Extensive efforts have been devoted to understanding material failure in the last several decades. A suitable numerical method and specific failure criteria are required for failure simulation. The finite element method (FEM) is the most widely used approach for material mechanical modelling. Since FEM is based on partial differential equations, it is hard to solve problems involving spatial discontinuities, such as fracture and material interface. Due to their intrinsic characteristics of integro-differential governing equations, discontinuous approaches are more suitable for problems involving spatial discontinuities, such as lattice spring method, discrete element method, and peridynamics. A recently proposed lattice particle method is shown to have no restriction of Poisson’s ratio, which is very common in discontinuous methods. In this study, the lattice particle method is adopted to study failure problems. In addition of numerical method, failure criterion is essential for failure simulations. In this study, multiaxial fatigue failure is investigated and then applied to the adopted method. Another critical issue of failure simulation is that the simulation process is time-consuming. To reduce computational cost, the lattice particle method can be partly replaced by neural network model.First, the development of a nonlocal maximum distortion energy criterion in the framework of a Lattice Particle Model (LPM) is presented for modeling of elastoplastic materials. The basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. Then, two multiaxial fatigue models are proposed for random loading and biaxial tension-tension loading, respectively. Following this, fatigue cracking in homogeneous and composite materials is studied using the lattice particle method and the proposed multiaxial fatigue model. Bi-phase material fatigue crack simulation is performed. Next, an integration of an efficient deep learning model and the lattice particle method is presented to predict fracture pattern for arbitrary microstructure and loading conditions. With this integration, computational accuracy and efficiency are both considered. Finally, some conclusion and discussion based on this study are drawn.

Polyurea is a highly versatile material used in coatings and armor systems to protect against extreme conditions such as ballistic impact, cavitation erosion, and blast loading. However, the relationships between microstructurally-dependent deformation mechanisms and the mechanical properties of polyurea are not yet fully understood, especially under extreme conditions. In this work, multi-scale coarse-grained models are developed to probe molecular dynamics across the wide range of time and length scales that these fundamental deformation mechanisms operate. In the first of these models, a high-resolution coarse-grained model of polyurea is developed, where similar to united-atom models, hydrogen atoms are modeled implicitly. This model was trained using a modified iterative Boltzmann inversion method that dramatically reduces the number of iterations required. Coarse-grained simulations using this model demonstrate that multiblock systems evolve to form a more interconnected hard phase, compared to the more interrupted hard phase composed of distinct ribbon-shaped domains found in diblock systems. Next, a reactive coarse-grained model is developed to simulate the influence of the difference in time scales for step-growth polymerization and phase segregation in polyurea. Analysis of the simulated cured polyurea systems reveals that more rapid reaction rates produce a smaller diameter ligaments in the gyroidal hard phase as well as increased covalent bonding connecting the hard domain ligaments as evidenced by a larger fraction of bridging segments and larger mean radius of gyration of the copolymer chains. The effect that these processing-induced structural variations have on the mechanical properties of the polymer was tested by simulating uniaxial compression, which revealed that the higher degree of hard domain connectivity leads to a 20% increase in the flow stress. A hierarchical multiresolution framework is proposed to fully link coarse-grained molecular simulations across a broader range of time scales, in which a family of coarse-grained models are developed. The models are connected using an incremental reverse–mapping scheme allowing for long time scale dynamics simulated at a highly coarsened resolution to be passed all the way to an atomistic representation.

The focus of this dissertation is first on understanding the difficulties involved in constructing reduced order models of structures that exhibit a strong nonlinearity/strongly nonlinear events such as snap-through, buckling (local or global), mode switching, symmetry breaking. Next, based on this understanding, it is desired to modify/extend the current Nonlinear Reduced Order Modeling (NLROM) methodology, basis selection and/or identification methodology, to obtain reliable reduced order models of these structures. Focusing on these goals, the work carried out addressed more specifically the following issues:

i) optimization of the basis to capture at best the response in the smallest number of modes,

ii) improved identification of the reduced order model stiffness coefficients,

iii) detection of strongly nonlinear events using NLROM.

For the first issue, an approach was proposed to rotate a limited number of linear modes to become more dominant in the response of the structure. This step was achieved through a proper orthogonal decomposition of the projection on these linear modes of a series of representative nonlinear displacements. This rotation does not expand the modal space but renders that part of the basis more efficient, the identification of stiffness coefficients more reliable, and the selection of dual modes more compact. In fact, a separate approach was also proposed for an independent optimization of the duals. Regarding the second issue, two tuning approaches of the stiffness coefficients were proposed to improve the identification of a limited set of critical coefficients based on independent response data of the structure. Both approaches led to a significant improvement of the static prediction for the clamped-clamped curved beam model. Extensive validations of the NLROMs based on the above novel approaches was carried out by comparisons with full finite element response data. The third issue, the detection of nonlinear events, was finally addressed by building connections between the eigenvalues of the finite element software (Nastran here) and NLROM tangent stiffness matrices and the occurrence of the ‘events’ which is further extended to the assessment of the accuracy with which the NLROM captures the full finite element behavior after the event has occurred.

