Fracture in soft and biological solids
Soft and biological materials exhibit a hierarchical structure and highly nonlinear (“squishy” and “flowy”) behavior with distinct fracture behavior. Understanding this fracture behavior is essential to a bunch of emerging technologies such as soft robotics, wearable sensors, and tissue-like synthetic materials, as well as to studying critical phenomena like traumatic brain injuries. It is also likely to provide a unified understanding of fracture in all materials.
A distinct fracture phenomenon that happens in soft, incompressible solids is the phenomenon of cavitation, marked by sudden formation of irreversibly growing cavities. It is seen in adhesives and thought to be the key mechanism behind adhesive failure. It also happens in brain tissue during traumatic brain injury. This phenomenon has been poorly understood for a long time, and there were essentially no theoretical explanation for majority of cavitation experiments. In a series of papers over the last 9 years, we have managed to successfully explain cavitation through the development of a new fracture theory.
We are working on extending this understanding to penetration fracture behavior of soft solids, failure of adhesives, breaking of blood clots, and the behavior of brain tissue under impact loading.
Fracture and healing of elastomers: A phase-transition theory and numerical implementation
Main contribution: Phase-field models of fracture provide a computationally tractable way to simulate fracture nucleation and propagation in soft materials. However, we show that the classical phase-field models, constructed in a variational form, are incapable of capturing cavitation, and a new, more generalized approach is needed.
The poker-chip experiments of Gent and Lindley (1959) explained
Main contribution: Gent and Lindley’s landmark experiments were the beginning of investigations in cavitation, but they had remained unexplained for 60 years. In this work, we quantitatively explain every single observation from the experiments with the newly developed theory
The poker-chip experiments of synthetic elastomers explained
Main contribution: A recent set of experiments from Guo and Ravi-Chandar provided an intriguing new observation regarding nucleation of first cavity in synthetic elastomers. We explain this and the other observations from the experiments in this new work. The explanation for the new observation, in particular, provided strong support for our theoretical approach.
Unified theory of fracture
The work in understanding fracture in soft solids provided unexpected motivation to revisit the nucleation of fracture in brittle materials at large, not just elastomers, and led to a general model for nucleation and propagation of brittle fracture in all materials, soft and hard. This model has proven remarkably successful in unifying the study of fracture in vastly different materials. We are working on extending the unified framework to also include ductile and poroelastic materials.
Revisiting nucleation in the phase-field approach to brittle fracture
Main contribution: This work, for the first time, introduces clearly the ingredients necessary for modeling nucleation and propagation for arbitrary loading and geometry in brittle materials. These ingredients are then cast in a phase-field framework.
The strength of the Brazilian fracture test
Main contribution: Brazilian fracture test, used to measure tensile strength, has proven to be an exceptionally hard model for fracture models historically. Due to the lack of theoretical understanding, there has been a lot of confusion about its applicability for more than 50 years. We explain in this paper the source of the confusion, and analyze the problem with the new phase-field approach.
Emergence of tension-compression asymmetry in the complete phase-field approach to brittle fracture
Main contribution: Energy-driven phase-field models result in compression cracks. We show that our complete approach which bring the information about material strength into the model do not suffer from this limitation.
Growth and remodeling in biological tissues
The mechanics of how biological tissues respond to mechanical forces and adapt, grow and evolve is not well understood. The goal is to constitutively define these evolutions in a rational mechanics framework. Along with colleague Prof. Arash Yavari, we have proposed a new variational approach to explain the remodeling of collagen fibers in soft tissues. Currently, we are working on extending the understanding to arterial growth with the same variational framework utilizing differential geometry.
Nonlinear mechanics of remodeling
Main contribution: Previous work empirically defined the evolution of remodeling variable based on stress/strain. However, the empirical laws adopted would not generalize indicating that they are fundamentally not representative of the underlying physics. Our work is motivated by describing the equilibrium of the remodeling process through quantifying the various energy storage/dissipation mechanisms.
Homogenization of fracture
We are working on homogenization methods that bridge micro- to macro-scale phenomena in hierarchical materials, including elastomeric composites, ceramic composites, epoxy composites among other heterogeneous materials.