International Journal of Applied Mechanics

Contact usually results in stress concentration which can easily cause the yield of materials and structures. The classic elastic–plastic yield criterion needs to utilize stress or strain field for calculation. However, most advanced full-field measurement methods output the displacement as the original data, and the fitting from displacement to strain will induce error accumulation in applications. In this paper, a plastic domain characterization method is developed that can directly judge the elastic–plastic state of materials based on the full-field displacement and neural network. By establishing and training a three-layer-based neural network, the relationship between the displacement and the elastic/plastic stage of the sampling points is modeled. A physical model is formulated based on the yield criterion and embedded in the layer of the network, which can increase the convergence rate and accuracy. Only the displacements of the contact member are required in this method, which can be easily measured by the optical metrologies. The performances of the developed method are carefully discussed through simulated data and real-world tests. Results show that the method can accurately identify the plastic domain during the tests.

This paper constructs and analyzes a generalized composite two-sub-step explicit method to solve various dynamical problems effectively. Via the accuracy and dissipation analysis, the constructed explicit method is further developed into two novel members that achieve identical second-order accuracy, controllable algorithmic dissipation, and desired stability. Unlike all existing explicit schemes, the novel members employ two independent integration parameters ($\gamma$ and ${\rho }_b$) to control numerical features. The parameter $\gamma$, denoting the splitting ratio of sub-step size, can determine the instant at which external loads are calculated, whereas another parameter ${\rho }_b$, denoting the spectral radius at the bifurcation point, can control numerical dissipation imposed. Independently adjusting the sub-step size is one significant advantage for solving dynamical problems triggered by discontinuous loads. This paper also provides two novel explicit members’ single-parameter versions for inexperienced users. Besides, the novel explicit members achieve a smaller local truncation error in acceleration, thus enhancing the solution accuracy in displacement and velocity. Numerical examples are solved to validate the significant superiority of the novel members in the solution accuracy.

Shape memory alloys (SMA) exhibit the shape memory effect (SME), allowing the alloy which is upon a cyclic thermal loading to return to its original shape after heating beyond the transformation temperature. Two-way SMAs deform during heating and cooling and are suitable for thermal energy harvesting applications. Also, piezoelectric materials (PM) can convert mechanical strain into electrical voltage or current. In this work, a thermal energy harvesting structure is introduced and analyzed. The structure is a composite cantilever beam, comprising two layers, i.e., one-way or two-way SMA and PM. The beam is subjected to different fluctuating temperature ranges, and then we obtain results about energy harvesting performance such as phase transformation strain and output voltage. After developing the nonlinear constitutive equations for one-way and two-way SMEs, the effect of pre-strain and two types of SMAs, i.e., one-way and two-way SMAs are compared with each other under a particular thermal loading. Moreover, the effect of the SMA thickness layer on the output voltage and power has been investigated. Regarding the results, we conclude that for larger pre-strains and maximum temperature of the cycle, greater piezoelectric power is induced. But for a small pre-strain (0.2%), no phase transformation and no output power are observed. Furthermore, it is concluded that in a thermal loading by using two-way SMAs, an electrical potential can be derived without any pre-strain, and increasing the thickness of SMA can rise output power remarkably.

The surface effects play an important role in nanobeams. Based on a recently developed theory of surface elastodynamics, a model of the flexural wave propagation in Timoshenko nanobeams is established, in which the surface effects characterized by surface energy and surface inertia are introduced. It is found that when the size of a beam is comparable with nanometers, the surface energy effect would enhance the wave speed, while the surface inertial one would reduce it. An interesting phenomenon discovered is that with an increasing wave frequency, the dominant role transits from the surface energy effect to the surface inertial effect. The two kinds of surface effects exhibit a frequency-dependent competitive mechanism. In contrast to the macroscopic beams, due to the surface effects, the frequency dispersion of flexural waves in nanobeams becomes size-dependent. Furthermore, a comparison of the Timoshenko nanobeam and the Euler one indicates that the shear deformation effect and rotary inertial one cannot be neglected for a large wave number, which would prominently decrease the wave speed. Besides, when the size of the beam is large enough, the surface effects can be neglected and the present results can degenerate to the classical Timoshenko ones. The present results should be helpful not only for deep understanding of the dispersive mechanism of flexural waves in nanobeams, but also for optimal design of nanobeam-based acoustic wave devices.

The mechanical properties of functional-graded shape memory alloy (FG-SMA) is of highly significance for its applications and structural design. This paper establishes a constitutive model of the FG-SMA beam, considering the influence of the temperature variation and the tension-compression asymmetry coefficient. The fiber element method and the virtual work principle were employed to establish the governing equation of the bending of FG-SMA beam, which is solved using the Newton–Raphson algorithm. Furthermore, the effect of the tension-compression asymmetry coefficient, temperature, gradient index, bending moment, and axial load on the mechanical properties of the FG-SMA beams was analyzed. The results showed that the tension-compression asymmetry coefficient, gradient index, bending moment, and axial load significantly have relatively obvious influence on the cross-sectional mechanical response of the FG-SMA beams, while the effect of the temperature was not noticeable.

