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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.

This thesis presents a study performed to validate the State-based Peridynamic Lattice Model (SPLM) using results obtained from laboratory experiments. The SPLM is capable of modeling cracking of solids using particle lattices. We use a plane stress, elastic-plastic damage SPLM model for the simulations. The SPLM model is appropriate for computational simulations of cementitious materials as it automatically allows cracks to develop. In this study, the lattices are rotated through different angles and the variations of the cracking patterns are studied. In the laboratory, we performed nine Brazilian split cylinder tests, three anchor pullout/direct tensile tests, and eight compression tests on cylinders of standard size. We also tested four beams as modulus of rupture tests. The results from the laboratory tests and the SPLM simulations were then compared. The comparison indicates that the SPLM produced similar results as the laboratory experiments and the ACI code predictions. These results indicate that SPLM is a reasonable simulation method for these types of specimens.

Porous media theories play an important role in many branches of engineering. Despite significant advances, the existing theories suffer from many limitations and drawbacks when dealing with problems with discontinuities like fractures. The difficulties inherent in these problems arise from the basic incompatibility of spatial discontinuities with the partial differential equations that are used in the classical porous media theories. Peridynamics, a relatively new nonlocal formulation of continuum mechanics based on integral equations, provides a path forward in modeling spatial discontinuities in the field of solid mechanics. In this thesis, the nonlocal formulation of peridynamics is successfully combined with finite deformation poroelasticity. First, a thorough derivation of finite deformation poroelasticity based on extended Hamilton's principle is conducted. Then we include the integral formulation of peridynamic theory when deriving the nonlocal momentum balance equations for poroelasticity once again using extended Hamilton's principle. To complete our nonlocal poroelasticity theory, we also develop a new class of peridynamic constitutive models. Finally, the correspondence of our peridynamic poroelasticity theory to the classical finite deformation poroelasticity theory is shown by demonstrating that our peridynamic equations can be reduced to the classical momentum balance equations for poroelasticity if smooth and homogeneous deformation is assumed.