International Journal of Applied Mechanics

This paper is concerned with the postbuckling problem of cantilevered nano rods/tubes under an end concentrated load. Eringen's nonlocal beam theory is used to account for the small length scale effect. The governing equation is derived from statical and geometrical considerations and Eringen's nonlocal constitutive relation. The nonlinear differential equation is solved using the shooting method for the postbuckling load and the buckled shape. By comparing with the classical postbuckling solutions, the sensitivity of the small length scale effect on the buckling load and buckled shape may be observed. It is found that the small length scale effect decreases the postbuckling load and increases the deflection of the rod.

This paper presents the calibration procedure for aluminum alloy 2024-T351 using a recently developed damage plasticity theory. The damage plasticity theory consists of a full three dimensional damage evolution law where the pressure sensitivity and the Lode angle dependence are included in a fracture envelope and the equivalent plastic strain is used as a time-like variable to determine the damage rate. Because of the coupled nature of the plastic strain and the damage, material parameters are calibrated from a parallel study of numerical simulations and experimental measurements. A set of 10 tests that cover a wide range stress states for both the hydrostatic pressure and the Lode angle are conducted in order to capture the fracture envelope in the interested stress range. The experimental setups include un-notched and notched round bars with three different notch radii, a doubly grooved flat plate and compressed cylinders of three different heights at two friction conditions. The detailed numerical and experimental procedure of calibration is demonstrated by using four of these tests. The accuracy of the calibrated material parameters is further assessed by the remainder of tests. Notch sensitivity in tensile round bars and the friction conditions in upsetting tests are discussed in detail. Good agreement in the tested load conditions is achieved for both the fracture patterns and the load-displacement curves.

The dynamics of a rotor system with axial contact/rub events between the disks and stator are investigated by numerical simulations. The formula for determining the contact/rub points, axial contact forces and dry friction forces are deduced. To account for their influence, the axial contact forces are substituted by equivalent forces acting at the disk centers, based on the equivalent moment rule. One-parametric model is used to estimate the contact-induced dry friction forces. The coupled equations of lateral and torsional motions of rotor and the lateral motion of disk are then established. Numerical simulations are carried out to reveal the lateral and torsional vibrations for both two-disk contact/rubs with different axial clearances, and one disk contact/rubs. Bifurcation diagrams, orbits, phase portraits, amplitude-frequency spectra and Poincaré maps are adopted to demonstrate the dynamical behaviors of the system. The results show that though both the lateral and torsional vibrations can reflect the influences of contact/rubs on rotor dynamics, the spectrum analyses of the torsional vibrations are more suitable to determine straight the extent of their effect.

In this paper, the pore opening and closure on the giant unilamellar vesicle GUV membrane are studied under different theoretical schemes. The opening process is considered as a dynamics process; while the closure process is considered as a quasi-static process. The opening criterion is set based on an energy release rate theory, similar to the Griffith theory for crack initiation. On the other hand, the closure process is described by a non-equilibrium thermodynamic theory. When the size of initial pore is smaller than a critical value, the pore is stable, and followed by the closure process. Otherwise, the pore is unstable, which leads to the rupture of the vesicle.

This paper presents finite element modelling of the deformation of a detached living cell subjected to microinjection and through the simulation, an investigation of the material properties of the cell components. The model is verified using images of the deformed cell as well as the measured penetration forces in the tests reported in the open literature. It is hoped that the modelling in this context will help to quantitatively evaluate the mechanical properties of the cells, and in particular, the failure strain of the cell cortex when penetration occurs.

This paper applies the homotopy perturbation method to the simulation of the static response of nano-switches to electrostatic actuation and intermolecular surface forces. The model accounts for the electric force nonlinearity of the excitation and for the fringing field effect. Using a mode approximation in the Galerkin projection method, the nonlinear boundary value differential equation describing the statical behavior of nano-switch is reduced to a nonlinear algebraic equation which is solved using the homotopy perturbation method. The number of included terms in the perturbation expansion for achieving a reasonable response has been investigated. Three cases have been specifically studied. These cases correspond to when the effective external force is the electrostatic force, the combined electrostatic and Casimir force and the combined electrostatic and van der Waals force. In all three cases the pull-in characteristics has been investigated thoroughly. Results have been compared with numerical results and also analytical results available in the literature. It was found that HPM modifies the overestimation of N/MEMS instability limits reported in the literature and can be used as an effective and accurate design tool in the analysis of N/MEMS.

Based on element-free Galerkin (EFG) method and the complex variable moving least-squares (CVMLS) approximation, the complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems is presented in this paper. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of moving least-squares (MLS) approximation, and we can thus select fewer nodes in the meshless method that is formed from the CVMLS approximation than are required in the meshless method of the MLS approximation with no loss of precision. The formulae of the CVEFG method for two-dimensional elasticity problems is obtained. Compared with the conventional meshless method, the CVEFG method has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVEFG method.

The prediction and prevention of spinal injury is an important aspect of preventive medical science. The spine, or vertebral column, represents a chain of 26 movable vertebral bodies, joint together by transversal viscoelastic intervertebral discs and longitudinal elastic tendons. This paper proposes a new locally–coupled loading–rate hypothesis, which states that the main cause of both soft- and hard-tissue spinal injury is a localized Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes a localized spinal section in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton–Euler dynamics of the local spinal motions and derive from it the corresponding coupled SE(3)-jolt dynamics (see our recent papers on new mechanics of traumatic brain injury [V. G. Ivancevic, New mechanics of traumatic brain injury, Cogn. Neurodyn. Springer (Online)]. and generic musculo-skeletal injury [V. G. Ivancevic, New mechanics of generic musculo-skeletal injury, Biophys. Rev. Let. (2009) (in press)]). The SE(3)-jolt is the main cause of two basic forms of spinal injury: (i) hard-tissue injury of local translational dislocations; and (ii) soft-tissue injury of local rotational disclinations. Both the spinal dislocations and disclinations, as caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum model.