Shock loading produces a compressive stress pulse with steep gradients in density, temperature, and pressure that are also often modeled as discontinuities. When a material is subject to these dynamic (shock) loading conditions, fracture and deformation patterns due to spall damage can arise. Spallation is a dynamic material failure that is caused by the nucleation, growth, and coalescence of voids, with possible ejection of the surface of the material. Intrinsic defects, such as grain boundaries are the preferred initiation sites of spall damage in high purity materials. The focus of this research is to study the phenomena that cause void nucleation and growth at a particular grain boundary (GB), chosen to maximize spall damage localization.

Bicrystal samples were shock loaded using flyer-plates via light gas gun and direct laser ablation. Stress, pulse duration, and crystal orientation along the shock direction were varied for a fixed boundary misorientation to determine thresholds for void nucleation and coalescence as functions of these parameters. Pressures for gas gun experiments ranged from 2 to 5 GPa, while pressures for laser ablation experiments varied from 17 to 25 GPa. Samples were soft recovered to perform damage characterization using electron backscattering diffraction (EBSD) and Scanning Electron Microscopy (SEM). Results showed a 14% difference in the thresholds for void nucleation and coalescence between samples with different orientations along the shock direction, which were affected by pulse duration and stress level. Fractography on boundaries with strong damage localization showed many small voids, indicating they experience rapid nucleation, causing early coalescence. Composition analysis was also performed to determine the effect of impurities on damage evolution. Results showed that higher levels of impurities led to more damage. ABAQUS/Explicit models were developed to simulate flyer-plate impact and void growth with the same crystal orientations and experimental conditions. Results are able to match the damage seen in each grain of the target experimentally. The Taylor Factor mismatch at the boundary can also be observed in the model with the higher Taylor Factor grain exhibiting more damage.

This paper discusses the design of experimental setup and procedures to characterize polymethyl methylate (PMMA) at its glass transition temperature by studying its strain fields, process zone, and crack speed under different loading conditions. These loading conditions are different steady-state temperatures and initial crack lengths. Steady-state temperature testing uses a temperature control loop. Crack speed / resistivity testing is set up using a voltage drop method. From initial steady-state temperature testing, it was confirmed that the behavior of a PMMA sample becomes more ductile at higher temperatures, and that it is plausible for a crack process zone to be measured using DIC as temperature increases. From finite element simulations, it was validated that the crack speed is not constant relative to an initial crack length.

Niobium is the primary material for fabricating superconducting radio-frequency (SRF) cavities. However, presence of impurities and defects degrade the superconducting behavior of niobium twofold, first by nucleating non-superconducting phases and second by increasing the residual surface resistance of cavities. In particular, niobium absorbs hydrogen during cavity fabrication and promotes precipitation of non-superconducting niobium hydride phases. Additionally, magnetic flux trapping at defects leads to a normal conducting (non-superconducting) core which increases surface resistance and negatively affects niobium performance for superconducting applications. However, undelaying mechanisms related to hydride formation and dissolution along with defect interaction with magnetic fields is still unclear. Therefore, this dissertation aims to investigate the role of defects and impurities on functional properties of niobium for SRF cavities using first-principles methods.

Here, density functional theory calculations revealed that nitrogen addition suppressed hydrogen absorption interstitially and at grain boundaries, and it also decreased the energetic stability of niobium hydride precipitates present in niobium. Further, hydrogen segregation at the screw dislocation was observed to transform the dislocation core structure and increase the barrier for screw dislocation motion. Valence charge transfer calculations displayed a strong tendency of nitrogen to accumulate charge around itself, thereby decreasing the strength of covalent bonds between niobium and hydrogen leading to a very unstable state for interstitial hydrogen and hydrides. Thus, presence of nitrogen during processing plays a critical role in controlling hydride precipitation and subsequent SRF properties.

First-principles methods were further implemented to gain a theoretical perspective about the experimental observations that lattice defects are effective at trapping magnetic flux in high-purity superconducting niobium. Full-potential linear augmented plane-wave methods were used to analyze the effects of magnetic field on the superconducting state surrounding these defects. A considerable amount of trapped flux was obtained at the dislocation core and grain boundaries which can be attributed to significantly different electronic structure of defects as compared to bulk niobium. Electron redistribution at defects enhances non-paramagnetic effects that perturb superconductivity, resulting in local conditions suitable for flux trapping. Therefore, controlling accumulation or depletion of charge at the defects could mitigate these tendencies and aid in improving superconductive behavior of niobium.

