoid volumetric and shear locking and save computational time. An approach for Hourglass Control is proposed such that the stabilization operators are obtained simply by taking the partial derivatives of the generalized strain rate vector with respect to the natural co-ordinates so that the elements require no stabilization parameter. To improve accuracy over the traditional one-point-quadrature elements, several quadrature points are used to integrate the internal forces, especially for tracing the plastic fronts in the mesh during loading and unloading in elastic–plastic analysis. Two- and four-point-quadrature elements are proposed for use in the two- and three-dimensional elements, respectively. Other multiple-quadrature points can also be employed. Several numerical examples such as thin beam, plate and shell problems are presented to demonstrate the applicability of the proposed elements.

G. C. Ganzenmüller - One of the best experts on this subject based on the ideXlab platform.

  • Hourglass Control for Smooth Particle Hydrodynamics removes tensile and rank-deficiency instabilities - Hourglass Control for SPH
    European Physical Journal-special Topics, 2016
    Co-Authors: G. C. Ganzenmüller, Martin Sauer, Michael May, Stefan Hiermaier
    Abstract:

    We present a stabilization scheme for elastoplastic Smooth-Particle Hydrodynamics (SPH) which overcomes two major challenges: (i) the tensile instability inherent to the updated Lagrangian approach is suppressed and (ii) the rank-deficiency instability inherent to the nodal integration approach is cured. To achieve these goals, lessons learned from the Finite-Element Method are transferred to SPH. In particular, an analogue of Hourglass Control is derived for SPH, which locally linearizes the deformation field to obtain stable and accurate solutions, without the need to resort to stabilization via excessive artificial viscosity. The resulting SPH scheme combines the ability of updated Lagrangian SPH to model truly large deformations with the accuracy and stability needed to faithfully perform simulations. This claim is supported by the analysis of problematic cases and the simulation of an impact scenario.

  • Smooth particle hydrodynamics simulation of damage induced by a spherical indenter scratching a viscoplastic material
    International Journal of Solids and Structures, 2016
    Co-Authors: S. Leroch, M. Varga, Stefan J. Eder, András Vernes, M. Rodríguez Ripoll, G. C. Ganzenmüller
    Abstract:

    Abstract We present an implementation of a (mesh-free) smooth particle hydrodynamics (SPH) algorithm, intended for the application to solid bodies, and use it to simulate scratch-induced surface damage on an elasto-viscoplastic material. If conventional SPH is used to simulate solids, an unphysically high artificial viscosity is required to damp strong oscillatory modes and thus stabilize the system. To overcome these intrinsic difficulties associated with modeling solid bodies, the recently implemented so-called total-Lagrangian SPH utilizes an Hourglass Control scheme similar to what is known from finite element algorithms. Elasto-viscoplastic material properties are modeled by using the Mie–Gruneisen equation of state and the Johnson–Cook model. The material parameters are selected to reproduce the strain-stress behavior of annealed oxygen-free high conductivity copper. The spherical indenter is modeled as a rigid sphere. The topographies of the calculated scratch-induced surface damage are in excellent agreement with experimental scratch tests carried out at comparable normal loads. We also calculate the real contact area between the indenter and the surface, allowing a sound estimation of the scratch hardness.

  • An Hourglass Control algorithm for Lagrangian Smooth Particle Hydrodynamics
    Computer Methods in Applied Mechanics and Engineering, 2015
    Co-Authors: G. C. Ganzenmüller
    Abstract:

    Abstract This paper presents a stabilization scheme which addresses the rank-deficiency problem in meshless collocation methods for solid mechanics. Specifically, Smooth-Particle Hydrodynamics (SPH) in the Total Lagrangian formalism is considered. This method is rank-deficient in the sense that the SPH approximation of the deformation gradient is not unique with respect to the positions of the integration points. The non-uniqueness can result in the formation of zero-energy modes. If undetected, these modes can grow and completely dominate the solution. Here, an algorithm is introduced, which effectively suppresses these modes in a fashion similar to hour-glass Control mechanisms in Finite-Element methods. Simulations utilizing this Control algorithm exhibit much improved stability, accuracy, and error convergence properties. In contrast to an alternative method which eliminates zero-energy modes, namely the use of additional integration points, the here presented algorithm is easy to implement and computationally very efficient.

Chong Peng - One of the best experts on this subject based on the ideXlab platform.

