Combining numerical simulation and machine learning - modeling coupled solid and fluid mechanics using mesh free methods

Abstract

The prediction and understanding of physical systems is largely divided into two camps, those based on data, and those based on the numerical models. These two approaches have long been developed independently of each other. This work shows further improvements of the modeling of physical systems and also presents a new way to inject the data from simulations into deep learning architecture to aid in the engineering design process. In this thesis the computational mechanics technique, the Material Point Method (MPM) is extended to model the mixed-failure of damage propagation and plasticity in the aggregate materials commonly found deep underground. To achieve this, the Grady-Kipp damage model and the pressure dependent Drucker-Prager plasticity model are coupled to allow for mixed-mode failure to develop in the material. This is tested against analytical results for brittle materials, as well as a series of experimental results. In addition, the brittle fracture in thin silicon wafers is also modeled to better understand the tolerances in manufacturing loads on these delicate objects. Finally, in a novel approach to combine the results of a numerical simulation and the power of a deep neural network, biomedical device design is studied. Here the simulation of the acoustofluidics of a microchip is performed to generate a large dataset of boundary conditions and solved pressure fields. This dataset is then used to train a neural network so that the inverse relationship between the boundary condition and the pressure field can be obtained. Once this training is complete, the network is used as a design tool for a specified pressure field and the results are fabricated and tested.