Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

A mathematical model for damage propagation based on nonlocal potentials is developed within the framework of peridynamics. This model is applied to simulate damage evolution in cyclically loaded structures. By neglecting inertial effects, a well-posed quasistatic formulation for cyclic loading is obtained.\\ The resulting equation is expressed as a nonlocal and nonlinear integral operator that couples damage evolution to the deformation field.\\ This coupling occurs through the product of a damage factor and the derivative of a force potential. The damage factor ranges between zero and one, where one represents undamaged material and zero indicates complete damage.\\ It serves to reduce the internal force contribution as damage accumulates, making it well-suited for modeling fatigue behavior.

The existence of a unique solution to the quasistatic evolution along load paths is established under the assumption that the Fréchet derivative of the integral operator is invertible. Although invertibility is ensured when the displacement lies within the strength domain, we show that this requirement can be relaxed by identifying more general sufficient conditions. Building on this, an iterative method for bond breaking is developed using the Newton–Kantorovich theorem.

Date

7-16-2025

Committee Chair

Lipton , Robert

DOI

10.31390/gradschool_dissertations.6869

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