  • Three-dimensional modeling of granular flow impact on rigid and deformable structures
    Computers and Geotechnics, 2019
    Co-Authors: Ling Zhan, Chong Peng, Bingyin Zhang
    Abstract:

    Abstract A stabilized coupled total-Lagrangian and conventional Euler kernel based smoothed particle hydrodynamics (TL-CE SPH) method is presented to model three-dimensional granular flow-structure interaction with rigid and deformable structures. In the coupled TL-CE SPH, the granular material is simulated using CESPH with the Dracker-Prager model, while the structure solver is based on TLSPH. The stabilized TLSPH with corrected kernel gradient, Lagrangian kernel function and Hourglass Control technique overcomes the common deficiencies of inconsistency, tensile instability and Hourglass mode in structure modeling. Based on the Adami boundary condition (Adami et al., 2012), a unified framework for modeling solid boundaries and the granular media-structure interfaces is presented. Furthermore, the advanced GPU-acceleration is employed to achieve high efficiency. The coupled method is employed to simulate problems of granular collapse, granular material-structure interaction at quasi-static regime and granular flows impact on rigid and deformable structures. The presented method can simulate granular flows, the flow-structure interactions, and the deformation and stress of the structures correctly. Furthermore, the GPU-acceleration gives hundreds times of speed-up over serial CPU implementation. The presented method can be applied to large scale three-dimensional cases.

  • A stabilized total-Lagrangian SPH method for large deformation and failure in geomaterials.
    arXiv: Computational Engineering Finance and Science, 2019
    Co-Authors: Rushdie Ibne Islam, Chong Peng
    Abstract:

    Conventional smoothed particle hydrodynamics based on Eulerian kernels (CESPH) is widely-used in large deformation analysis in geomaterials. Despite being popular, it suffers from tensile instability and rank-deficiency; thus, it needs several numerical treatments to be stable. In this work, we present a stabilized total-Lagrangian SPH method (TLSPH), which is inherently free of tensile instability. A stiffness-based Hourglass Control algorithm is employed to cure the Hourglass mode caused by rank-deficiency. Periodic update of reference configuration is used in simulations to allow TLSPH to model large deformation and post-failure flow in geomaterials. Several numerical examples are presented to show the performance of the stabilized TLSPH method. The comparison between TLSPH and CESPH are discussed. The influences of Hourglass Control and configuration update are also discussed and shown in the numerical examples. It is found that the presented stabilized TLSPH is robust and can model large deformation and plastic flows in geomaterials. Particularly, the stabilized TLSPH delivers accurate and smooth stress results.

  • A stabilized TL–WC SPH approach with GPU acceleration for three-dimensional fluid–structure interaction
    Journal of Fluids and Structures, 2019
    Co-Authors: Ling Zhan, Chong Peng, Bingyin Zhang
    Abstract:

    Abstract A coupled total Lagrangian (TL) and weakly compressible (WC) smoothed particle hydrodynamics (SPH) method is presented to model three-dimensional fluid–structure interactions (FSI) with deformable structures. In the coupled TL–WC SPH, the fluid phase is simulated using WCSPH, while the structure solver is based on TLSPH. The three main deficiencies of solid simulation using conventional SPH, i.e. inconsistency, tensile instability and Hourglass mode are circumvented in the stabilized TLSPH by means of corrected kernel gradient, Lagrangian kernel function and Hourglass Control technique, respectively. The resulted stabilized TLSPH is stable, accurate and has almost quadratic convergence rate in solid modeling. To increase the accuracy in FSI modeling, the δ − SPH technique is employed to improve the pressure results in the fluid phase. Based on the Adami boundary condition (Adami et al., 2012), a unified framework for modeling solid boundaries and the fluid–structure interfaces is presented. Furthermore, the GPU parallelization is employed to accelerate the proposed TL–WC SPH method for higher efficiency. The coupled method is employed to simulate problems of pure fluid flow, elastic solids with large deformation and fluid–structure interaction with deformable structures. The numerical results are compared with analytical solutions and results from literature. The GPU efficiency and speed-up compared with CPU implementations are analyzed. The novelty of this work consists: (1) three-dimensional SPH modeling of FSI problems with deformable structures, (2) stabilized structure simulation free of Hourglass mode, (3) a unified framework for FSI problems taking advantages of δ -SPH, TLSPH, Hourglass Control, and GPU acceleration. Importantly, with the Hourglass Control technique proposed by Ganzenmuller (2015), stresses can be captured accurately in the TL–WC SPH-based FSI simulations.

