Prof. Haim Waisman
Civil Engineering and Engineering Mechanics
Columbia University

Advances in Phase Field Fracture Methods and Topology Optimization of Structures

ABSTRACT: The phase field method (PFM) has been widely used to model fracture of solids due to its ability to handle crack initiation and propagation without the need for explicitly tracking fracture surfaces. I will start with a brief introduction and a few recent developments demonstrating fracture of bones, 3D printed hyperelastic polymers, and metals. While the PFM is a promising technique for fracture, it does require solution of coupled equations and fine meshes in the crack path, which is computationally expensive. To this end, I will discuss two new numerical approaches to expedite the PFM when solving fracture problems: (1) adaptive mesh refinement and (2) a new concept in domain decomposition preconditioning. The second part of the talk will be devoted to optimal design of structures for enhanced fracture resistance and buckling response. In contrast to the majority of the current relevant literature which favors stress constraints with linear elastic physics, we explicitly simulate brittle fracture using the PFM during the topology optimization procedure. In particular, we propose an efficient formulation for incorporating local ductile failure constraints and buckling resistance into elastoplastic structural design in the context of extreme loading. The optimized structures are then subjected to a post-optimization verification step which show significant gains in structural strength and toughness.

BIOGRAPHY: Haim Waisman is a Professor and Department Chair of Civil Engineering and Engineering Mechanics at Columbia University. His research interests are in computational mechanics, for which he develops advanced finite element methods for modeling fracture and design-optimization of structures under extreme conditions. Dr. Waisman obtained his Bachelor’s and Master’s degrees in Aerospace Engineering from the Technion-Israel Institute of Technology and a Doctorate in Civil Engineering from Rensselaer Polytechnic Institute (RPI) in 2005. He was a post-doctoral fellow at the Scientific Computing Research Center (SCOREC) at RPI and at the Mechanical Engineering department at Northwestern University, before joining Columbia University in 2008. Dr. Waisman is the recipient of the 2012 Department of Energy Early Career Award, the 2014 Leonardo Da Vinci Award from the Engineering Mechanics Institute (EMI) of American Society of Civil Engineers (ASCE), and several best paper awards. In 2022 he was elected fellow of the ASCE EMI institute.  He is currently serving as an Associate Editor of the ASCE Journal of Engineering Mechanics and on a few editorial boards. He is also the past chair of the ASCE-EMI Computational Mechanics technical committee.