Double network hydrogels (DN hydrogels) with high stretchability and toughness have attracted broad research interest. Recently, a kind of novel tough DN hydrogels was designed by means of the reactive strand extension strategy, which introduced mechanophores into the first network. When the strands of the first network reach their nominal stretching limit, the mechanophores allow the strands to survive through force-coupled reactions instead of fracture. As a consequence, the novel hydrogels can achieve a better mechanical performance compared with the conventional DN hydrogels. In this work, we aim to develop a constitutive model for the novel DN hydrogels. The model is based on the worm-like single-chain model by introducing bond deformation. The network alteration theory is used to account for the damage behaviors. The theoretical framework is capable of clarifying the difference in mechanical behaviors between conventional and novel DN hydrogels, which demonstrates the importance of bond deformation on the mechanical behaviors of DN hydrogels.

Tetrahedral lattice materials can be used as the core of a sandwich structure. The properties of tetrahedral lattice materials can be controlled by modifying their geometrical parameters and relative density. In this paper, a tetrahedral lattice structure deformation mechanism-based theoretical analysis model is established to predict the effective mechanical properties of the structure under compressive and shear loadings. The analytical solutions are subsequently verified by finite element analysis of a large-scale lattice material model. Based on the obtained results, the effects of the geometrical parameters, relative density, and shear deformation are discussed. At a specific relative density, as strut inclination angle increases: (1) the effective compressive modulus in the z-direction increases; (2) the effective compressive modulus in x- and y-directions, and the effective shear modulus in xy-, xz-, and yz-directions firstly increases but then decreases; (3) the effective Poisson’s ratios ${\nu }_{zx}$ and ${\nu }_{zy}$ increase, whereas, ${\nu }_{xz}$, ${\nu }_{yz}$, ${\nu }_{xy}$, and ${\nu }_{yx}$ decrease. With an increase in relative density, the effective compressive and shearing modulus increase, the effective Poisson’s ratios remain constant, ${\nu }_{xy}$ and ${\nu }_{yx}$ are always equal to 0 when the strut inclination angle is $45^{\circ }$. The effect of shear deformation on the effective mechanical properties increases as the slenderness ratio increases. The predicted effective properties enable the tetrahedral lattice unit cells to be treated as “material” in the design and analysis process.

In this work, a numerical analysis of the recently proposed rotational autofrettage method for strengthening hollow circular disks is carried out. The analysis of this new process is in nascent stage. Some analyses are available in the literature to study rotational autofrettage based on Tresca yield criterion. However, in general, the von Mises yield criterion closely replicates the yielding behavior of metals. Thus, in this work, the rotational autofrettage of disks is analyzed incorporating von Mises yield criterion. The governing differential equations are obtained for the elastic and plastic deformations in the disk under centrifugal loading based on the assumption of axisymmetric condition and plane stress incorporated in von Mises yield criterion. A numerical scheme is then followed to solve the set of governing differential equations along with the boundary conditions to obtain the stress distribution in an elastic-perfectly plastic disk during loading stage of rotational autofrettage. The residual stress distribution in the disk after unloading of the centrifugal loading are also obtained. The rotationally autofrettaged disk of typical radial dimension is numerically experimented for its different in-service load carrying capacities. Significant improvements are achieved in in-service pressure, radial temperature and centrifugal load carrying capacities in the autofrettaged disk as compared to their non-autofrettaged counterpart. Different numerical results are compared with corresponding solution due to Tresca yield criterion. Further, the present solution of rotational autofrettage is proposed to apply in strengthening industrial standard flanged disks of various dimensions used in connecting high pressure pipelines. It is found that the maximum pressure carrying capacity of flanged disk can be increased up to 77% for wall thickness ratios more than 3.5 by employing rotational autofrettage.

In this study, the dynamic responses of a cracked beam layed on a visco-elastic foundation subjected to moving loads are calculated. An Euler–Bernoulli beam model is used to describe the beam behaviors. In addition, the beam has several open cracks one-sided with different depths. By using the Fourier transform, the dynamic responses of the beam are determined analytically in the frequency domain with the help of Green’s function. By coupling with the periodic supported beam model, an analytical model of the railway sleeper is developed. This model allows the fast calculation of the dynamic responses of a damaged sleeper. A dynamic computational model using the FEM method was also developed and compared to the analytical model. The results from the two methods are relatively comparable for three cases of beams without cracks, beams with one crack, and beams with two cracks.

Layered structures consisting of stiff thin films and compliant matrixes are widely observed in flexible electronics, geology and composite materials. In this work, through analytic modelling and numerical simulations, we investigate the buckling instability of a stiff thin film embedded between two compliant substrates under uniaxial compression. Considering the shear stresses at the film/substrate interfaces and the finite geometry change of the film, the critical compressive strain, buckling wavelength and amplitude of sinusoidal wrinkles are analytically derived by the energy method. The analytic predictions agree well with the results obtained by finite element analysis. The post-buckling morphology may be sinusoidal or multiple-period, depending on the compressive strain and the modulus ratio of two compliant substrates. Our results aid in understanding the buckling of compliant substrate/film/compliant substrate tri-layer structures.