  • Large Deformation Modeling of Soil-Machine Interaction in Clay
    Springer Series in Geomechanics and Geoengineering, 2017
    Co-Authors: Chong Peng, Mozhen Zhou
    Abstract:

    The evaluation of soil reaction force on tillage tool is important for design and management optimization. The large deformation, dynamic nature and complex soil-tool contact in the problem make it a challenge in numerical modeling. The popular finite element method (FEM) has distorted mesh in large deformation, and complex adaptive remeshing techniques need to be used in soil-tool interaction simulation. On the other hand, numerical approaches based on computational fluid mechanics (CFD) and discrete element method (DEM), although avoid mesh distortion, have difficulties in capturing the true mechanical properties of soils. In this study, we develop a total Lagrangian SPH (TL-SPH) approach for simulating the large deformation soil-machine interaction in clay. The TL-SPH is simple in formulation and computationally efficient. The accuracy and stability of the method is improved by employing an Hourglass Control technique. Soil-tool contact is modeled using a node-to-segment (NTS) contact algorithm. Preliminary numerical studies are carried out, it is demonstrated that the presented approach is capable of capturing salient soil-tool interaction properties.

Claas Bierwisch - One of the best experts on this subject based on the ideXlab platform.

  • Application of Hourglass Control to Eulerian smoothed particle hydrodynamics
    Computational Particle Mechanics, 2020
    Co-Authors: Shoya Mohseni-mofidi, Claas Bierwisch
    Abstract:

    Being a truly meshless method, smoothed particle hydrodynamics (SPH) raises expectations to naturally handle solid mechanics problems of large deformations. However, in a simple formulation it severely suffers from two instabilities, namely tensile instability and zero-energy modes, which hinders SPH from being an popular numerical tool in that area. Although Lagrangian SPH completely removes tensile instability, it is not yet able to prevent zero-energy modes. Furthermore, kernel updates are required to properly handle very large deformations which again triggers tensile instability. Additionally, Lagrangian SPH cannot naturally deal with contact problems. Pursuing an alternative route, this paper aims at stabilizing Eulerian SPH in order to accurately deal with large deformations while preserving the fundamental properties of SPH to easily handle contact problems as well as fluid–structure interaction in a straightforward monolithic manner. For this purpose, an Hourglass Control scheme already employed to prevent zero-energy modes in Lagrangian SPH framework is used. The advantage of the present scheme is that the stabilization method can be easily implemented in any Eulerian SPH code by making only few changes to the code. The proposed scheme is employed to simulate several cases of elasticity, plasticity, fracture and fluid–structure interaction in order to assess its accuracy and effectiveness. The obtained results are compared with analytical solutions and finite element results where very good agreement is found.

  • Application of Hourglass Control to Eulerian smoothed particle hydrodynamics
    Computational Particle Mechanics, 2020
    Co-Authors: Shoya Mohseni-mofidi, Claas Bierwisch
    Abstract:

    Being a truly meshless method, smoothed particle hydrodynamics (SPH) raises expectations to naturally handle solid mechanics problems of large deformations. However, in a simple formulation it severely suffers from two instabilities, namely tensile instability and zero-energy modes, which hinders SPH from being an popular numerical tool in that area. Although Lagrangian SPH completely removes tensile instability, it is not yet able to prevent zero-energy modes. Furthermore, kernel updates are required to properly handle very large deformations which again triggers tensile instability. Additionally, Lagrangian SPH cannot naturally deal with contact problems. Pursuing an alternative route, this paper aims at stabilizing Eulerian SPH in order to accurately deal with large deformations while preserving the fundamental properties of SPH to easily handle contact problems as well as fluid–structure interaction in a straightforward monolithic manner. For this purpose, an Hourglass Control scheme already employed to prevent zero-energy modes in Lagrangian SPH framework is used. The advantage of the present scheme is that the stabilization method can be easily implemented in any Eulerian SPH code by making only few changes to the code. The proposed scheme is employed to simulate several cases of elasticity, plasticity, fracture and fluid–structure interaction in order to assess its accuracy and effectiveness. The obtained results are compared with analytical solutions and finite element results where very good agreement is found.

  • A stabilization method for smoothed particle hydrodynamics preventing tensile instability and zero-energy modes
    2018
    Co-Authors: Shoya Mohseni-mofidi, Claas Bierwisch
    Abstract:

    Smoothed particle hydrodynamics (SPH) is conventionally described in spatial coordinates hence employs Eulerian kernels which are updated each time step. That is proved to be the source of the tensile instability. Furthermore, SPH like other rank deficient methods such as reduced integration finite element method (FEM) and nodally integrated meshfree methods suffers from zero-energy modes. Ganzenmueller 2015 [1] and Ganzenmueller et al. 2016 [2] proposed an Hourglass Control scheme in analogy to FEM and showed it can effectively prevent tensile instability and zero-energy modes when it is applied to SPH described in material coordinates. Here, we introduce the Hourglass Control scheme which makes use of Lagrangian kernels to conventional SPH. The advantage of the method is that it only needs a few changes to incorporate the scheme into an already implemented SPH code. Several 2d and 3d simulations are carried out with and without the Hourglass Control scheme. The results prove the ability of the method to prevent both instabilities. Besides, the comparison between SPH results and FEM ones shows a good agreement between two methods.

