EAGER: Integrating Fracture Nucleation and Propagation into Optimization: Towards Materials with Optimal Fracture Properties

To date, the vast majority of topology optimization advancements have restricted attention to problems where the underlying materials are assumed to deform elastically without ever fracturing. However, it is well established that even a simple variation in microstructure can have a profound influence on the effective fracture properties of materials.

Hence, optimization of microstructural topology has the potential to revolutionize the discovery of materials with unprecedented fracture properties. This EArly-concept Grant for Exploratory Research (EAGER) award supports fundamental research to put forth a theoretical and computational framework that identifies linear elastic brittle materials whose microstructures have optimized fracture nucleation and propagation behaviors.

This research will explore the topological space to create microstructures in linear elastic brittle materials that lead to improved fracture behaviors and enhanced energy dissipation. The insights generated will contribute to the progress of science by paving the way required to formulate a theory that systematically discovers novel geometries and mechanisms toward enhanced toughness.

This research will allow advancement in other fields, such as civil and aerospace structures and medical implants, ultimately contributing towards a broad range of applications for national health and prosperity. The project will also enrich the multidisciplinary course curriculum and provide opportunities to educate and train graduate students in theoretical optimization, advanced modeling, and experimental techniques.

The objective of the research is to create a transformative and mathematically rigorous approach to optimize microstructures with maximized fracture properties. A formulation of topology optimization that integrates fracture nucleation and propagation into the mechanical response of materials, which can both deform elastically and fracture, will be derived and implemented numerically.

A specific subset of materials, linear elastic brittle materials with two phases, will be addressed in this project. The derived formulation will be employed to identify optimal microstructural topologies in linear elastic brittle porous composite materials with improved fracture properties. These optimized topologies will be fabricated and systematically validated by experiments.

This work will generate new insights about the optimal geometries and dominating mechanisms that enhance fracture performance. The project will also build the foundation of a new ability to manipulate cracks and opens up possibilities for a wide range of applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.