International Journal of Applied Mechanics

Interface problems exist widely in various engineering problems and their high-precision simulation is of great importance. A new computational approach for dealing with interface problems is proposed based on the recently developed integral-generalized finite difference (IGFD) scheme. In this method, the research domain is divided into several subdomains by interfaces, and discretization schemes are established independently in each subdomain. A new cross-subdomain integration scheme is introduced to connect these subdomains. Several two-dimensional elasticity models containing material interfaces are studied to test the effectiveness of the proposed method. The results show that the recently proposed approach without the help of discontinuous functions or auxiliary equations that are commonly used in other numerical methods (e.g., extended finite element method and boundary element method) enables obtaining high accuracy and efficiency in interface problems. The proposed method has great potential in the application of material interface problems in solid mechanics and, furthermore, weak discontinuity problems in various fields.

The stresses and deformations of a functionally graded piezoelectric material (FGPM) non-uniform thickness rotating disc under magneto-thermo-mechanical loads including convection and radiation heat transfer were examined in this paper. The material constants were considered to be a power-law function of radius. Also, the heat convection coefficient and heat conduction coefficient are functions of radius and temperature. The equation of heat transfer was derived considering thermal gradient, convection thermal boundary, and solar radiation. The nonlinear final differential equation was solved using the Differential Transformation Method (DTM). Then, the equilibrium equation together with the electrostatic equation of the disc was derived and solved analytically. So, the radial and circumferential stress, radial deformation, and electric potential were obtained. Finally, the effects of solar radiation, convection heat transfer, temperature dependency, inhomogeneity index, angular velocity, and magnetic field on the stress, deformation, and electric potential of the disc were investigated in numerical examples. The results show that solar radiation, convection boundary, thickness function, and inhomogeneity index have a considerable effect on the responses of the rotating FGPM disc.

The rapid development of additive manufacturing has made coated structures an innovative configuration with high design flexibility. However, poor forming accuracy and surface roughness during manufacturing will cause uncertainty in surface layer thickness, which results in structure performance deviation and failure to achieve the expected goals. This paper proposes a robust topology optimization method for coated structures considering the surface layer thickness uncertainty to obtain high-quality designs that can resist disturbance by uncertainties. First, an erosion-based approach is used to establish the model of the coated structure surface layer. Second, modeling the surface layer thickness uncertainty applies a random field whose dimensionality of the random fields is reduced by the Expansion Optimal Linear Estimation (EOLE) method. Then, minimizing the weighted sum of the mean and standard deviation of structural compliance is taken as the optimization objective, and robust topology optimization considering uncertainty is established. Finally, estimate the stochastic response by the perturbation technique, then the sensitivity of the objective function with respect to the design variables is derived. Numerical examples show that the structural design obtained with the proposed method has a stronger resistance to uncertainty than the deterministic topology optimization method, proving the method’s effectiveness in this paper.

This paper investigates the effects of a foundation movement on the vibration instability of axial-field permanent magnet motors (AFPMM). Different from previous studies focusing on the effects of the rotor’s rotation on its vibration instability, this paper introduces a revolution around a space axis as the foundation movement and investigates its effect on the vibration characteristics of the rotor. For an annular rotor with this foundation movement and a rotation around an axis passing through its own geometrical center, a dynamic model is established in this paper. Magnet-field-synchronous frame is introduced to describe the out-of-plane displacement. Hamilton’s principle and Galerkin method are involved to obtain dynamic mode. Closed-form expressions of eigenvalues and the boundaries of flutter and divergent instabilities are determined. The analytical results claim that the instabilities can be suppressed. Particularly, the divergent instabilities can even be eliminated by adjusting combinations of parameters. To verify the results, the stability analyses and numerical calculations regarding the revolution are given for a sample AFPMM revolving around a space axis at different speeds. Based on these analytical boundaries, the unstable regions of a sample motor with different parameter combinations are plotted in terms of foundation movement, which can be used to suppress the vibration instabilities with the design of parameters such as rotation speed, web thickness, magnetization thickness, air-gap length and remanence. Six states of instabilities are summarized as a guidance to determine the range of the stable operation of the motor.

