Speaker: Gilles Francfort, Ph.D., Research Scientist
Topic: The role of stability in macroscopic solids with defects
This is meant to be a short narration of the efforts of the last 30 years to insert a modicum of reason in the erratic modeling and analysis of the macroscopic behavior of solids in the presence of defects.
Starting with a simplistic one dimensional setting I will introduce the overly vague notion of damage, show how the resulting models are unsatisfactory and force the introduction of thermodynamically dubious regularizations. However, those have an arguable merit: they generate sharp interface models when correctly calibrated. The resulting models may be viewed as a rethinking of the theory of brittle fracture. Because they are amenable to numerical implementation, they actually offer quantitative comparison tools for experimental data, as illustrated on an example.
Finally, time permitting, I will show that classical macroscopic plasticity falls squarely within that kind of modeling. There, the resulting evolutions are well behaved although many issues — such as uniqueness — have yet to be adjudicated.
In all described models, the microscopic underpinnings are complex. They range from ill-defined cohesive inter-atomic forces to the motion and pinning of billions of dislocations. Upscaling those to the macroscopic level is a task happily entrusted to you, the future generations.