|主題||Special Finite Elements with Displacement Discontinuity across Internal Interfaces|
|筆頭著者||Moharrmad Afifuddin（Saitama University）|
|連名者1||Zhishen Wu（Saitama University）|
|連名者2||Atsuhiko Mashida（Saitama University）|
In the recent year, the modeling of localization problem involving a wide variety of material, and geometrical discontinuities like discrete cracks in concrete, joints in rock and bold-slip layers in reinforced concrete, has become an intriguing issue in the fields of computational failure mechanics. Most of the available finite element techniques for dealing with these discontinuities were developed in the context brittle failure in concrete. As the result, two main development routes, which are closely related, discrete crack model and smeared crack model approach, have been proposed. In the discrete crack approach, crack or other discontinuities are modeled as interelement displacement discontinuities. A stress-displacement relation is specified for the discrete crack;i.e. for the localization summed with no width. When the localization extends through a certain node, this node must be split into two in order to allow the new crack element insertion. The need for repeated changes in the topological connectivity of the mesh is a very serious drawback of this implementation. Despite current attempts to remove the drawbacks of the original representation. Such as the emergence of powerful mesh generators and improved computer hardware, discrete representation of localized failure in three dimensional structure still seems an insurmountable task. Because of these drawbacks, discrete crack models were rapidly replaced by smeared crack models, introduced by Rashid. Smeared crack models are conceptually simple, and can be easily implemented in a general-purpose finite element program. Although these models have been widely used in the analysis of fracture, they still suffer from a number of shortcomings. The main difficulties of spurious mesh-size sensitivity caused by strain softening has been avoided by the introduction of the regularization concepts such as the fracture energy concept, rate-dependent model, and non-local concept. Although the smeared crack approach gives objective results with regard to mesh size when using non-distorted finite elements, the behavior is not clear when mesh distortions are necessary for modelling requirements; remarkably in these cases a correct energy dissipation cannot be assured, even when the mesh size tends to zero. On the other hand, smeared crack models seem to overestimate the stifness and strength of structures that exhibits shear-dominated behavior. Rots has applied different smeared crack models to cases of localized fracture, and has pointed three problems namely, directional bias, spurious kinematic modes, and stress locking. Regarding these, some formulations aimed at modelling strain localization are found in the literature. In these researches, localization zone of constant width, localized strain modes or discontinuous strain fields are embedded in the finite element. In this paper, we interested to develop new formulations, which are free from the shortcomings of smeared crack and discrete crack model. The study addresses to present an identical model to illustrate interface problems like bond-slip problems, and other localized failure problems within an element. As a main differences between this model and Ortiz's or Dvorkin's model is any interface constitutive model can be adopted to represent the behavior of the internal crack.
In this paper we develop an identical formulation for localization and other local discontinuous problems, where for the discontinuous interface a local stress-displacement constitutive relation is used. The new formulation keeps objectivity with regard to regular mesh refinements.
Although the new formulation introduces a non symmetric consistent stiffness matrix, only the symmetric part of the consistent stiffness matrix can be used with a limited efficiency decrease. This makes the finite element with embedded discontinuous interface easy to implement in standard non linear finite element codes, and therefore all the existing finite element libraries and constitutive models for the material outside the discontinuous interface can be readily used in combination with them.
From comparison between smeared crack concept model, it shows that smeared crack model is too stiff, and new formulation method is almost same with the experimental result or the calculated result by discrete crack model which has been done by Rots. Recently, the application of the proposed model for solving the behavior of bond-slip interfaces between steel and concrete is in progress.