Martin W. Heinstein - One of the best experts on this subject based on the ideXlab platform.

  • Solution verification for explicit transient dynamics problems in the presence of Hourglass and contact forces
    Computer Methods in Applied Mechanics and Engineering, 2006
    Co-Authors: James A. Stewart, Arne S. Gullerud, Martin W. Heinstein
    Abstract:

    Abstract This paper presents solution verification studies applicable to a class of problems involving wave propagation, frictional contact, geometrical complexity, and localized incompressibility. The studies are in support of a validation exercise of a phenomenological screw failure model. The numerical simulations are performed using a fully explicit transient dynamics finite element code, employing both standard four-node tetrahedral and eight-node mean quadrature hexahedral elements. It is demonstrated that verifying the accuracy of the simulation involves not only consideration of the mesh discretization error, but also the effect of the Hourglass Control and the contact enforcement. In particular, the proper amount of Hourglass Control and the behavior of the contact search and enforcement algorithms depend greatly on the mesh resolution. We carry out the solution verification exercise using mesh refinement studies and describe our systematic approach to handling the complicating issues. It is shown that Hourglassing and contact must both be carefully monitored as the mesh is refined, and it is often necessary to make adjustments to the Hourglass and contact user input parameters to accommodate finer meshes. We introduce in this paper the Hourglass energy, which is used as an “error indicator” for the Hourglass Control. If the Hourglass energy does not tend to zero with mesh refinement, then an Hourglass Control parameter is changed and the calculation is repeated.

  • Solution verification for explicit transient dynamics problems in the presence of Hourglass and contact forces.
    2004
    Co-Authors: Martin W. Heinstein, Arne S. Gullerud, James Richard Stewart
    Abstract:

    This paper presents solution verification studies applicable to a class of problems involving wave propagation, frictional contact, geometrical complexity, and localized incompressibility. The studies are in support of a validation exercise of a phenomenological screw failure model. The numerical simulations are performed using a fully explicit transient dynamics finite element code, employing both standard four-node tetrahedral and eight-node mean quadrature hexahedral elements. It is demonstrated that verifying the accuracy of the simulation involves not only consideration of the mesh discretization error, but also the effect of the Hourglass Control and the contact enforcement. In particular, the proper amount of Hourglass Control and the behavior of the contact search and enforcement algorithms depend greatly on the mesh resolution. We carry out the solution verification exercise using mesh refinement studies and describe our systematic approach to handling the complicating issues. It is shown that Hourglassing and contact must both be carefully monitored as the mesh is refined, and it is often necessary to make adjustments to the Hourglass and contact user input parameters to accommodate finer meshes. We introduce in this paper the Hourglass energy, which is used as an 'error indicator' for the Hourglass Control. If the Hourglass energy does notmore » tend to zero with mesh refinement, then an Hourglass Control parameter is changed and the calculation is repeated.« less

  • PRONTO3D users` instructions: A transient dynamic code for nonlinear structural analysis
    1998
    Co-Authors: S.w. Attaway, Martin W. Heinstein, F.j. Mello, J.w. Swegle, J.a. Ratner, R.i. Zadoks
    Abstract:

    This report provides an updated set of users` instructions for PRONTO3D. PRONTO3D is a three-dimensional, transient, solid dynamics code for analyzing large deformations of highly nonlinear materials subjected to extremely high strain rates. This Lagrangian finite element program uses an explicit time integration operator to integrate the equations of motion. Eight-node, uniform strain, hexahedral elements and four-node, quadrilateral, uniform strain shells are used in the finite element formulation. An adaptive time step Control algorithm is used to improve stability and performance in plasticity problems. Hourglass distortions can be eliminated without disturbing the finite element solution using either the Flanagan-Belytschko Hourglass Control scheme or an assumed strain Hourglass Control scheme. All constitutive models in PRONTO3D are cast in an unrotated configuration defined using the rotation determined from the polar decomposition of the deformation gradient. A robust contact algorithm allows for the impact and interaction of deforming contact surfaces of quite general geometry. The Smooth Particle Hydrodynamics method has been embedded into PRONTO3D using the contact algorithm to couple it with the finite element method.