Finite Element Modeling of Strain Localization Initiated by Geometric Irregularities
Keppel, Michael
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https://hdl.handle.net/2142/72198
Description
Title
Finite Element Modeling of Strain Localization Initiated by Geometric Irregularities
Author(s)
Keppel, Michael
Issue Date
1993
Doctoral Committee Chair(s)
Dodds, Robert H., Jr.
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Engineering, Civil
Abstract
The localization of deformation into zones of intense straining, known as shear bands, is a common phenomenon in inelastic deformation. The modeling of this phenomenon by the finite element method is hampered by a number of factors; the lack of a priori knowledge of the location, direction, and onset of the localized zones, and the inability of conventional isoparametric elements to model the high strain gradients which occur in these zones.
This study develops new techniques for the finite element modeling of strain localization. Special isoparametric elements with enhanced strain fields derived from incompatible modes are designed to model the high gradients which occur during strain localization. Families of elements are derived based on various formulations of the incompatible modes. In all cases, the incompatible modes are modified to insure that the derived element satisfies the patch test, thereby preserving the convergence properties of the parent element. Use of these elements in place of conventional isoparametric elements allows equivalent results to be obtained with much less computational effort. Additionally, simple criteria for mode addition predict the onset, direction, and location of the strain localization, allowing the enhanced elements to be used only when and where they are needed, further reducing the computational effort.
A number of examples which demonstrate the features of these new techniques are presented. Comparison of the strains computed from the elements containing incompatible modes with the strains computed from the corresponding parent elements shows the improvement in solution accuracy produced by the addition of the incompatible modes. Convergence studies quantify the reduction in computational effort possible with the addition of the incompatible modes and quantify the differences between the various families of elements. Further analyses show the relative effectiveness of the various criteria for mode addition and elucidate the properties of an effective criterion. Analysis of an experimental specimen shows that the convergence properties of the parent element are preserved in the element containing incompatible modes. Consideration of the fracture mechanics parameters J and CTOD shows that the formulation remains unchanged and the computation of these parameters is not adversely affected by the addition of the incompatible modes.
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