Variational model order reduction for the prediction of plastic events in disordered materials

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Disordered materials, such as glasses and amorphous solids, are ubiquitous in engineering and everyday life. The complex mechanics of disordered solids is governed by elementary inelastic events that happen on the nanoscale and are decoded in the local microscopic picture of the material. Consequently, the essential behavior of disordered materials can only be captured using molecular descriptions, which considerably limits the capability to describe such materials on larger scales. Thus, this project aims to develop a reduced-order model for the mechanical response description of disordered solids. Our objective builds on the idea that only a few response patterns, so-called soft vibrational modes, are activated during elementary inelastic events. Due to the high level of nonlinearity and the unpredictability of such slowly driven dynamics, we will predict the zones susceptible to local events using a new mechanical probing technique, which we will enhance using machine learning algorithms. This way, one can predict these elementary inelastic events before mechanical loading, identifying so-called local variation modes. A reduced order model will mathematically be realized using the Empirical Interpolation method, while the change in the reduced basis obtained by the eigenmodes of the Hessian occurring due to the high nonlinearity of the system will be considered using the perturbation theory and Grassmann extrapolation. The powerful high-fidelity reduced order model will be formulated by extending the reduced order basis by the local variation modes. The method will, firstly, be tested on two-dimensional benchmark molecular models and then on larger three-dimensional disordered materials.