Mechanical Behavior of Materials at Multiscale Peridynamic Theory and Learning-based Approaches
Classical continuum mechanics has been widely used in the failure analysis of materials for decades. However, spatial partial derivatives in governing equations of the conventional theory are not valid along the discontinuities. Alternatively, peridynamic (PD) theory, as a nonlocal continuum theory, eliminates this shortcoming by using integro-differential equations which do not contain spatial derivatives. This feature makes PD theory very attractive for problems including discontinuities such as cracks.
In this study we have extended PD formulation to multiscale problems involving friction, wear, and delamination of thin films. We have formulated a nonlocal ordinary state-based peridynamic formulation for plastic deformation based on the idea of mechanical sublayers which is successfully applied in modeling ductile fracture. In addition, we demonstrated how PD can be used as an efficient and accurate analysis tool in designing real-world applications such as body armor systems using bio-inspired structures with the goal of minimizing the effect of the ballistic impact and bullet penetration depth while being lightweight and comfortable to wear. All our obtained results are validated against experimental observations and an excellent agreement has been achieved. Similar to other mesh-free methods, PD is massively parallelizable. We built parallel PD algorithms leveraging shared and distributed memory systems on CPU as well as CUDA architecture on GPU. We provide extensive experiments showing scalability and bottlenecks associated with each parallelization technique.
In the second part of this dissertation, we introduce a new class of learnable forward and inference models, using graph neural networks (GNN) which develops relational behavior between material points. We demonstrate these models are surprisingly accurate to generalize remarkably well to challenging unseen loading conditions. Our framework offers new opportunities for harnessing and exploiting non-local continuum theory and powerful statistical learning frameworks to take a key step toward building accurate, robust, and efficient patterns of reasoning about materials behavior.