Spacetime damage-based cohesive model for elastodynamic fracture with dynamic contact
type: CreativeWork
description: Dynamic material failure is important in a number of scientific and engineering applications and a variety of numerical methods for its modeling have been proposed. This thesis presents the formulation and implementation of an interfacial-damage, cohesive-fracture model, including contact and friction effects, for dynamic failure of brittle materials. The model is implemented within a spacetime discontinuous Galerkin (SDG) finite element method. An adaptive meshing procedure generates %When implemented on suitable spacetime grids that satisfy a special causality constraint to enable an efficient patch-by-patch, advancing-front solution scheme with O(N) computational complexity. Per-element balance properties, local adaptive operations, and the use of Riemann fluxes provide to the SDG method the extreme accuracy and efficiency required to solve multiscale fracture problems. A dimensional analysis of linear elastodynamics, with extensions to fracture models based on cohesive traction--separation laws, supports the formulation. The problem is formulated and analyzed using differential forms and the exterior calculus in spacetime. The analysis demonstrates that the velocity scalings implied by the spatial and temporal coordinate scalings and by the scalings of the material properties must be identical to obtain a self-similar scaling of an elastodynamic process. The use of differential forms reveals intrinsic structure and relations between the spacetime mechanics fields which are otherwise obscured by conventional tensorial analysis. For example, only four distinct scalings are required to define a scaled elastodynamic process when we work directly with forms, while eight are required when tensorial analysis is used. In the context of dynamic cohesive fracture, the analysis shows that, among the nondimensional variables, the ratio of the stress-loading scale to the cohesive strength is proportional to the ratio of the radius of the singularity-dominant zone from Linear…
abstract: Dynamic material failure is important in a number of scientific and engineering applications and a variety of numerical methods for its modeling have been proposed. This thesis presents the formulation and implementation of an interfacial-damage, cohesive-fracture model, including contact and friction effects, for dynamic failure of brittle materials. The model is implemented within a spacetime discontinuous Galerkin (SDG) finite element method. An adaptive meshing procedure generates %When implemented on suitable spacetime grids that satisfy a special causality constraint to enable an efficient patch-by-patch, advancing-front solution scheme with O(N) computational complexity. Per-element balance properties, local adaptive operations, and the use of Riemann fluxes provide to the SDG method the extreme accuracy and efficiency required to solve multiscale fracture problems. A dimensional analysis of linear elastodynamics, with extensions to fracture models based on cohesive traction--separation laws, supports the formulation. The problem is formulated and analyzed using differential forms and the exterior calculus in spacetime. The analysis demonstrates that the velocity scalings implied by the spatial and temporal coordinate scalings and by the scalings of the material properties must be identical to obtain a self-similar scaling of an elastodynamic process. The use of differential forms reveals intrinsic structure and relations between the spacetime mechanics fields which are otherwise obscured by conventional tensorial analysis. For example, only four distinct scalings are required to define a scaled elastodynamic process when we work directly with forms, while eight are required when tensorial analysis is used. In the context of dynamic cohesive fracture, the analysis shows that, among the nondimensional variables, the ratio of the stress-loading scale to the cohesive strength is proportional to the ratio of the radius of the singularity-dominant zone from Linear…
author: Abedi, Reza
language: en
keywords: fracture, finite element methods, spacetime discontinuous, cohesive models, interfacial damage, Riemann solution, dimensional analysis, Linear Elastodynamic Fracture Mechanics (LEFM)
date published: 2010-05-14T20:43:09Z
date modified: 2026-07-22T22:25:08Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/15502