Executive Summary : | The engineering problem of modeling damage and fracture in structural components is a long-standing issue, with applications in design and health monitoring. The continuum damage mechanics (CDM) theory is preferred for its balance between efficiency and fidelity. However, existing definitions for nonlocal CDM suffer from inconsistencies, including stability issues. This research project proposes an integrated theoretical, numerical, and experimental plan to develop a fractional-calculus framework for Continuum Damage Mechanics (f-CDM). The framework will leverage the differ-integral definition of fractional-order derivatives for developing a nonlocal constitutive theory of CDM. In-house numerical methods and strategies will be developed, and computational studies will be undertaken to capture progressive damage in standard test cases. The framework will be validated by experiments on PMMA test samples subject to axial and bending loads. Artificial Neural Networks (ANN) will be proposed to provide form-free functions for the damage evolution law, critical to progressive damage response. This will alleviate errors and facilitate modelling complex damage mechanisms within heterogeneous structures like composites. The project's significance lies in laying the foundation for a multiscale suite of constitutive models based on fractional calculus, analyzing progressive damage and fracture in quasi-brittle materials, and providing fundamental insight into the interplay of nonlocal interactions and progressive damage. |