Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model

A mechanism-based constitutive model is presented for the inelastic deformation and fracture of ceramics. The model comprises four essential features: (i) micro-crack extension rates based on stress-intensity calculations and a crack growth law, (ii) the effect of the crack density on the stiffness, inclusive of crack closure, (iii) plasticity at high confining pressures, and (iv) initial flaws that scale with the grain size. Predictions of stress/strain responses for a range of stress states demonstrate that the model captures the transition from deformation by micro-cracking at low triaxiality to plastic slip at high triaxialities. Moreover, natural outcomes of the model include dilation (or bulking) upon micro-cracking, as well as the increase in the shear strength of the damaged ceramic with increasing triaxiality. Cavity expansion calculations are used to extract some key physics relevant to penetration. Three domains have been identified: (i) quasi-static, where the ceramic fails due to the outward propagation of a compression damage front, (ii) intermediate velocity, where an outward propagating compression damage front is accompanied by an inward propagating tensile (or spallation) front caused by the reflection of the elastic wave from the outer surface and (iii) high velocity, wherein plastic deformation initiates at the inner surface of the shell followed by spalling within a tensile damage front when the elastic wave reflects from the outer surface. Consistent with experimental observations, the cavity pressure is sensitive to the grain size under quasi-static conditions but relatively insensitive under dynamic loadings.     

双相干态光场与原子依赖强度耦合过程的腔场谱

研究了依赖强度耦合双模J-C模型的腔场谱,给出了激发态原子与双相干态光场双光子共振相互作用过程光谱结构的数值结果.发现腔场谱呈现出复杂的多峰结构.腔场谱的频率灵敏地受两模光子数差q的调谐.     

Calibration of a simple cone-penetration model for snow

Numerical studies using the Material Point Method (MPM) have been conducted recently to model snow penetration tests for fine-grained and coarse-grained snows using small cones with diameters ranging from 2.5 mm to 4 mm, and cone half-angles between 15° and 45°. Although numerical studies have gained physical insight of these tests, due to the lengthy computation time needed for the MPM simulations, it is not feasible to use these simulations to develop a stochastic model to assess the large variations of the mechanical properties of snow typically shown in tests. In this paper, we present a simple and efficient physics-based analytical model based on equilibrium and a cavity expansion solution upon which a stochastic model is built to obtain calibrated material parameters for a Drucker–Prager (DP) model such that prediction of the model can be made. Sensitivity analysis of the analytical model indicates that cohesion and interfacial shear (friction) factor contribute significantly to the penetration hardness whereas the friction angle has little contribution. The calibrated material parameters are similar to those estimated via the MPM simulations. The quality of the stochastic model, when compared with test data, was assessed using four interval-based validation metrics with good results.     

Analytic combinatorics of chord and hyperchord diagrams with k crossings

Using methods from Analytic Combinatorics, we study the families of perfect matchings, partitions, chord diagrams, and hyperchord diagrams on a disk with a prescribed number of crossings. For each family, we express the generating function of the configurations with exactly k crossings as a rational function of the generating function of crossing-free configurations. Using these expressions, we study the singular behavior of these generating functions and derive asymptotic results on the counting sequences of the configurations with precisely k crossings. Limiting distributions and random generators are also studied.     

On ferroelectric crystals with engineered domain configurations

This paper examines the engineered domain configurations and the macroscopic properties of ferroelectric crystals using an energy minimization theory. The energy minimizing domain configurations have been constructed, and their macroscopic properties have been calculated and compared well with experiments. The optimal domain configurations have also been identified.     

Effect of the rate of deformation on the crystallization behavior of polymers

Deformation has a significant influence on the crystallization process in a number of polymers. In this paper, the response of a recently developed model for crystallizing polymers is investigated when subject to uni-, bi-axial and constant width extensions for a range of strain rates. Both the loading and unloading behavior are examined for these deformations. The particular model studied here was developed to capture the effect of strain induced crystallization in polymers and has been applied to model crystallization in polyethylene terephthalate at temperatures just above its glass transition temperature. The model has been formulated using the notion of multiple natural configurations within a full thermodynamic framework. The connection between micro-structural changes taking place in the polymer and the form of the model are elucidated. The interplay between the relaxation processes, the rate of deformation and their combined effect on crystallization is illustrated. The results show an earlier onset of crystallization for high strain rates due to stretching of the polymer network. At low strain rates however, crystallization is not observed as the polymer network is able to relax during the deformation. A sharp upturn in the stress is observed after the onset of crystallization due to the formation of a rigid crystalline phase. The unloading curves clearly show a hysteric behavior with the amount of dissipation increasing for increasing values of strain rate. These results compare favorably with experimental observations available in literature.     

Attenuation of cavity internal pressure oscillations by shear layer forcing with pulsed micro-jets

Experimental results concerning the pressure oscillations induced by a grazing flow over a deep cavity like a Helmholtz resonator are presented. The study deals with the forcing of the neck shear layer instability in an opened-loop control scheme by means of pulsed micro-jets. The effects of the frequency and amplitude are investigated. It is found that efficient attenuation of the pressure oscillations can be reached when the forcing frequency is larger than the cavity resonance frequency. Then the shear layer is locked with the forcing and resonance with the cavity is lost, inducing a significant decrease of the acoustic pressure level in the cavity. Effects of the jet amplitude are weak, a very small amplitude being capable of forcing the shear layer. By contrast, when the forcing frequency is lower than the cavity resonance frequency (the forcing wave length is greater than twice the neck length) the forcing is ineffective.     

Stress function determination for dislocation configurations obtained from Kröner’s theory

Based on the work of Borisova, a more general method is proposed to determine the stress functions, from which the stress field is derived, of an edge dislocation pile-up and wall. For this purpose, Kröner’s theory of discrete dislocation in a continuum is applied to these two typical infinite and periodic configurations of edge dislocations. It is shown that the calculated stress functions can be used to easily determine the stress field of other configurations like screw dislocation pile-up or symmetrical tilt boundary.     

Planar symmetric concave central configurations in Newtonian four-body problems

In this paper, we consider the problem: given a symmetric concave configuration of four bodies, under what conditions is it possible to choose positive masses which make it central. We show that there are some regions in which no central configuration is possible for positive masses. Conversely, for any configuration in the complement of the union of these regions, it is always possible to choose positive masses to make the configuration be a central configuration.     

Slight disorder effects in two dimensional photonic crystal structures

In the actual manufacturing process of photonic crystal structure, unavoidable error can generate slight disorder which may influence the performance of photonic crystal based device. In this work, randomly distributional disorders are applied to the air holes in the photonic crystal structure. Based on this, we investigate the influence of the slight disorder on the photonic crystal band structure and the performance of photonic crystal based devices (waveguide and slab cavity). The studies indicate that the slight disorder provides small influence on the band structure of the photonic crystal. But, the random disorder in photonic crystal waveguide may increase transmission loss obviously when the wavelength of the light and the distribution of disorder break the balance of multiple interferences. Also, the slight disorder can reduce the Q factor of the photonic crystal cavity at a certain degree. The studies may provide some useful guides for further photonic crystal device research.