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Discontinuity Approach (discontinuity + approach)

Distribution by Scientific Domains
Engineering100%

Kinds of Discontinuity Approach

  • strong discontinuity approach
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    Selected Abstracts

    One fragmentation procedure for brittle material cracking

    PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006
    S. H. Reese
    Realistic modeling of 3D fragmentation procedures with minimal incorporation of restrictions to the crack path is still a challenge in modern computational engineering simulations. The presented approach is used to model failure and cracking in concrete structures, applying an explicit finite element integration scheme. Within this model the Strong Discontinuity Approach (SDA) is used to handle the failure process until the material is fully damaged. At stage an adaptive refinement technique is incorporated in ordner to introduce real cracks which are suitable for DEM / FEM coupling or contact formulations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Energy driven crack propagation at finite strains based on the embedded strong discontinuity approach

    PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
    Radan Radulovic
    New advances in three-dimensional finite element modeling of crack propagation at finite strains are presented. The proposed numerical model is based on the Enhanced Assumed Strain concept. The enhanced part of the deformation gradient is associated with a displacement discontinuity. In contrast to previous works, a new, energy based criterion for crack propagation is presented. The necessity for a tracking algorithm for the crack path is avoided by using more than one discontinuity within each finite element. This leads to a strictly local formulation, i.e., no information about the neighboring elements are required. Further advantages of such a formulation are a symmetric tangent stiffness matrix and the reduction of locking effects. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    A Finite Element Approach for the Simulation of Quasi-Brittle Fracture

    PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005
    Oliver Hilgert
    In the context of a strong discontinuity approach, we propose a finite element formulation with an embedded displacement discontinuity. The basic assumption of the proposed approach is the additive split of the total displacement field in a continuous and a discontinuous part. An arbitrary crack splits the linear triangular finite element into two parts, namely a triangular and a quadrilateral part. The discontinuous part of the displacement field in the quadrilateral portion is approximated using linear shape functions. For these purposes, the quadrilateral portion is divided into two triangular parts which is in this way similar to the approach proposed in [5]. In contrast, the discretisation is different compared to formulations proposed in [1] and [3], where the discontinuous part of the displacement field is approximated using bilinear shape functions. The basic theory of the underlying finite element formulation and a cohesive interface model to simulate brittle fracture are presented. By means of representative numerical examples differences and similarities of the present formulation and the formulations proposed in [1] and [3] are highlighted. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [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]