Droplet-structure interactions play a pivotal role in many engineering applications as droplet-based solutions are evolving. This work explores the physical understanding of these interactions through systematic research leading to improvements in thermal management via dropwise condensation (DWC), and breathable protective wearables against chemical aerosols for better thermoregulation.

In DWC, the heat transfer rate can be further increased by increasing the nucleation and by optimally ‘refreshing’ the surface via droplet shedding. Softening of surfaces favor the former while having an adverse effect on the latter. This optimization problem is addressed by investigating how mechanical properties of a substrate impact relevant droplet-surface interactions and DWC heat transfer rate. The results obtained by combining droplet induced surface deformation with finite element model show that softening of the substrates below a shear modulus of 500 kPa results in a significant reduction in the condensation heat transfer rate.

On the other hand, interactions between droplet and polymer leading to polymer swelling can be used to develop breathable wearables for use in chemically harsh environments. Chemical aerosols are hazardous and conventional protective measures include impermeable barriers which limit the thermoregulation. To solve this, a solution is proposed consisting of a superabsorbent polymer developed to selectively absorb these chemicals and closing the pores in the fabric. Starting from understanding and modeling the droplet induced swelling in elastomers, the extent and topological characteristic of swelling is shown to depend on the relative comparison of the polymer and aerosol geometries. Then, this modeling is extended to a customized polymer, through a simplified characterization paradigm. In that, a new method is proposed to measure the swelling parameters of the polymer-solvent pair and develop a validated model for swelling. Through this study, it is shown that for this polymer, the concentration-dependent diffusion coefficient can be measured through gravimetry and Poroelastic Relaxation Indentation, simplifying the characterization effort. Finally, this model is used to design composite fabric. Specifically, using model results, the SAP geometry, base fabric design, method of composition is optimized, and the effectiveness of the composite fabric highlighted in moderate-to-high concentrations over short durations.

With the advancements in technology, it is now possible to synthesize new materials with specific microstructures, and enhanced mechanical and physical properties. One of the new class of materials are nanoscale metallic multilayers, often referred to as nanolaminates. Nanolaminates are composed of alternating, nanometer-thick layers of multiple materials (typically metals or ceramics), and exhibit very high strength, wear resistance and radiation tolerance. This thesis is focused on the fabrication and mechanical characterization of nanolaminates composed of Copper and Cobalt, two metals which are nearly immiscible across the entire composition range. The synthesis of these Cu-Co nanolaminates is performed using sputtering, a well-known and technologically relevant physical vapor deposition process. X-ray diffraction is used to characterize the microstructure of the nanolaminates. Cu-Co nanolaminates with different layer thicknesses are tested using microelectromechanical systems (MEMS) based tensile testing devices fabricated using photolithography and etching processes. The stress-strain behavior of nanolaminates with varying layer thicknesses are analysed and correlated to their microstructure.

One of the fundamental aspects of cellular material design is cell shape selection. Of particular interest is how this selection can be made in the context of a realistic three-dimensional structure. Towards this goal, this work studied the stiffness response of periodic and stochastic lattice structures for the loading conditions of bending, torsion and tension/compression using commercially available lattice design optimization software. The goal of this computational study was to examine the feasibility of developing a ranking order based on minimum compliance or maximum stiffness for enabling cell selection. A study of stochastic shapes with different seeds was also performed. Experimental compression testing was also performed to validate a sample space of the simulations. The findings of this study suggest that under certain circumstances, stochastic shapes have the potential to generate the highest stiffness-to-weight ratio in the test environments considered.

Owing to the surge in development of endovascular devices such as coils and flow diverter stents, doctors are inclined to approach surgical cases non-invasively more often than before. Treating brain aneurysms as a bulging of a weakened area of a blood vessel is no exception. Therefore, promoting techniques that can help surgeons have a better idea of treatment outcomes are of invaluable importance.

In order to investigate the effects of these devices on intra-aneurysmal hemodynamics, the conventional computational fluid dynamics (CFD) approach uses the explicit geometry of the device within an aneurysm and discretizes the fluid domain to solve the Navier-Stokes equations. However, since the devices are made of small struts, the number of mesh elements in the boundary layer region would be considerable. This cumbersome task led to the implementation of the porous medium assumption. In this approach, the explicit geometry of the device is eliminated, and relevant porous medium assumptions are applied. Unfortunately, as it will be shown in this research, some of the porous medium approaches used in the literature are over-simplified. For example, considering the porous domain to be homogeneous is one major drawback which leads to significant errors in capturing the intra-aneurysmal flow features. Specifically, since the devices must comply with the complex geometry of an aneurysm, the homogeneity assumption is not valid.

In this research, a novel heterogeneous porous medium approach is introduced. This results in a substantial reduction in the total number of mesh elements required to discretize the flow domain while not sacrificing the accuracy of the method by over-simplifying the utilized assumptions.