A new type of adiabatic invariants for disturbed Birkhoffian system of Herglotz type

The generalized variational principle of Herglotz type provides an effective way to study the problems of conservative and non-conservative systems in a unified way. According to the differential variational principle of Herglotz type, we study the adiabatic invariants for a disturbed Birkhoffian system in this paper. Firstly, the differential equations of motion of the Birkhoffian system based upon this variational principle are given, and the exact invariant of Herglotz type of the system is introduced. Secondly, a new type of adiabatic invariants for the system under the action of small perturbation is obtained. Thirdly, the inverse theorem of adiabatic invariant for the disturbed Birkhoffian system of Herglotz type is obtained. Finally, an example is given.     

Band structure computation of two-dimensional and three-dimensional phononic crystals using a finite element-least square point interpolation method

In the present study, a finite element-least square point interpolation method (FE-LSPIM) is proposed for calculating the band structures of in-plane elastic waves in two-dimensional (2D) and three-dimensional (3D) phononic crystals (PCs). This method utilizes new shape functions by combining mesh-free shape functions and finite element shape functions to exploit the specific advantages of the mesh-free method and finite element method (FEM). As a result, FE-LSPIM inherits the completeness properties of the mesh-free method and the compatibility properties of FEM, and thus the solutions obtained tend to be more accurate. Indeed, according to our previous research, the present method obtains excellent accuracy, especially in the high-frequency domain. The proposed FE-LSPIM was combined with Bloch's theory and applied to compute the band gaps (BGs) for 2D PCs and 3D PCs in the present study, where several PCs were investigated to verify the high accuracy when computing the BGs. Numerical analysis showed that the proposed method can predict the BGs more precisely compared with the FEM and modified FEM.     

Twin boundary and grain boundary effects on cyclic responses of tensile pre-deformed highly oriented nanotwinned Cu: Molecular dynamics simulation

Molecular dynamics method is performed for analyzing the relationship of the twin boundary and grain boundary on the cyclic response of nanotwinned Cu. Results show that the strength difference among the grain boundary, the twin boundary and the variation of dislocation density are nearly 2-2.5 times. We predict twin boundary is only a factor that affects the stable response, however, the dislocation form and the time to reach stability is caused by the grain boundary. Furthermore, the phenomenon of cyclic hardening is found in all the nanotwinned Cu samples.     

Advances and challenges of sulfur-driven autotrophic denitrification (SDAD) for nitrogen removal

Sulfur-driven autotrophic denitrification (SDAD), a process suited for the treatment of nitrogen and sulfur-polluted wastewater without extra supplement of organic carbon, is a promising biological nitrogen removal process. However, the SDAD process was affected by many factors such as various electron donors, organic carbon and exogenous substances (e.g., antibiotics and heavy metal), which prevent further application. Thus, we conducted a detailed review of previous studies on such influence factors and its current application. Besides, a comparative analysis was adopted to recognize the current challenges and future needs for feasible application, so as to ultimately perfect the SDAD process and extend its application scope.     

Neutral nano-inhomogeneities in hyperelastic materials with a hyperelastic interface model

We examine the existence of neutral nano-inhomogeneities in a hyperelastic inhomogeneity-matrix system subjected to finite plane deformations when uniform (in-plane) external loading is imposed on the matrix. We incorporate nanoscale interface effects by representing the material interface as a separate hyperelastic membrane, perfectly bonded to the surrounding bulk material. We show that for any type of hyperelastic bulk material and practically any type of hyperelastic membrane representing the interface, neutral nano-inhomogeneities do exist but are necessarily circular in shape. We show further that the radius of the circular neutral nano-inhomogeneity is determined by the (uniform) external loading (which must be hydrostatic) and the respective strain energy density functions associated with the hyperelastic bulk and interface materials.     

