Despite the exceptional mechanical properties of individual carbon nanotubes (CNTs), the effective properties of CNT-reinforced composites remain below expectations. The composite's microstructure has been identified as a key factor in explaining this discrepancy. In this contribution, a method for generating representative volume elements of aligned CNT sheets is presented. The model captures material characteristics such as random waviness and entanglement of individual nanotubes. Thus it allows studying microstructural effects on the composite's effective properties. Simulations investigating the strengthening effect of the application of a pre-stretch on the CNTs are carried out and found to be in very good agreement with experimental values. They highlight the importance of the nanotube's waviness and entanglement for the mechanical behavior of the composite. The presented representative volume elements are the first to accurately capture the waviness and entanglement of CNT sheets for realistically high volume fractions.

In this work, we extend the previously developed split kinetic energy (dubbed KEP) method by Mineo and Chao (2012) by modifying the mass parameter to include the negative mass. We first show how to separate the total system into the subsystems with 3 attractive delta potentials by using the KEP method. For repulsive delta potentials, we introduce "negative" mass terms. Two cases are demonstrated using the "negative" mass terms for repulsive delta potential problems in quantum mechanics. Our work shows that the KEP solution scheme can be used to obtain not only the exact energies but also the exact wavefunctions very precisely.

This work employed density functional theory to investigate the structural and ferroelectric properties of the Ruddlesden-Popper (RP) phase of lead titanate, $Pb_2TiO_4$, as well as its phase transitions with epitaxial strain. A wealth of novel structural instabilities, which are absent in the host $PbTiO_3$ material, were identified in the RP phase through phonon soft-mode analysis. Our calculations showed that the ground state of $Pb_2TiO_4$ is antiferroelectric, distinct from the dominant ferroelectric phase in the corresponding host material. In addition, applied epitaxial strain was found to play a key role in the interactions among the instabilities. The induction of a sequence of antiferroelectric and antiferrodistortive (AFD) phase transitions by epitaxial strain was demonstrated, in which the ferroic instability and AFD distortion were cooperative rather than competitive, as is the case in the host $PbTiO_3$. The RP phase in conjunction with strain engineering thus represents a new approach to creating ferroic orders and modifying the interplay among structural instabilities in the same constituent materials, enabling us to tailor the functionality of perovskite oxides for novel device applications.

Shape-memory alloys (SMA) have interesting behaviors and important mechanical properties due to the solid-solid phase transformation. These phenomena are dominated by the evolution of microstructures. In recent years, the microstructures in SMAs have been studied extensively and modeled using molecular dynamics (MD) simulations. However, it remains difficult to identify the crystal variants in the simulation results, which consist of large numbers of atoms. In the present work, a method is developed to identify the austenite phase and the monoclinic martensite crystal variants in MD results. The transformation matrix of each lattice is calculated to determine the corresponding crystal variant. Evolution of the volume fraction of the crystal variants and the microstructure in Ni-Ti SMAs under thermal and mechanical boundary conditions are examined. The method is validated by comparing MD-simulated interface normals with theoretical solutions. In addition, the results show that, in certain cases, the interatomic potential used in the current study leads to inconsistent monoclinic lattices compared with crystallographic theory. Thus, a specific modification is applied and the applicability of the potential is discussed.

The evaluation of torsional effects on multistory buildings remains an open issue, despite considerable research efforts and numerous publications. In this study, a large number of multiple test structures are considered with normally distributed topological attributes, in order to quantify the statistically derived relationships between the torsional criteria and response parameters. The linear regression analysis results, depict that the center of twist and the ratio of torsion (ROT) index proved numerically to be the most reliable criteria for the prediction of the modal rotation and displacements, however the residuals distribution and R-squared derived for the ductility demands prediction, was not constant and low respectively. Thus, the assessment of the torsional parameters' contribution to the nonlinear structural response was investigated using artificial neural networks. Utilizing the connection weights approach, the Center of Strength, Torsional Stiffness and the Base Shear Torque curves were found to exhibit the highest impact numerically, while all the other torsional indices' contribution was investigated and quantified.

As electron donor/acceptor materials for organic photovoltaic cells, small-molecules donors/acceptor are attracting more and more attention. In this work, we investigated the electronic structures, electrochemical properties, and charge carrier transport properties of four recently-synthesized small-molecule donors/acceptor, namely, DPDCPB (A), DPDCTB (B), DTDCPB (A1), and DTDCTB (B1), by a series of ab initio calculations. The calculations look into the electronic structure of singly oxidized and reduced molecules, the first anodic and cathodic potentials, and the electrochemical gaps. Results of our calculations were in accord with those from experiments. Using Marcus theory, we also computed the reorganization energies of hole/electron hoppings, as well as hole/electron transfer integrals of multiple possible molecular dimer configurations. Our calculations indicated that the electron/hole transport properties are very sensitive to the relative separations/orientations between neighboring molecules. Due to high reorganization energies for electron hopping, the hole mobilities in the molecular crystals are at least an order of magnitude higher than the electron mobilities.

The present paper reports an analytical study of delamination fracture in the Mixed Mode Flexure (MMF) functionally graded beam with considering the material non-linearity. The mechanical behavior of MMF beam is modeled by using a non-linear stress-strain relation. It is assumed that the material is functionally graded along the beam height. Fracture behavior is analyzed by the J-integral approach. Non-linear analytical solution is derived of the J-integral for a delamination located arbitrary along the beam height. The J-integral solution derived is verified by analyzing the strain energy release rate with considering the non-linear material behavior. The effects of material gradient, crack location along the beam height and material non-linearity on the fracture are evaluated. It is found that the J-integral value decreases with increasing the upper crack arm thickness. Concerning the influence of material gradient on the non-linear fracture, the analysis reveals that the J-integral value decreases with increasing the ratio of modulus of elasticity in the lower and upper edge of the beam. It is found also that non-linear material behavior leads to increase of the J-integral value. The present study contributes for the understanding of fracture in functionally graded beams that exhibit material non-linearity.