A coupling model of peridynamics and finite element method is proposed to study the interfacial delamination influenced by vertical crack density in thermal barrier coating (TBC) systems. Specifically, the progressive failure progress under static and fatigue loads in TBCs, including vertical cracks propagation, the evolution of vertical cracks to interfacial cracks, and interfacial delamination, is simulated by the proposed model. The difference between static failure mechanism and fatigue failure mechanism of TBCs is numerically elucidated. The simulated fracture morphology is in good agreement with the experiential observation. In both static and fatigue loads, a higher vertical crack density is found to correspond to a shorter delamination length, and there is no interfacial delamination when the vertical crack density is high enough. The results provide important insight of vertical crack density on interfacial delamination, and the durability of TBCs can be enhanced by ensuring an appropriately high vertical crack density.

In this work, by breaking the structural six-fold symmetry and isotropy, we propose a simple design to drastically improve the elastic deformability and stiffness of gardenia-shaped honeycomb (GSH) structures, with a lower structural relative density. In the developed structural design, the enhancement of the mechanical response is achieved by locally shortening the beams that caused the intracellular extrusion. Studies that focused on simultaneously strengthening the two above-mentioned characteristics are rarely seen. Unlike the isotropy of the previous GSH structures, the elastic modulus of the reinforced GSH (RGSH) structures in both two principal directions is investigated via performing a complete parametric study. To visualize the utterly different mechanical response between the GSH and RGSH structures, the elastic properties-comparison are presented theoretically, numerically, and experimentally. The developed structural reinforcing method, combining the stiffness and deformability regulation, provides a valuable way to redesign multifunctional lattice structures for meeting the various requirements regarding mechanical characteristics.

An anisotropic visco-hyperelastic constitutive model for rate-temperature-dependent deformation during one-step hot stamping forming simulation of unidirectional (UD) CF/PEEK prepregs is presented. This constitutive model is based on strain energy decomposition and a multiplicative decomposition of the deformation gradient. Two simple Maxwell models are used to characterize the viscoelastic behavior of the melted PEEK matrix and longitudinal shear deformation, respectively, and a shear invariant of $I_{\mathrm{\text{sh}}}=I_5-I_4$ is proposed to calculate the shear deformation. Moreover, the fiber stretching deformation is modeled by an anisotropic hyperelastic model. To obtain the model parameters, tensile tests at different strain rates and temperatures above the melt temperature of PEEK are performed on $0^{\circ }$, $10^{\circ }$, and $90^{\circ }$ CF/PEEK prepreg specimens, respectively. In parallel, the [0]₈ and [45]₈ curved beam specimens are experimentally fabricated to validate the constitutive model. The VUMAT subroutine is developed according to the proposed constitutive model and applied for a $10-40^{\circ }$ off-axis tensile simulation and hot-stamping forming simulation of CF/PEEK prepregs. The experimental and simulation results show that the materials flow, distribution of strain and stress, forming defects (wrinkles and overlap) of CF/PEEK curved beam can be captured by the proposed model.

In this work, the mixed local/nonlocal elasticity theory is developed for the investigation of the vibration of a circular graphene sheet with a structural defect located in a magnetic field. When graphene is placed in a magnetic field, the Lorentz force is applied to it, which is calculated using Maxwell’s equations. The insufficiency of Eringen’s nonlocal theory (ENT) caused some authors to employ the two-phase theory (TPT) to study nanostructures. Geometric imperfections can happen in the manufacturing process of graphene sheets. Lots of these imperfections can be modeled as a hole. So, in this work, an imperfection is considered as the centric hole. Governing equations, in Newtonian formulation, are extracted in the integrodifferential form. The boundary conditions are selected as clamped at inner and outer edges. To discretize the equation of motion we employ Galerkin’s approach. The solution is validated using a comparison study between the presented results and those that exist in the literature, and the accuracy of the suggested approach is verified. The effectiveness of the mixture parameter, magnetic field, radius of imperfection, and nonlocal parameter is examined on the natural frequency. The results exhibit that an increase in the mixture parameter and magnetic field increases the natural frequency of the graphene sheet.

In this work, a study on curved electrostatically-actuated nanobeams incorporating surface energy is presented. The beam is modeled according to Euler–Bernoulli beam theory and the Gurtin–Murdoch theory of surface stress is used to incorporate surface energy effects in beam modeling. To verify the accuracy of the model, its predictions were compared to numerical results reported in previous literature on the static behavior of fixed-fixed and fixed-free nanobeams subjected to DC electrostatic potential. The results of this study demonstrate that the stiffness of both fixed–fixed and fixed-free nanobeams is influenced by surface stress. Furthermore, the findings highlight the significant impact of the electrostatic fringing field on the response of the nanobeams.

