Session: 16-01-01: Poster Session: NSF-Funded Research (Grad & Undergrad)

Paper Number: 100112

100112 - Integrating Fracture Nucleation and Propagation Into Optimization: Towards Materials With Enhanced Fracture Properties 

Since its first appearance in 1988, topology optimization has been massively employed to generate designs in structural and multi-disciplinary fields. The vast majority of efforts using topology optimization focus on materials or structures that deform elastically without ever fracturing. Accordingly, their applications could be limited. However, the improvement of fracture behaviors of structures and materials is relevant for most engineering fields, and topology optimization holds the potential to discover materials and structures with improved fracture properties.

In this work, by integrating both fracture nucleation and propagation, we create a fracture-mechanics-based topology optimization framework, which systematically explores the topological space to discover mechanisms in brittle materials that lead to improved fracture behaviors. Specifically, we first introduce the phase-field model integrating both fracture nucleation and propagation. Next, we propose the physics-based interpolation relationships of material properties used in the aforementioned fracture model. Thereon, a topology optimization formulation is presented by leveraging the phase-field model and interpolation relationships. Moreover, several numerical examples are examined to show the effectiveness of the proposed framework in improving structural fracture behaviors and underlying mechanisms. These examples are tested accounting for different types of crack nucleation. The results demonstrate that, compared to traditional stiffness or fracture designs, the crack displacement and effective toughness (herein defined as required energy to make structures completely fail) of proposed fracture designs can be significantly improved while maintaining sufficient initial stiffness.

Crucial to the objective of this work is the fact that the fracture formulation is given in terms of partial differential equations (PDEs). This makes it mathematically amenable for use in topology optimization theories. The key challenges include (1) correct coupling of topology optimization and fracture mechanics to physically account for crack nucleation at any domain location; (2) accurate capturing of the complex temporal evolution and interactions among nucleating and propagating cracks during the topological space exploration; (3) construction of an effective parameterization of the topological space and heterogeneous elastic and fracture properties of microstructures for topology optimization so that the solutions are less susceptible to ill-posed local optima; and (4) stabilization of the optimization process despite the high sensitivity of fracture properties to the structural topology variation (due to the local nature of fracture). By solving these four challenges, we show that the proposed topology optimization framework is promising for designing structures and materials with improved crack displacement and effective toughness, and thus generating robust and sustainable designs for engineering fields.

Presenting Author: Yingqi Jia University of Illinois Urbana-Champaign

Presenting Author Biography: Yingqi Jia is a Ph.D. student working in the Department of Civil and Environmental Engineering at the University of Illinois Urbana-Champaign. His research interest mainly focuses on fracture-mechanics-based topology optimization for improving structural and material fracture properties.

Authors:

Yingqi Jia University of Illinois Urbana-Champaign
Oscar Lopez-Pamies University of Illinois Urbana-Champaign
Xiaojia Shelly Zhang University of Illinois Urbana-Champaign