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Strong Discontinuities (strong + discontinuity)

Distribution by Scientific Domains

Engineering	92%

Terms modified by Strong Discontinuities

strong discontinuity approach

Selected Abstracts

The response of an elastic half-space under a momentary shear line impulse

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2003
Moche Ziv
Abstract The response of an ideal elastic half-space to a line-concentrated impulsive vector shear force applied momentarily is obtained by an analytical,numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half-space, while being normal to that line as well as to the axis of symmetry of the half-space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half-space; in this sense, the source configuration is exact. For the transient boundary-value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half-space. A numerical integration of these extended differential equations is then carried out in a three-dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half-space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Source signature and elastic waves in a half-space under a sustainable line-concentrated impulsive normal force

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2002
Moche Ziv
Abstract First, the response of an ideal elastic half-space to a line-concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature,the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress-free surface of the half-space to three points located on the other two boundaries of the solution domain. These four wave-arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface-axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface-axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint-Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line-concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Towards the algorithmic treatment of 3D strong discontinuities

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2007
J. Mergheim
Abstract A geometrically non-linear finite element framework for the modelling of propagating discontinuities in three-dimensional continua is presented. By doubling the degrees of freedom in the discontinuous elements, the algorithm allows for arbitrary discontinuities which are not restricted to inter-element boundaries. The deformation field is interpolated independently on both sides of the discontinuity. In contrast to the X-FEM, the suggested approach thus relies exclusively on displacement degrees of freedom. On the discontinuity surface, the jump in the deformation is related to the cohesive tractions to account for smooth crack opening. Computational difficulties characteristic of three-dimensional crack propagation are addressed. The performance of the method is elaborated by means of a homogeneous three-dimensional tension problem and by means of the classical peel test. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Failure of heterogeneous materials: 3D meso-scale FE models with embedded discontinuities

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010
N. Benkemoun
Abstract We present a meso-scale model for failure of heterogeneous quasi-brittle materials. The model problem of heterogeneous materials that is addressed in detail is based on two-phase 3D representation of reinforced heterogeneous materials, such as concrete, where the inclusions are melt within the matrix. The quasi-brittle failure mechanisms are described by the spatial truss representation, which is defined by the chosen Voronoi mesh. In order to explicitly incorporate heterogeneities with no need to change this mesh, some bar elements are cut by the phase-interface and must be split into two parts. Any such element is enhanced using both weak and strong discontinuities, based upon the Incompatible Mode Method. Furthermore, a dedicated operator split solution procedure is proposed to keep local any additional computation on elements with embedded discontinuities. The results for several numerical simulations are presented to illustrate the capabilities of the proposed model to provide an excellent representation of failure mechanisms for any different macroscopic loading path. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Higher-order XFEM for curved strong and weak discontinuities

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2010
Kwok Wah Cheng
Abstract The extended finite element method (XFEM) enables the accurate approximation of solutions with jumps or kinks within elements. Optimal convergence rates have frequently been achieved for linear elements and piecewise planar interfaces. Higher-order convergence for arbitrary curved interfaces relies on two major issues: (i) an accurate quadrature of the Galerkin weak form for the cut elements and (ii) a careful formulation of the enrichment, which should preclude any problems in the blending elements. For (i), we employ a strategy of subdividing the elements into subcells with only one curved side. Reference elements that are higher-order on only one side are then used to map the integration points to the real element. For (ii), we find that enrichments for strong discontinuities are easily extended to higher-order accuracy. In contrast, problems in blending elements may hinder optimal convergence for weak discontinuities. Different formulations are investigated, including the corrected XFEM. Numerical results for several test cases involving strong or weak curved discontinuities are presented. Quadratic and cubic approximations are investigated. Optimal convergence rates are achieved using the standard XFEM for the case of a strong discontinuity. Close-to-optimal convergence rates for the case of a weak discontinuity are achieved using the corrected XFEM. Copyright © 2009 John Wiley & Sons, Ltd. [source]

