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A Finite Element Approach for the Simulation of Quasi‐Brittle Fracture
Author(s) -
Hilgert Oliver,
Schröder Jörg,
Löblein Joachim
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510144
Subject(s) - quadrilateral , discontinuity (linguistics) , finite element method , displacement field , bilinear interpolation , displacement (psychology) , extended finite element method , discretization , mathematics , context (archaeology) , geometry , mathematical analysis , structural engineering , engineering , geology , psychology , paleontology , statistics , psychotherapist
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)