Fracture in viscoelastic elastomers: A complete phase-field theory

After months of cloistering myself in the lab to work on a new phase-field theory of fracture in viscoelastic elastomers, I’m happy that the paper is finally published and can be accessed here.

Besides my personal attachment to this paper, coming from the fact that it forms the backbone of my Ph.D. thesis and reflects many weekends of work (on top of a regular work schedule), I believe the theory contains many new ideas that will take time to be fully appreciated.

What truly separates this theory from earlier efforts or from the common, incremental extension (I personally do not like this word in this context, but could not come up with a better alternative) of an existing model to “handle” more complex behavior is that we tried to rethink all the existing and proven to be true assumptions of theoretical approaches. For instance, if we have viscous dissipation, do the same type of energy competition or strength surface dependency on loading paths in the elastic brittle fracture theory still apply? If so, what experimental evidence supports this, and if not, what alternatives are there?

Once the theory is in place, the real computational battles begin. Solving a coupled system of two PDEs plus an ODE is not trivial; each challenge has to be addressed on its own before you can form a robust numerical scheme capable of accurately producing solutions. Fortunately, the result turned out to be more robust than I initially expected. Nevertheless, I believe the problem is sufficiently deep that many follow-up studies on the computational side will come, such as exploring alternative approaches to reduce runtime or further strengthen the algorithm under complex loading paths.

Of course, this work is not merely a result of months of my work. It is coming out of my advisor’s years of boundless curiosity and his remarkable intellectual engagement with the problem, plus the computational groundwork initially started by my colleagues. I’m genuinely grateful I happened to be here when the pieces came together.