On the computation of steady-state compressible flows using a discontinuous Galerkin method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008
Hong Luo
Abstract Computation of compressible steady-state flows using a high-order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics-based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low-storage p -multigrid method is used for solving the governing compressible Euler equations to obtain steady-state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady-state flows. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004
J. E. Dolbow
Abstract We present a geometrically non-linear assumed strain method that allows for the presence of arbitrary, intra-finite element discontinuities in the deformation map. Special attention is placed on the coarse-mesh accuracy of these methods and their ability to avoid mesh locking in the incompressible limit. Given an underlying mesh and an arbitrary failure surface, we first construct an enriched approximation for the deformation map with the non-linear analogue of the extended finite element method (X-FEM). With regard to the richer space of functions spanned by the gradient of the enriched approximation, we then adopt a broader interpretation of variational consistency for the construction of the enhanced strain. In particular, in those elements intersected by the failure surface, we construct enhanced strain approximations which are orthogonal to piecewise-constant stress fields. Contrast is drawn with existing strong discontinuity approaches where the enhanced strain variations in localized elements were constructed to be orthogonal to constant nominal stress fields. Importantly, the present formulation gives rise to a symmetric tangent stiffness matrix, even in localized elements. The present modification also allows for the satisfaction of a discontinuous patch test, wherein two different constant stress fields (on each side of the failure surface) lie in the solution space. We demonstrate how the proposed modifications eliminate spurious stress oscillations along the failure surface, particularly for nearly incompressible material response. Additional numerical examples are provided to illustrate the efficacy of the modified method for problems in hyperelastic fracture mechanics. Copyright © 2003 John Wiley & Sons, Ltd. [source]

PATTERN RECOGNITION VIA ROBUST SMOOTHING WITH APPLICATION TO LASER DATA

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2007
Carlo Grillenzoni
Summary Nowadays airborne laser scanning is used in many territorial studies, providing point data which may contain strong discontinuities. Motivated by the need to interpolate such data and preserve their edges, this paper considers robust nonparametric smoothers. These estimators, when implemented with bounded loss functions, have suitable jump-preserving properties. Iterative algorithms are developed here, and are equivalent to nonlinear M-smoothers, but have the advantage of resembling the linear Kernel regression. The selection of their coefficients is carried out by combining cross-validation and robust-tuning techniques. Two real case studies and a simulation experiment confirm the validity of the method; in particular, the performance in building recognition is excellent. [source]

Smeared crack approach: back to the original track

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006
M. Cervera
Abstract This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh-size and mesh-bias spurious dependence when the method is applied ,straightly'. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Higher-order XFEM for curved strong and weak discontinuities

An extended finite element method with analytical enrichment for cohesive crack modeling

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009
James V. CoxArticle first published online: 28 NOV 200
Abstract A recent approach to fracture modeling has combined the extended finite element method (XFEM) with cohesive zone models. Most studies have used simplified enrichment functions to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. In this study enrichment functions based upon an existing analytical investigation of the cohesive crack problem are proposed. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation and enrichment functions are discussed. A parameter study for a simple mode I model problem is presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. The effects of mesh refinement and mesh orientation are considered. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are examined. The analysis results indicate that the analytically based enrichment functions can accurately track the cohesive crack propagation of a mode I crack independent of mesh orientation. A mixed mode example further demonstrates the potential of the formulation. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Geometrically non-linear damage interface based on regularized strong discontinuity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002
Ragnar Larsson
Abstract The contribution of this paper concerns the fracture modelling of an interface with a fixed internal material surface in the context of geometrically non-linear kinematics. Typical applications are composite laminates and adhesive/frictional joints in general. In the model development, a key feature is the concept of regularized strong discontinuity, which provides a regular deformation gradient within the interface. The deformation gradient within the interface is formulated in a multiplicative structure with a continuous part and a discontinuous part, whereby the interface deformation is interpreted as a transformation between the material damaged configuration and the actual spatial configuration. In analogy with the continuum formulation of hyper-inelasticity, a constitutive framework is defined for the relation between the induced material traction and the displacement jump vector, which are defined on the material damaged interface configuration. Within this framework, a simple, but yet still representative, model for the delamination problem is proposed on the basis of a damage,plasticity coupling for the interface. The model is calibrated analytically in the large deformation context with respect to energy dissipation in mode I so that a predefined amount of fracture energy is dissipated. The paper is concluded with a couple of numerical examples that display the properties of the interface. Copyright © 2002 John Wiley & Sons, Ltd. [source]