On energy balance and the structure of radiated waves in kinetics of crystalline defects

Traveling waves, with well-known closed form expressions, in the context of the defects kinetics in crystals are excavated further with respect to their inherent structure of oscillatory components. These are associated with, so called, Frenkel–Kontorova model with a piecewise quadratic substrate potential, corresponding to the symmetric as well as asymmetric energy wells of the substrate, displacive phase transitions in bistable chains, and brittle fracture in triangular lattice strips under mode III conditions. The paper demonstrates that the power expended theorem holds so that the sum of rate of working and the rate of total energy flux into a control strip moving steadily with the defect equals the rate of energy sinking into the defect, in the sense of N.F. Mott. In the conservative case of the Frenkel–Kontorova model with asymmetric energy wells, this leads to an alternative expression for the mobility in terms of the energy flux through radiated lattice waves. An application of the same to the case of martensitic phase boundary and a crack, propagating uniformly in bistable chains and triangular lattice strips, respectively, is also provided and the energy release is expressed in terms of the radiated energy flux directly. The equivalence between the well-known expressions and their alternative is established via an elementary identity, which is stated and proved in the paper as the zero lemma. An intimate connection between the three distinct types of defects is, thus, revealed in the framework of energy balance, via a structural similarity between the corresponding variants of the ‘zero’ lemma containing the information about radiated energy flux. An extension to the dissipative models, in the presence of linear viscous damping, is detailed and analog of the zero lemma is proved. The analysis is relevant to the dynamics of dislocations, brittle cracks, and martensitic phase boundaries, besides possible applications to analogous physical contexts which are marked by macroscopic energy release through emission of waves and possibly linear viscous damping.     

Razor clam-inspired burrowing in dry soil

RoboClam is a biomimetic burrowing robot that imitates the valve expansion/contraction digging pattern of the Atlantic razor clam, Ensis directus, to dig into submerged soil using an order of magnitude less energy than would be required to push into the soil with brute force. This paper examines whether it would theoretically be possible to use the same method to dig into dry soil. The stress state of the soil around the contracting robot was analyzed, and a target zero-stress state for dry soil digging was found. Then, the two possible modes of soil collapse were investigated and used to determine how quickly the robot would have to contract to achieve the target zero-stress state. It was found that for most dry soils, a RoboClam-like device would have to contract in 0.02 s, a speed slightly faster than the current robot is capable of, but still within the realm of possibility for a similar machine. These results suggest that the biomimetic approach successfully used by RoboClam to dig into submerged soil could feasibly be used to dig into dry soil as well.     

Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials

The free vibration and stability of axially functionally graded tapered Euler–Bernoulli beams are studied through solving the governing differential equations of motion. Observing the fact that the conventional differential transform method (DTM) does not necessarily converge to satisfactory results, a new approach based on DTM called differential transform element method (DTEM) is introduced which considerably improves the convergence rate of the method. In addition to DTEM, differential quadrature element method of lowest-order (DQEL) is used to solve the governing differential equation, as well. Carrying out several numerical examples, the competency of DQEL and DTEM in determination of free longitudinal and free transverse frequencies and critical buckling load of tapered Euler–Bernoulli beams made of axially functionally graded materials is verified.     

Inverse method for estimating shear stress in machining

An inverse method is presented for estimating shear stress in the work material in the region of chip–tool contact along the rake face of the tool during orthogonal machining. The method is motivated by a model of heat generation in the chip, which is based on a two-zone contact model for friction along the rake face, and an estimate of the steady-state flow of heat into the cutting tool. Given an experimentally determined discrete set of steady-state temperature measurements along the rake face of the tool, it is shown how to estimate the corresponding shear stress distribution on the rake face, even when no friction model is specified.     

On variational formulations with rigid-body constraints for finite elasticity: Applications to 2D and 3D finite element simulations

We investigate a recently proposed variational principle with rigid-body constraints and present an extension of its implementation in three dimensional finite elasticity problems. Through numerical examples, we illustrate that the proposed variational principle with rigid-body constraints is applicable to both single field and mixed finite elements of arbitrary order and geometry, e.g. triangular/tetrahedral and quadrilateral/hexagonal elements, in two and three dimensions. Moreover, we demonstrate that, as compared to the commonly adopted approach of discretizing the rigid domains with standard finite elements, the proposed formulation requires neither discretization nor numerical integration in the interior of each rigid domain. As a comparative result, the variational formulation may reduce the total number of degrees of freedom of the resulting finite element system and provide improved accuracy.