Plastic deformation of solids is a paradigmatic problem for multiscale materials modeling.
Relevant processes range from the atomistic scale where the detailed atomic arrangement of a material is of crucial importance for its deformation properties, up to macroscopic scales where deformation instabilities manifest themselves in the form of various macroscopic plastic localisation and oscillation phenomena. However, the crucial question of how the properties of defects and microstructure of the material link to the macroscopic constitutive equations of continuum mechanics is still open. Homogenisation, where the transition from discrete defects (dislocations in the case of crystal plasticity) to an appropriate “smooth” continuum description is assumed to be reached by simple averaging of the dynamics of individual defects, has not been accomplished.
The use of AI methods has recently exploded in two relevant fields for the proposed workshop: materials science and statistical physics. Computational materials science allows – compared to most experiments – to pose well-defined problems for AI applications in the presence of large enough datasets for the typical AI paradigm of teaching algorithms with sufficient data. Much of this effort is on the atomistic level, both for short-cutting heavy calculations via learning faster potentials and for the sake of classifying and predicting novel compounds. Likewise, the classification problem is close to one of the key questions of both equilibrium and non-equilibrium statistical physics: can we work from the data and establish from that the whole phase diagram of a system. This can be tried in various contexts from models (classical and quantum) and in and out of equilibrium systems like for instance for active matter. The progress in this direction itself would seem to encourage us to try seriously to understand plasticity by the toolbox of AI.
Experiments show that plastic deformation occurs in a spatially heterogeneous and temporally intermittent fashion on scales well above that of the defects/dislocations [Zaiser(2006)]. Such observations have been made both via recording the intermittent and bursty acoustic emission signal from macroscopic crystals [Miguel(2001a), Weiss(2003), Richeton(2005)], as well as through direct measurements of the fluctuating stress-strain curves in micron-scale samples or computationally [Uchic(2005), Dimiduk(2006), Csikor(2007)]]. Now, the first progress has been made in utilizing AI to classify and comprehend the complexity of plastic deformation [Papanikolau(2018), Salmenjoki(2018), Papanikolau(2019)]. The main advance here is that dislocation plasticity is full of memory effects from the history of the sample, whether created by loading or sample (metallurgical) preparation. This allows to find for AI descriptors of samples and their behavior and presents on the other hand interesting directions for exploration.
In amorphous systems, avalanches of events coarse-grained from STZ dynamics are the hall-mark of complexity and often lead as in metallic glasses to the formation of a shear-band. The understanding of this localization behavior is crucial since it eventually controls the strength of these materials. Still, little understanding is currently available to relate the details of an amorphous structure with its mechanical behavior. Here AI offers a promising route toward a local dynamically informed characterization of the structure going beyond the classical spatial correlation tools used to describe amorphous ordering [Schoenholz(2017)].
From a theoretical perspective, the intermittent fluctuations in the deformation process have often been linked to an underlying non-equilibrium yielding phase transition, separating “quiescent” and “active” phases of the system, with the applied stress as the control parameter. While some studies have suggested that this transition would be closely related to the mean field limit of non-equilibrium depinning phase transitions (as encountered e.g. in the context of driven elastic interfaces in random media), recent results indicate that this is not true in general [Ispanovity(2014)]. In the case of amorphous solids, the yielding transition also appears to be not fully reducible to the classical depinning transition [Lin(2014)]. Contrary to this paradigm, the first applications of AI have been established in the last two years.