This paper presents a new approach named optimization-oriented exponential–polynomial-closure (OEPC) to study the behavior of stochastic nonlinear oscillators under both displacement-multiplicative and additive excitations that are Gaussian white noise. In addition to the original projection exponential–polynomial-closure (PEPC) solution procedure, the OEPC method provides an alternative procedure for solving the Fokker–Planck–Kolmogorov (FPK) equation. The OEPC method is formulated by constructing an objective function with the residue of FPK equation. By minimizing the objective function with a gradient-based method, the parameters in the exponential polynomial can be determined and the approximate PDF solution of the nonlinear random oscillator can be obtained. The solutions obtained through the OEPC approach are highly consistent with the available true solutions in special case or the Monte Carlo simulations (MCS). They are much more accurate than those obtained using the Gaussian closure method when the nonlinearity is strong. In addition, the OEPC method is computationally more efficient than MCS. The difference of the results from the OEPC and PEPC is compared and the advantage of the OEPC over PEPC is also shown when the system nonlinearity is strong and complicated.

With the development of structural metamaterials and 3D printing technology, the polymorphic shape-memory metamaterials have attracted extensive attention. This study aims to design a structural 3D printed shape-memory metamaterial, of which the epigenetic bi-stability of shape-fixity and recovery behaviors have been achieved by means of the dual matching nominal moduli and geometrical size optimization. Epigenetic bi-stability and dual matching refer to the combination of bi-materials in a specific structure, in response to external stimuli to show adjustable bi-stability. Elastic thermoplastic polyurethane (TPU) and viscoelastic polylactic acid (PLA) both are thermally responsive shape-memory polymers (SMPs) and have been employed to fabricate the structural metamaterial, of which the nominal modulus is tailorable owing to the dual matching shape-memory effects (SMEs) of two SMP components. Furthermore, the effects of structural parameters, i.e., width of framework and width of internal support, on the nominal modulus have been investigated for the structural metamaterials, of which the shape-fixity and recovery ratios have been characterized using finite element method (FEM) analyses and experimental measurements. Finally, a constitutive relationship among structural parameters, dual matching SME and nominal modulus has been identified to explore the working principle of epigenetic bi-stability in shape-memory metamaterials. This study provides a design strategy for a shape-memory metamaterial with a post-switchable bi-stability, through dual matching SME and geometrical size optimization.

In order to explain and predict the pseudo-ductility behavior and mechanical properties of ${\mathrm{\text{SiC}}}_{\mathrm{\text{f}}}/\mathrm{\text{SiC}}$ composite material, a thermodynamic strength theoretical model based on fracture mechanics and thermodynamic method has been established. Compared with other theoretical models, the model proposed in this investigation unifies different cracks and defects based on energy method. Meanwhile, the stress–strain behavior of materials can be obtained with as few parameters as possible. Compared with previous experimental data, the correctness of this theoretical model has been verified. Some key material properties, such as elastic modulus, proportional limit stress (PLS) and yield stress (YS), have been investigated by calculating based on the theoretical model. The effect of the initial matrix porosity and the material properties of the matrix and fiber have been investigated. Results show that PLS and YS are almost not influenced by initial matrix porosity and can be seen as intrinsic parameters. Elastic modulus of the SiC reinforced fiber and the matrix can also affect material properties. Compared with the SiC matrix, PLS of the ${\mathrm{\text{SiC}}}_{\mathrm{\text{f}}}/\mathrm{\text{SiC}}$ composite material is more sensitive to changes in elastic modulus of the SiC reinforced fiber. However, the improvement of elastic modulus and shear modulus of the ${\mathrm{\text{SiC}}}_{\mathrm{\text{f}}}/\mathrm{\text{SiC}}$ composite material is much more difficult. For this purpose, the elastic modulus of both the SiC reinforced fiber and the matrix need to be enhanced. Results and conclusions in this investigation can provide guidance for predicting material properties of ${\mathrm{\text{SiC}}}_{\mathrm{\text{f}}}/\mathrm{\text{SiC}}$ composite material and preparation in industry.