Date of Award

2013

Document Type

Thesis

Degree Name

Master of Science in Engineering (MSE)

Department

Mechanical and Aerospace Engineering

Committee Chair

Q. H. Zuo

Committee Member

Babak Shotorban

Committee Member

Gang Wang

Subject(s)

Perturbation (Mathematics), Boundary valve problems., Strains and stresses., Plasticity.

Abstract

This thesis presents an analysis of the stability and well-posedness of the Dominant Crack Algorithm (DCA) model for damage in brittle materials. The DCA model's prediction for the behavior of a brittle material under uniaxial tension forms the basis of the analysis. It is shown through the perturbation analysis of a one-dimensional steady-state solution that the DCA model reflects the underlying instability of the material but is mathematically well-posed. Thus perturbations to the steady-state solution remain bounded in finite time. This result has an important implication in the numerical solution of the initial boundary-value problems implicit in the DCA model. Namely, the error introduced by mesh refinement will not lead to unbounded growth.

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