Assessment of the local stress state through macroscopic variables

Macroscopic quantities beyond effective elastic tensors are presented that can be used to assess the local state of stress within a composite in the linear elastic regime. These are presented in a general homogenization context. It is shown that the gradient of the effective elastic property can be used to develop a lower bound on the maximum pointwise equivalent stress in the fine-scale limit. Upper bounds are more sensitive and are correlated with the distribution of states of the equivalent stress in the fine-scale limit. The upper bounds are given in terms of the macrostress modulation function. This function gauges the magnitude of the actual stress. For l ≤ p \u3c ∞, upper bounds are found on the limit superior of the sequence of Lp norms of stresses associated with discrete microstructure in the fine-scale limit. Conditions are given for which upper bounds can be found on the limit superior of the sequence of L∞ norms of stresses associated with the discrete microstructure in the fine-scale limit. For microstructure with oscillation on a sufficiently small scale we are able to give pointwise bounds on the actual stress in terms of the macrostress modulation function

Resonance and Double Negative Behavior in Metamaterials

A generic class of metamaterials is introduced and is shown to exhibit frequency dependent double negative effective properties. We develop a rigorous method for calculating the frequency intervals where either double negative or double positive effective properties appear and show how these intervals imply the existence of propagating Bloch waves inside sub-wavelength structures. The branches of the dispersion relation associated with Bloch modes are shown to be explicitly determined by the Dirichlet spectrum of the high dielectric phase and the generalized electrostatic spectra of the complement.Comment: This is the final version of the paper accepted for publication in Archive for Rational Mechanics and Analysis March 4, 201

Simulating grain shape effects and damage in granular media using PeriDEM

We provide a numerical platform for the analysis of particle shape and topology effect on the macroscopic behavior of granular media. We work within a Discrete Element Method (DEM) framework and apply a peridynamic model for deformable particles accounting for deformation and damage of individual particles. To accommodate arbitrary particle shapes including nonconvex ones as well as particle topology, an efficient method is developed to keep intra-particle peridynamic interaction within particle boundaries. Particle contact with the rigid boundary wall is computed analytically to improve accuracy. To speed up simulations with particles of different shapes and sizes the initial configuration is chosen using security disks containing different particle shapes that are placed in a jammed state using an optimization-based method. The effect of particle shape and topology on settling and compaction of the aggregate for deformable particles is analyzed.Comment: Revisio

Nonlocal elastodynamics and fracture

A nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane elastodynamics associated with a running crack.Comment: 32 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1908.0758

Optimization of Resonances in Photonic Crystal Slabs

Variational methods are applied to the design of a two-dimensional lossless photonic crystal slab to optimize resonant scattering phenomena. The method is based on varying properties of the transmission coefficient that are connected to resonant behavior. Numerical studies are based on boundary-integral methods for crystals consisting of multiple scatterers. We present an example in which we modify a photonic crystal consisting of an array of dielectric rods in air so that a weak transmission anomaly is transformed into a sharp resonance

Convergent power series for fields in positive or negative high-contrast periodic media

We obtain convergent power series representations for Bloch waves in periodic highcontrast media. The material coefficient in the inclusions can be positive or negative. The small expansion parameter is the ratio of period cell width to wavelength, and the coefficient functions are solutions of the cell problems arising from formal asymptotic expansion. In the case of positive coefficient, the dispersion relation has an infinite sequence of branches, each represented by a convergent even power series whose leading term is a branch of the dispersion relation for the homogenized medium. In the negative case, there is a single branch. © Taylor & Francis Group, LLC

Tunable Double Negative Band Structure from Non-Magnetic Coated Rods

A system of periodic poly-disperse coated nano-rods is considered. Both the coated nano-rods and host material are non-magnetic. The exterior nano-coating has a frequency dependent dielectric constant and the rod has a high dielectric constant. A negative effective magnetic permeability is generated near the Mie resonances of the rods while the coating generates a negative permittivity through a field resonance controlled by the plasma frequency of the coating and the geometry of the crystal. The explicit band structure for the system is calculated in the sub-wavelength limit. Tunable pass bands exhibiting negative group velocity are generated and correspond to simultaneously negative effective dielectric permittivity and magnetic permeability. These can be explicitly controlled by adjusting the distance between rods, the coating thickness, and rod diameters

Natural history of malignant bone disease in breast cancer and the use of cumulative mean functions to measure skeletal morbidity

BACKGROUND: Bone metastases are a common cause of skeletal morbidity in patients with advanced cancer. The pattern of skeletal morbidity is complex, and the number of skeletal complications is influenced by the duration of survival. Because many patients with cancer die before trial completion, there is a need for survival-adjusted methods to accurately assess the effects of treatment on skeletal morbidity. METHODS: Recently, a survival-adjusted cumulative mean function model has been generated that can provide an intuitive graphic representation of skeletal morbidity throughout a study. This model was applied to the placebo-control arm of a pamidronate study in patients with malignant bone disease from breast cancer. RESULTS: Analysis by bone lesion location showed that spinal metastases were associated with the highest cumulative mean incidence of skeletal-related events (SREs), followed by chest and pelvic metastases. Metastases located in the extremities were associated with an intermediate incidence of SREs, and those in the skull were associated with the lowest incidence of SREs. CONCLUSION: Application of this model to data from the placebo arm of this trial revealed important insight into the natural history of skeletal morbidity in patients with bone metastases. Based on these observations, treatment for the prevention of SREs is warranted regardless of lesion location except for metastases on the skull