Date of Award
Master of Science in Engineering (MSE)
Mechanical and Aerospace Engineering
Q. H. Zuo
Perturbation (Mathematics), Boundary valve problems., Strains and stresses., Plasticity.
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.
Kunin, Abraham B., "Stability and well-posedness of a rate-dependent damage model for brittle materials" (2013). Theses. 45.