abstract: Fracture phenomena have been extensively studied in the last several decades. Continuum mechanics-based approaches, such as finite element methods and extended finite element methods, are widely used for fracture simulation. One well-known issue of these approaches is the stress singularity resulted from the spatial discontinuity at the crack tip/front. The requirement of guiding criteria for various cracking behaviors, such as initiation, propagation, and branching, also poses some challenges. Comparing to the continuum based formulation, the discrete approaches, such as lattice spring method, discrete element method, and peridynamics, have certain advantages when modeling various fracture problems due to their intrinsic characteristics in modeling discontinuities. A novel, alternative, and systematic framework based on a nonlocal lattice particle model is proposed in this study. The uniqueness of the proposed model is the inclusion of both pair-wise local and multi-body nonlocal potentials in the formulation. First, the basic ideas of the proposed framework for 2D isotropic solid are presented. Derivations for triangular and square lattice structure are discussed in detail. Both mechanical deformation and fracture process are simulated and model verification and validation are performed with existing analytical solutions and experimental observations. Following this, the extension to general 3D isotropic solids based on the proposed local and nonlocal potentials is given. Three cubic lattice structures are discussed in detail. Failure predictions using the 3D simulation are compared with experimental testing results and very good agreement is observed. Next, a lattice rotation scheme is proposed to account for the material orientation in modeling anisotropic solids. The consistency and difference compared to the classical material tangent stiffness transformation method are discussed in detail. The implicit and explicit solution methods for the proposed lattice particle model are also discussed. Finally, some conclusions and discussions based on the current study are drawn at the end. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2015

Microcantilever sensor has gained much popularity because of its high sensitivity and selectivity. It consists of a micro-sized cantilever that is usually coated on one side with chemical/biological probe agents to generate strong attraction to target molecules. The interactions between the probe and target molecules induce surface stress that bends the microcantilever. This current work applied the molecular dynamics simulation to study the microcantilever system. Lennard-Jones potentials were used to model the target-target and target-probe interactions and bond bending potentials to model the solid cantilever beam. In addition, this work studied the effect of probe locations on the microcantilever deflection. The simulation results suggest that both target-target and target-probe interactions as well as the probe locations affect the arrangement of the bonds; in term of the bonding number, the area containing the bonded molecules, and the distances between them. All these factors influence the microcantilever deflection.

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