Stochastic modeling of plastic flow and failure in disordered materials

I wrote my doctoral thesis during my time at the Institute of Materials Simulation in Fürth (Germany) under the supervision of Prof. Michael Zaiser. My thesis builds upon my previous research:

I discuss in length how to understand, from a statistical perspective, the plastic deformation, and failure of disordered materials. I explore different numerical approaches based on stochastic processes to implement the models and describe diverse analytical techniques to help interpret their outcomes. If you are interested, the links above provide a good introductory overview to the topics contained in my thesis, which you can find here.

Would you like to learn more? You can find a comprehensive introduction and an overview of my research here.

Thesis Abstract

The plastic deformation of solids has been historically understood as a smooth and deterministic process. However, experiments on plastic activity at small scales report a widely different picture, where plastic activity at the scale is perceived as a stochastic and highly fluctuating phenomenon occurring in the form of intermittent bursts, known as avalanches. Moreover, similar behavior has been reported for a wide diversity of materials and microstructures such as, e.g., crystals, glasses, rocks, wood, porous materials or even fluids which can deform elastically under an applied . This suggests understanding plastic activity within a unified conceptual framework independent of microstructural details. To this end, we present a stochastic mesoscale elastoplastic model which establishes links between the understanding of plastic deformation at the , based on the concept of the potential energy landscape, and the understanding at the , based on the yield function of continuum plasticity theories. The model coarse-grains microscopic details into representative elements equal to or larger than the characteristic length scale of the elementary flow events characteristic of a particular microstructure. The behavior of the elements is defined according to a simple set of local rules, aimed at retaining only the fundamental characteristics of the elementary events relevant to the description of plastic deformation at the mesoscopic scale. behavior is introduced into the model by considering a statistically distributed local resistance to plastic deformation, aimed at representing at the mesoscopic scale the effects of the underlying disordered microstructure. We study the avalanche statistics, strain localization and related phenomenology on the approach to and near plastic yielding. Using a tensorial description of the fields, we simulate finite-size samples under loading conditions such as bending or indentation. We find that, although the strain localization patterns are highly dependent on loading mode or local flow rule, the statistics of avalanches exhibit a high degree of universality. Afterward, we consider both plastic deformation and failure within a unified framework. To this end, we introduce structural damage and thermal activation of plastic activity. Such generalization of the model allows us to study the interplay between avalanches, structural damage accumulation and strain localization on the approach to mechanical failure. Although the model does not assume any phenomenological statistical law for the description of avalanches, it can reproduce well-established experimental behavior found in materials failure and geosciences. Such predictions are based only on simple physically-grounded rules of local plastic flow and damage accumulation, consequently shedding light on the physical origins of such phenomenological laws. We establish links between the phenomenology observed on the approach to failure and seismic activity, and show how mesoscopic spatio-temporal processes can be linked to quantities, frequently used for reproducing earthquake statistics.

David F. Castellanos

Doctoral dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg (2009)