Accepted Manuscripts

Siyuan Bao, Shuodao Wang and Bo Wang
J. Appl. Mech   doi: 10.1115/1.4037030
A modified Fourier-Ritz approach is developed in this study to analyze the free in-plane vibration of orthotropic annular sector plates with general boundary conditions. In this approach, two auxiliary sine functions are added to the standard Fourier cosine series to obtain a robust function set. The introduction of a logarithmic radial variable simplifies the expressions of total energy and the Lagrangian function. The improved Fourier expansion based on the new variable eliminates all the potential discontinuities of the original displacement function and its derivatives in the entire domain, and effectively improves the convergence of the results. The radial and circumferential displacements are formulated with the modified Fourier series expansion, and the arbitrary boundary conditions are simulated by the artificial boundary spring technique. The number of terms in the truncated Fourier series and the appropriate value of the boundary spring retraining stiffness are discussed. The developed Ritz procedure is used to obtain accurate solution with adequately smooth displacement field in the entire solution domain. Numerical examples involving plates with various boundary conditions demonstrate the robustness, precision and versatility of this method. The method developed here is found to be computationally economic compared with the previous method that does not adopt the logarithmic radial variable.
TOPICS: Plates (structures), Free vibrations, Boundary-value problems, Displacement, Fourier series, Springs, Stiffness, Robustness, Vibration
Wenhao Shen and Ya-Pu Zhao
J. Appl. Mech   doi: 10.1115/1.4036988
Symmetrical load on the crack surfaces is found in many fluid-solid problems. The combined effect of symmetrical normal and shear stresses is investigated, which impacts on the displacement and stress fields and the predictions of crack initiation and deflection. The boundary integral equations of displacement and stress fields are formulated using the integral-transform method. The equations of the displacement and stress are reduced using the Abel integral equations. The analytical solution of the full space for uniform normal and shear stresses is obtained. The asymptotic solution of the displacement of the crack surface is obtained near the crack tip under specific normal and shear stresses. Results show that shear stress tends to inhibit the crack, and the predictions of crack initiation and deflection could be inappropriate for a slit crack under a singular shear stress. This study may be useful for future investigations of the fluid-solid problems and help to understand the hydraulic fracturing.
TOPICS: Symmetry (Physics), Stress, Fracture (Materials), Hydraulic fracturing, Shear stress, Displacement, Integral equations, Fluids, Deflection
Bin Ding and Xiaoyan Li
J. Appl. Mech   doi: 10.1115/1.4036943
We proposed an eccentric ellipse criterion to describe the tensile failure of amorphous materials under a combination of normal and shear stresses in 2D stress space. This criterion can reflect a tension-compression strength asymmetry, and unify four previous failure criteria in 2D stress space, including von Mises criterion, Drucker-Prager criterion, Christensen criterion and ellipse criterion. We examined the validity of the eccentric ellipse criterion in the tensile failure regimes using the results from our atomistic simulations for two typical amorphous CuZr and LiSi, and recent torsion-tension experiments on metallic glasses. The predictions from the eccentric ellipse criterion agree well with these results from atomistic simulations and experiments. It indicates that this eccentric ellipse criterion is essential for the tensile failure of amorphous materials.
TOPICS: Amorphous materials, Failure, Tension, Engineering simulation, Simulation, Stress, Torsion, Metallic glasses, Compression, Shear stress
Hong Gao, Hongwei Zhang, Zhengrong Guo, Tienchong Chang and Li-Qun Chen
J. Appl. Mech   doi: 10.1115/1.4036938
Intrinsic driving mechanism is of particular significance to nanoscale mass delivery and device design. Stiffness gradient driven directional motion, i.e., nanodurotaxis, provides an intrinsic driving mechanism, but an in-depth understanding of the driving force is still required. Based on molecular dynamics simulations, here we investigate the motion behavior of a graphene flake on a graphene substrate with a stiffness jump. The effects of the temperature and the stiffness configuration on the driving force are discussed in detail. It is found that the driving force is almost totally contributed by the unbalanced edge force, and increases with the temperature and the stiffness difference, but decreases with the stiffness level. We demonstrate also that the shuttle behavior of the flake between two stiffness jumps on the substrate can be controlled by the working temperature and stiffness configuration of the system. These findings may have general implications for the design of nanodevices driven by stiffness jumps.
TOPICS: Graphene, Stiffness, Temperature, Design, Nanoscale phenomena, Molecular dynamics simulation
Feng Deng, Qian Deng, WenShan Yu and Shengping Shen
J. Appl. Mech   doi: 10.1115/1.4036939
Flexoelectricity refers to the two-way coupling between strain gradients and the electric field in dielectric materials, and is universal compare to piezoelectricity which is restricted to dielectrics with noncentralsymmetric crystalline structure. Involving strain gradients makes the phenomenon of flexoelectricity size dependent and more desirable for nanoscale applications. However, strain gradients involve higher order spatial derivate of displacements and bring difficulties to the solution of flexoelectric problems. This dilemma impedes the application of such universal phenomenon in multiple fields, such as sensors, actuators and nanogenerators. In this study, we develop a mixed finite element method (FEM) for the study of problems with both strain gradient elasticity and flexoelectricity being taken into account. To use C0 continuous elements in mixed FEM, the kinematic relationship between displacement field and its gradient is enforced by Lagrangian multipliers. Besides, four types of 2D mixed finite elements are developed to study the flexoelectric effect. Verification as well as validation of the present mixed FEM is performed through comparing numerical results with analytical solutions for an infinite tube problem. Finally, mixed FEM is used to simulate the electromechanical behavior of a 2D block subjected to concentrated force or voltage. This study proves that the present mixed FEM is an effective tool to explore the electromechancial behaviors of materials with the consideration of flexoelectricity.
TOPICS: Solids, Finite element analysis, Finite element methods, Strain gradient, Dielectric materials, Nanoscale phenomena, Displacement, Electromechanical effects, Actuators, Sensors, Kinematics, Piezoelectricity, Elasticity, Electric fields
Ruike Zhao and Xuanhe Zhao
J. Appl. Mech   doi: 10.1115/1.4036940
Structures of thin films bonded on thick substrates are abundant in biological systems and engineering applications. Mismatch strains due to expansion of the films or shrinkage of the substrates can induce various modes of surface instabilities such as wrinkling, creasing, period doubling, folding, ridging and delamination. In many cases, the film-substrate structures are not flat but curved. While it is known that the surface instabilities can be controlled by film-substrate mechanical properties, adhesion and mismatch strain; effects of the structures’ curvature on multiple modes of instabilities have not been well understood. In this paper, we provide a systematic study on the formation of multimodal surface instabilities on film-substrate tubular structures with different curvatures through combined theoretical analysis and numerical simulation. We first introduce a method to quantitatively categorize various instability patterns by analyzing their wave frequencies using Fast Fourier Transform. We show that the curved film-substrate structures delay the critical mismatch strain for wrinkling when the system modulus ratio between the film and substrate is relatively large, compared with flat ones with otherwise the same properties. In addition, concave structures promote creasing and folding, and suppress ridging. On the contrary, convex structures promote ridging and suppress creasing and folding. A set of phase diagrams are calculated to guide future design and analysis of multimodal surface instabilities in curved structures.
TOPICS: Thin films, Wave frequency, Adhesion, Computer simulation, Phase diagrams, Mechanical properties, Shrinkage (Materials), Design, Engineering systems and industry applications, Delays, Fast Fourier transforms, Theoretical analysis, Delamination

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