Failure Criteria for Brittle Notched Specimens

Recently, new failure criteria were proposed for brittle materials to predict their failure loads regardless of the shapes of a notch or a crack in the material. This paper is to further evaluate the failure criteria for different shapes of notches and different materials. A circular hole, elliptical hole or crack-like slit with a different angle with respect to the loading direction was considered. Double circular holes were also studied. The materials studied were an isotropic material like polymethyl methacrylate (PMMA) as well as laminated carbon fiber composites. Both cross-ply and quasi-isotropic layup orientations were examined. The lamination theory was used for the composite materials so that they can be modelled as an anisotropic and homogeneous material. The test results were compared to the theoretical predictions using the finite element analysis with 2-D plane stress models. Both theoretical failure stresses agreed well with the experimental data for the materials and notch geometries studied herein.

Modeling and Analysis of D–shaped Plasmonic Refractive Index and Temperature Sensor Using Photonic Crystal Fiber

A plasmonic D–shaped photonic crystal fiber (PCF) sensor for refractive index (RI) and temperature is designed and studied in this paper. The RI channel is made up of a silver thin layer deposited on the plane of the D–type structure, and the temperature sensing channel is formed by a silver nanowire and benzene filled in an elliptical hole in the PCF. The designed structure can be used for temperature and RI sensing via coupling between the core–guided modes and the surface plasmon modes around Ag nanowire and Ag thin layer. The coupling characteristic and sensing performance of the proposed dual–functional sensor is studied in the present work. Results show that the maximum sensitivity in terms of RI units (RIU) is 6.9 µm/RIU in the range of 1.33–1.38, and the maximum temperature sensitivity is 3 µm /°C in the range of 27°C–67°C.

Stress analysis of finite orthotropic composite containing an elliptical hole

Although the mechanical integrity of a member can be highly influenced by associated stresses, determining the latter can be very challenging for finite orthotropic composites containing cutouts. This is particularly so if the external loading is not well known, a common situation in practical situations. Acknowledging the above, a finite elliptically-perforated orthotropic tensile laminate is stress analyzed by combining measured displacement data with relevant analytical and numerical tools. Knowledge of the external loading is unnecessary. Results are verified independently and the concepts are applicable to other situations. The developed technology can provide important design-type information for orthotropic composites. In particular, the ability to apply analyses for perforated composite structures which assume infinite geometry to finite geometries is demonstrated.

Optimized lattice-based metamaterials for elastostatic cloaking

An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.

Studying nonlinear vibrations of composite conical panels with arbitrary-shaped cutout reinforced with graphene platelets based on higher-order shear deformation theory

In this article, the vibrational behavior of conical panels in the nonlinear regime made of functionally graded graphene platelet–reinforced composite having a hole with various shapes is investigated in the context of higher-order shear deformation theory. To achieve this aim, a numerical approach is used based on the variational differential quadrature and finite element methods. The geometrical nonlinearity is captured using the von Karman hypothesis. Also, the modified Halpin–Tsai model and rule of mixture are applied to calculate the material properties of graphene platelet–reinforced composite for various functionally graded distribution patterns of graphene platelets. The governing equations are derived by a variational approach and represented in matrix-vector form for the computational purposes. Moreover, attributable to using higher-order shear deformation theory, a mixed formulation approach is presented to consider the continuity of first-order derivatives on the common boundaries of elements. In the numerical results, the nonlinear free vibration behaviors of functionally graded graphene platelet–reinforced composite conical panels including square/circular/elliptical hole and with crack are studied. The effects of boundary conditions, graphene platelet reinforcement, and other important parameters on the vibrational response of panels are comprehensively analyzed.

Dynamic performance for piezoelectric bi-materials with an interfacial crack near an eccentric elliptical hole under anti-plane shearing

The purpose of this paper is to evaluate the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bi-materials under anti-plane shearing. Fracture analysis is performed by Green’s function method and the conformal mapping method, which are used to solve the boundary conditions problem. The mechanical model of the interfacial crack is constructed by interface-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack-tips can be derived. The validity of the present method is verified by comparing with a crack emerging from the edge of a circular hole as a reference. Numerical cases reveal parametric dependence of DSIFs on the geometry of eccentric elliptical holes and interfacial cracks, the characteristics of the incident wave, the equivalent piezoelectric elastic modulus and piezoelectric parameters. The results illustrate that the eccentric distance has a great effect on the stress concentration at the crack tip, which may be harmful to the normal service of piezoelectric devices and materials. In addition, the method proposed in this paper can also deal with non-eccentric problems and has wider applicability.

Surface effects on a mode-III reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals

To effectively reduce the field concentration around a hole or crack, an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) is investigated subject to remotely mechanical and electrical loadings. The surface effect and dielectric characteristics inside the hole are considered for actuality. By utilizing the technique of conformal mapping and the complex variable method, the phonon stresses, phason stresses, and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions. Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack. Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer, the aspect ratio of the hole, and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip. The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack, which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.