Identifier

etd-11172014-003502

Degree

Master of Science (MS)

Department

Mathematics

Document Type

Thesis

Abstract

Construction of appropriate models through mathematical analysis for materials in order to find their main properties and ingredients and enhance the numerical simulations to predict their behavior under specific conditions is in interest even in mathematics departments rather than material science and engineering branches. Among these models, gradient damage models have reached to the specific stage because of their ability to bring the effects of micro cracks propagation into conventional continuum mechanics formulation and approximate brittle fracture as one of the most phenomena in the area of material behavior simulation. This thesis includes the application and extension of a previously proposed gradient damage model through the mathematical analysis on a specific 2D problem i.e. axisymmetric domain with internal pressure, which is in interest for designing reservoirs and investigating crack propagation around oil wells. To accomplish this task, this thesis is organized as following. In the first chapter, general framework and fundamentals of damage models is discussed in details including standard models and incorporation of gradient term into standard models through variational approach. Main properties of gradient damage models are derived and all details of derivations including proofs of some propositions are added to show the flow of the presentation. In the second chapter, presented formulation is applied on a desired problem in details to show the application of the model in 2D. Discussion on main results and some recommendations are given in the last chapter.

Date

2014

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Bourdin, Blaise

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