A Mixed Eulerian-Lagrangian Model for the Analysis of Dynamic Fracture (Finite Element Method, Moving Mesh, Virtual Energy Release Rate)
Koh, Hyun Moo
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https://hdl.handle.net/2142/69959
Description
Title
A Mixed Eulerian-Lagrangian Model for the Analysis of Dynamic Fracture (Finite Element Method, Moving Mesh, Virtual Energy Release Rate)
Author(s)
Koh, Hyun Moo
Issue Date
1986
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)
Engineering, Civil
Abstract
This study is concerned with the development of continuum formulations for the analysis of static and dynamic brittle fracture problems based on a mixed Eulerian-Lagrangian kinematic model. Effective finite element computational methods based on the continuum formulations are also described.
Explicit expressions for instantaneous energy release rates are developed by modeling virtual crack extensions with the Eulerian-Lagrangian kinematic description (ELD). The ELD can model true variations of the crack geometry, so the need for a finite difference approximation of a virtual crack extension is eliminated. Accurate estimates of mixed-mode stress intensity factors are obtained from the mutual potential energy release rate expression by simple computational procedures.
An elastodynamic formulation of the ELD for small-deformation analysis is developed. Time rate expressions for field variables are derived using the dynamic ELD model. Convective terms in the ELD introduce more stringent continuity requirements in the variational equations of motion than Lagrangian formulations. A special weak form of the variational equations of motion relaxes these requirements, and is the basis of a finite element formulation using moving isoparametric elements. The ELD kinematic model allows the finite element mesh to continuously adjust for time-dependent changes in structural geometry, material interfaces or the domain of the boundary conditions.
Dynamic crack propagation problems are analyzed using the moving isoparametric finite element method. In general, the geometric changes due to crack growth and their effects on material motion can be more simply and effectively modeled by the ELD than by conventional Lagrangian models. Continuous mesh motion models the crack growth without discrete remeshing and interpolation of field variables as in Lagrangian models. The dynamic ELD automatically incorporates the proper singular forms in the stress and material velocity fields when quarter-point singular isoparametric elements are used to model the crack-tip region. Significantly more accurate numerical predictions of brittle crack propagation behavior, particularly in the transient stages of sudden crack acceleration and arrest, are obtained with the dynamic ELD relative to Lagrangian models. Several example computations demonstrate this result.
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