Mathematical Sciences: Crack Propagation in Linear and Nonlinear Viscoelastic Material

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The investigators will continue their investigation in crack propagation phenomena in solids. They will construct analytical solutions to canonical initial/boundary value problems relevant to the modeling of dynamically accelerating cracks in viscoelastic composites. Various crack-tip failure zone constitutive models, both linear and nonlinear, will be investigated. For nonlinear models, numerical simulations will be performed of the dynamically growing cracks. The transition from quasi-static to dynamic crack propagation will be investigated. Cracks from a common mode of failure in structural members of most engineering structures. The analytical study and numerical simulations of this project will help the engineers to better understand such failure mechanisms.